%PDF-1.2 %âãÏÓ 10 0 obj << /Length 11 0 R >> stream BT 112.32 681.36 TD 0 0 0 rg /F0 12 Tf -0.0142 Tc 0.1342 Tw (Wavelet-based Compared to Function-based On-line Signature Verification) Tj 72.24 -23.04 TD /F1 10.08 Tf -0.0778 Tc 0 Tw (A) Tj 7.2 0 TD /F1 7.92 Tf 0.0167 Tc -0.3167 Tw (NDR\311A ) Tj 29.28 0 TD /F1 10.08 Tf -0.0778 Tc 0 Tw (V) Tj 7.44 0 TD /F1 7.92 Tf 0.0505 Tc -0.2305 Tw (ERGARA DA ) Tj 48.24 0 TD /F1 10.08 Tf -0.0845 Tc 0 Tw (S) Tj 5.52 0 TD /F1 7.92 Tf 0.1318 Tc (ILVA) Tj 19.2 0 TD /F1 10.08 Tf 0.1411 Tc -0.0211 Tw (, D) Tj 12.48 0 TD /F1 7.92 Tf 0.0016 Tc -0.0616 Tw (ANIEL ) Tj 25.68 0 TD /F1 10.08 Tf -0.0845 Tc 0 Tw (S) Tj 5.76 0 TD /F1 7.92 Tf 0.0515 Tc -0.1115 Tw (ANTANA DE ) Tj 48.24 0 TD /F1 10.08 Tf -0.0845 Tc 0 Tw (F) Tj 5.52 0 TD /F1 7.92 Tf 0.1 Tc (REITAS) Tj -263.52 -23.04 TD /F1 10.08 Tf -0.0612 Tc 0.1512 Tw (UFSC \226 Universidade Federal de Santa Catarina - ) Tj 202.32 0 TD -0.0622 Tc 0.1822 Tw (Depto. de Inform\341tica e Estat\355stica) Tj -141.12 -11.52 TD -0.0556 Tc 0.1756 Tw (Caixa Postal 476, 88049-900 Florian\363polis, SC, Brasil) Tj 48 -11.52 TD -0.0384 Tc 0 Tw ({) Tj 4.8 0 TD -0.05 Tc (vergara,santana}@inf.ufsc.br) Tj -167.28 -23.76 TD /F0 10.08 Tf -0.0475 Tc (Abstract.) Tj 39.84 0 TD /F1 10.08 Tf -0.0635 Tc 1.6749 Tw ( We implemented two direct methods for on-line signature verification. First, data produced by ) Tj 1.7645 Tc 0 Tw (a) Tj -39.84 -12 TD -0.0549 Tc 0.4008 Tw (graphics tablet describing a signature to be tested are treated with wavelet transforms to generate features to be) Tj 0 -12 TD -0.0483 Tc 1.2483 Tw (nonlinearly confronted with a reference signature chosen among 10 previously stored) Tj 0 Tc 0.12 Tw ( ) Tj 356.64 0 TD -0.0394 Tc 1.2794 Tw (tryings from the same) Tj -356.64 -12 TD -0.0426 Tc 0.2159 Tw (writer. In order to recover the time dependence lost in the wavelet treatment, we included the level of departure) Tj 0 -12 TD -0.0525 Tc 0.4972 Tw (from the diagonal line in the warping function as a complementary measure of distance. In a second approach,) Tj T* -0.0549 Tc 1.4016 Tw (the functions x\(t\) and y\(t\) describing position in time of each pixel of the same test signature were directly) Tj T* -0.0444 Tc 1.3275 Tw (\(though nonlinearly\) compared to their counterparts from the reference. We concluded that both approaches) Tj T* -0.0488 Tc 0.8288 Tw (showed good fidelity to all details in the signatures, with acceptable false rejection rates \(we obtained around) Tj T* -0.058 Tc 0.55 Tw (30% FRR\) to this kind of biometry. On the other hand, the inclusion of the wavelet transform turned out to be) Tj T* -0.0562 Tc 1.9762 Tw (an essential step for the achievement of low false acceptation rates. It was only with the inclusion of the) Tj T* -0.0429 Tc 0.7479 Tw (wavelet transform, at the right level of resolution, that we managed to completely prevent trained forgeries to) Tj 0 -11.52 TD -0.0526 Tc 0.1383 Tw (be accepted \(0% FAR\) in the cases studied.) Tj -22.8 -27.12 TD /F0 10.08 Tf 0.06 Tc 0 Tw (1.) Tj 7.68 0 TD /F2 10.08 Tf 0 Tc 0.0778 Tw ( ) Tj 10.32 0 TD /F0 10.08 Tf -0.0738 Tc 0 Tw (Introduction) Tj -18 -15.36 TD /F1 10.08 Tf -0.0456 Tc 0.9122 Tw (This work deals with practical issues related to the safety) Tj 0 -12 TD -0.0509 Tc 2.0223 Tw (of digital signatures. Under normal conditions, a digital) Tj T* -0.0575 Tc 4.9375 Tw (signature is just an alphanumerical password which) Tj T* -0.0401 Tc 2.4229 Tw (confirms authenticity of a document in electronic form) Tj T* -0.056 Tc 1.436 Tw (based upon solely on the information that this document) Tj T* -0.048 Tc 3.288 Tw (contains. All the security associated with this scheme) Tj T* -0.0593 Tc 1.0593 Tw (relies on the assumption that only the person who signed) Tj T* -0.0445 Tc 1.5245 Tw (the document knows the right password ) Tj 1.4434 Tc 0 Tw (\() Tj 173.76 0 TD -0.0586 Tc 1.6186 Tw (Schneier [10]\).) Tj -173.76 -12 TD -0.0628 Tc 0.4528 Tw (However, since the copy of an electronic password cannot) Tj 0 -12 TD -0.0435 Tc 3.4035 Tw (be easily distinguished from the original, it is highly) Tj T* -0.0387 Tc 1.5987 Tw (recommended the inclusion of additional mechanisms to) Tj T* -0.0491 Tc 0.9371 Tw (connect a digital signature and its author, such as the use) Tj T* -0.0636 Tc 0.7969 Tw (of tokens \(smart cards, for example\) or the verification of) Tj T* -0.0497 Tc 0.3068 Tw (some physical or behavioral trace \(biometrics\) collected at) Tj T* -0.0602 Tc 1.0717 Tw (the moment of signing. Among all methodologies related) Tj T* -0.0438 Tc 0.4038 Tw (to biometrics, we decided to choose signature verification.) Tj T* -0.0623 Tc 3.9423 Tw (This choice can be justified because it is very well) Tj T* -0.0638 Tc 0.5138 Tw (accepted outside electronic media. People are used to sign) Tj T* -0.0316 Tc 7.4716 Tw (papers to confirm authenticity and the signature) Tj T* -0.032 Tc 2.432 Tw (verification process is not different or intrusive, as the) Tj T* -0.0333 Tc 0.6333 Tw (most part of other biometrics \() Tj 124.56 0 TD -0.1033 Tc 0.7633 Tw (Newham [1]\). On the other) Tj -124.56 -12 TD -0.0071 Tc 0.1271 Tw (hand, ) Tj 24.72 0 TD -0.0475 Tc 0.2875 Tw (Ruggles [13] states that a person's signature is prone) Tj -24.72 -12 TD -0.0692 Tc 4.0292 Tw (to variability and this would imply that systems for) Tj 0 -12 TD -0.0536 Tc 3.2936 Tw (signature recognition must allow for a wide range of) Tj T* -0.0433 Tc 0.1033 Tw (possibilities, being not very reliable.) Tj 19.92 -18 TD -0.0679 Tc 2.5479 Tw (Signature verification can be performed on-line or) Tj -19.92 -12 TD -0.0432 Tc 0.6432 Tw (off-line. These two approaches and several other practical) Tj 0 -12 TD -0.0406 Tc 1.0606 Tw (aspects related to the more general theme of handwriting) Tj 258 357.12 TD -0.0601 Tc 2.7601 Tw (recognition are discussed at length in the survey from) Tj 0 -12 TD -0.0327 Tc 11.9127 Tw (Plamondon [12]. On-line verification signature) Tj T* -0.0615 Tc 4.0215 Tw (verification methods can be further divided into two) Tj T* -0.0467 Tc 1.8467 Tw (groups \(see) Tj 0 Tc -0.12 Tw ( ) Tj 51.84 0 TD -0.0278 Tc 1.8278 Tw (Plamondon [12]\): direct methods \(using the) Tj -51.84 -12 TD -0.0347 Tc 4.6805 Tw (raw functions of time\) and indirect methods \(using) Tj 0 -12 TD -0.0413 Tc 1.1933 Tw (parameters\). In the first case, the signature is stored as ) Tj 1.0445 Tc 0 Tw (a) Tj T* -0.0476 Tc 1.7143 Tw (discrete function to be compared to a standard from the) Tj T* -0.0506 Tc 2.7306 Tw (same writer, previously computed during an enrolment) Tj T* -0.0456 Tc 6.2056 Tw (stage. Such methods simplify data acquisition but) Tj T* -0.0515 Tc 1.5581 Tw (comparison can become a hard task. On the other hand,) Tj T* -0.0316 Tc 1.3249 Tw (indirect methods require a lot of effort preparing data to) Tj T* -0.0404 Tc 3.1304 Tw (be processed, but the comparison is quite simple and) Tj T* -0.0428 Tc 3.8828 Tw (efficient. Examples of the implementation of indirect) Tj T* -0.0743 Tc 1.3724 Tw (methods can be found in the papers from Lee et al. [15]) Tj T* 0.0282 Tc 0.0918 Tw (and ) Tj 17.28 0 TD -0.0389 Tc 0 Tw (Griess[16].) Tj 2.64 -18 TD -0.0454 Tc 1.8454 Tw (Sato and) Tj 0 Tc -0.12 Tw ( ) Tj 40.8 0 TD -0.065 Tc 1.9679 Tw (Kogure [3] present one of the first direct) Tj -60.72 -12 TD -0.0567 Tc 2.8167 Tw (methods to be successful. They propose a system that) Tj 0 -12 TD -0.0537 Tc 1.7337 Tw (relies on three pseudo-distance measures \(shape, motion) Tj T* -0.0518 Tc 0.5489 Tw (and writing pressure\) derived from coordinate and writing) Tj T* -0.0328 Tc 1.1471 Tw (pressure functions through the application of a technique) Tj T* -0.0446 Tc 1.9131 Tw (known as Dynamic Time Warping \(DTW\). They report) Tj T* -0.0541 Tc 1.4084 Tw (reasonable error taxes \(over 90% success\) applying their) Tj T* -0.0706 Tc 1.1506 Tw (system to) Tj 0 Tc -0.12 Tw ( ) Tj 42.48 0 TD -0.0463 Tc 1.2703 Tw (japanese signatures, using forgeries trained for) Tj -42.48 -12 TD -0.0417 Tc 0.1084 Tw (10 minutes. Some authors tried to improve this idea. ) Tj 212.64 0 TD -0.0304 Tc 0 Tw (Wirtz) Tj -212.64 -12 TD -0.0561 Tc 2.1861 Tw ([4] presents a very similar system but with verification) Tj 0 -12 TD -0.0424 Tc 0.3491 Tw (based on strokes \(rather than points\) as the structural units) Tj T* -0.0392 Tc 2.2163 Tw (of the signature. There is also Munich and) Tj 0 Tc 0.12 Tw ( ) Tj 188.88 0 TD -0.0505 Tc 2.3305 Tw (Perona [8],) Tj -188.88 -12 TD -0.0616 Tc 2.1316 Tw (who propose a continuous DTW as an improvement of) Tj 0 -12 TD -0.0581 Tc 1.3781 Tw (precision in the comparison process and Huang and) Tj 0 Tc -0.12 Tw ( ) Tj 218.64 0 TD -0.1578 Tc 0 Tw (Yan) Tj -218.64 -12 TD -0.0457 Tc 2.9857 Tw ([11], who segment the signature based on the writing) Tj ET endstream endobj 11 0 obj 8976 endobj 4 0 obj << /Type /Page /Parent 5 0 R /Resources << /Font << /F0 6 0 R /F1 8 0 R /F2 12 0 R >> /ProcSet 2 0 R >> /Contents 10 0 R >> endobj 15 0 obj << /Length 16 0 R >> stream BT 59.52 710.4 TD 0 0 0 rg /F1 10.08 Tf -0.04 Tc 6.5714 Tw (velocity before applying the DTW. None of the) Tj 0 -12 TD -0.0236 Tc 8.4476 Tw (modifications seems to represent any significant) Tj T* -0.0608 Tc 0.1508 Tw (improvement over the original idea of Sato and ) Tj 191.76 0 TD -0.05 Tc 0 Tw (Kogure.) Tj -171.84 -18 TD -0.0254 Tc 4.4654 Tw (Lam and) Tj 0 Tc -0.12 Tw ( ) Tj 47.04 0 TD -0.0847 Tc 4.8127 Tw (Kamins [5] propose the Fast Fourier) Tj -66.96 -12 TD -0.0675 Tc 2.3475 Tw (Transform as an alternative to time warping. Basically,) Tj 0 -12 TD -0.0522 Tc 0.7122 Tw (they suggest that working in the frequency domain would) Tj T* -0.0322 Tc 0.2894 Tw (eliminate the need to worry about temporal misalignments) Tj T* -0.0643 Tc 0.4543 Tw (between the functions to be compared. They achieve good) Tj T* -0.0597 Tc 3.0117 Tw (results and conclude that the FFT can be useful as ) Tj 2.9645 Tc 0 Tw (a) Tj T* -0.0417 Tc 5.8531 Tw (method for the selection of features for signature) Tj T* -0.0448 Tc 1.7248 Tw (verification. On the other hand,) Tj 0 Tc -0.12 Tw ( ) Tj 136.32 0 TD -0.0419 Tc 1.6019 Tw (Sundaresan and) Tj 0 Tc -0.12 Tw ( ) Tj 68.88 0 TD -0.0328 Tc 0 Tw (Keerthi) Tj -205.2 -12 TD -0.0506 Tc 6.5306 Tw ([6], while studying possible ways of representing) Tj 0 -12 TD -0.049 Tc 0.569 Tw (characters of an ) Tj 67.92 0 TD -0.047 Tc 0.487 Tw (indian language called ) Tj 94.56 0 TD -0.0567 Tc 0.6567 Tw (Tamil, discovered) Tj -162.48 -12 TD -0.0456 Tc 1.3656 Tw (that, because differences among) Tj 0 Tc 0.12 Tw ( ) Tj 135.84 0 TD -0.0661 Tc 1.6261 Tw (Tamil characters can be) Tj -135.84 -12 TD -0.0569 Tc 0.6351 Tw (very subtle, the best way to represent them is with the aid) Tj 0 -12 TD -0.0601 Tc 8.2201 Tw (of wavelet transforms. They noted that Fourier) Tj T* -0.0511 Tc 0.8911 Tw (coefficients would not be a good alternative because they) Tj T* -0.0521 Tc 0.1241 Tw (are not very sensitive to small variations in style or shape.) Tj 19.92 -18 TD -0.0596 Tc 4.1567 Tw (The idea of employing wavelet transforms as ) Tj 4.1645 Tc 0 Tw (a) Tj -19.92 -12 TD -0.0451 Tc 0.6108 Tw (means of generating features from signatures appears also) Tj 0 -12 TD -0.0361 Tc 0.2761 Tw (in the work from ) Tj 71.28 0 TD -0.0387 Tc 0.3987 Tw (Deng et al. [9]. They propose an off-line) Tj -71.28 -12 TD -0.04 Tc 2.1486 Tw (verification system that uses wavelet transforms for the) Tj 0 -12 TD -0.0411 Tc 2.5611 Tw (decomposition and analysis of the coordinate functions) Tj T* -0.0384 Tc 4.5684 Tw (and the tangential angle of points obtained from ) Tj 4.4045 Tc 0 Tw (a) Tj T* -0.0339 Tc 3.7539 Tw (signature image.) Tj 0 Tc 0.12 Tw ( ) Tj 76.08 0 TD -0.0441 Tc 3.6441 Tw (Deng et al. acquire their data from) Tj -76.08 -12 TD -0.0554 Tc 2.1854 Tw (scanned samples of signatures, so they must use image) Tj 0 -12 TD -0.05 Tc 2.01 Tw (processing techniques to identify closed contours which) Tj T* -0.0405 Tc 1.0805 Tw (conveniently represent each signature. Coordinates of the) Tj T* -0.0572 Tc 3.3272 Tw (points that compose each contour are stored as polar) Tj T* -0.0542 Tc 5.2622 Tw (functions of angles measured counterclockwise with) Tj T* -0.0308 Tc 2.7608 Tw (respect to some reference internal to the contour. The) Tj T* -0.0459 Tc 1.9145 Tw (functions obtained are submitted to a wavelet transform) Tj T* -0.0471 Tc 1.1571 Tw (and the authors take zero-crossings of the detail function) Tj T* -0.0586 Tc 0.6586 Tw (in a certain level as features. They complement this set of) Tj T* -0.0411 Tc 0.2091 Tw (features with integrals between consecutive zero-crossings) Tj T* -0.0411 Tc 0.9111 Tw (and corresponding amplitudes to the same abscissa in the) Tj T* -0.0373 Tc 0.9733 Tw (approximation function one resolution up. Experimenting) Tj T* -0.0425 Tc 3.2482 Tw (with occidental signatures, these authors were able to) Tj T* -0.0358 Tc 1.8838 Tw (achieve error taxes as low as 5,6 % false rejection rate) Tj T* -0.0501 Tc 3.2901 Tw (\(FRR\) and 10,98% false acceptation rate \(FAR\), thus) Tj T* -0.0396 Tc 0.8796 Tw (showing the applicability of the wavelet transform to this) Tj T* -0.054 Tc 0.174 Tw (kind of problem.) Tj 19.92 -18 TD -0.0473 Tc 3.9045 Tw (Wavelet transforms can also be found in works) Tj -19.92 -12 TD -0.0587 Tc 4.773 Tw (related to other biometrics. Boles [7], for example,) Tj 0 -12 TD -0.0408 Tc 0.6408 Tw (presents a security system that uses the wavelet transform) Tj T* -0.0347 Tc 1.9681 Tw (for iris recognition. In order to extract features that are) Tj T* -0.0385 Tc 2.3905 Tw (unique to the gray level profiles of the iris image, the) Tj T* -0.0616 Tc 4.2616 Tw (author uses \(similarly to) Tj 0 Tc -0.12 Tw ( ) Tj 115.68 0 TD -0.0762 Tc 4.3242 Tw (Deng et al. [9]\) the zero-) Tj -115.68 -12 TD -0.06 Tc 1.08 Tw (crossings of the detail function and the integrals between) Tj 0 -12 TD -0.0343 Tc 4.8515 Tw (consecutive zero-crossings in a certain level of the) Tj T* -0.0482 Tc 0.1682 Tw (wavelet transform.) Tj 277.92 618 TD -0.0528 Tc 0.6828 Tw (The present work describes an extension of the work) Tj -19.92 -12 TD -0.0389 Tc 0.1589 Tw (from ) Tj 24.96 0 TD -0.045 Tc 3.1517 Tw (Deng et al. [9] to the case of on-line signature) Tj -24.96 -12 TD -0.0433 Tc 1.7633 Tw (verification. Though a powerful technique, their method) Tj 0 -12 TD -0.0382 Tc 1.5382 Tw (for off-line verification cannot be directly applied to the) Tj T* -0.0636 Tc 0.2369 Tw (on-line case, mainly because it was developed to deal with) Tj T* -0.0374 Tc 1.6874 Tw (situations in which the only available information is the) Tj T* -0.0546 Tc 1.9918 Tw (complete signature image. Data obtained on-line do not) Tj T* -0.0523 Tc 3.738 Tw (demand image processing techniques to be used but,) Tj T* -0.0321 Tc 8.3121 Tw (besides shape, they provide important additional) Tj T* -0.0587 Tc 0.3287 Tw (information which should be considered, such as the order) Tj T* -0.0448 Tc 0.7515 Tw (in which points were created in the original signature and) Tj T* -0.0356 Tc 6.0756 Tw (the writing velocity. Specifically, we compare the) Tj T* -0.0644 Tc 2.7044 Tw (functions x\(t\) and y\(t\) describing a test signature with) Tj T* -0.0289 Tc 3.7089 Tw (their counterparts in a reference signature, previously) Tj T* -0.0454 Tc 1.1494 Tw (chosen in an enrolment stage. Our aim is to determine if) Tj T* -0.0375 Tc 5.3775 Tw (this test signature can be taken for original. This) Tj T* -0.0607 Tc 2.4207 Tw (comparison is based on dissimilarity measures between) Tj T* -0.0587 Tc 1.6787 Tw (features that are obtained from the wavelet transform of) Tj T* -0.0619 Tc 3.5719 Tw (the functions x\(t\) and y\(t\) through the calculation of) Tj T* -0.0286 Tc 3.0629 Tw (certain parameters related to the zero-crossings of the) Tj T* -0.0391 Tc 3.2524 Tw (detail function in the right level of resolution to this) Tj T* -0.0573 Tc 2.8573 Tw (problem \(level 4\). These parameters \(described below\)) Tj T* -0.0527 Tc 3.0527 Tw (contain, theoretically, the same amount of information) Tj T* -0.0503 Tc 0.7703 Tw (associated to the complete set of coordinates \(x\(t\),y\(t\)\). If) Tj T* -0.0353 Tc 2.8353 Tw (these dissimilarity measures between the test signature) Tj T* -0.0416 Tc 0.7016 Tw (and the reference lie into an acceptable range, established) Tj T* -0.0516 Tc 0.8316 Tw (in a previous enrolment stage with 10 original signatures,) Tj T* -0.0463 Tc 0.0863 Tw (the test signature is accepted as true.) Tj 19.92 -18 TD -0.0461 Tc 1.2461 Tw (Before the calculation of the dissimilarity measures,) Tj -19.92 -12 TD -0.0549 Tc 0.7749 Tw (the functions x\(t\) and y\(t\) from the test signature must be) Tj 0 -12 TD -0.0337 Tc 2.0737 Tw (aligned in time with the corresponding functions in the) Tj T* -0.029 Tc 5.789 Tw (reference signature. This is accomplished with the) Tj T* -0.0626 Tc 1.5266 Tw (Dynamic Time Warping from Sato and) Tj 0 Tc -0.12 Tw ( ) Tj 167.76 0 TD -0.0137 Tc 1.4537 Tw (Kogure [3]. The) Tj -167.76 -12 TD -0.0326 Tc 4.3226 Tw (information related to the writing motion, lost in ) Tj 4.4045 Tc 0 Tw (a) Tj 0 -12 TD -0.0528 Tc 0.6528 Tw (preparation process to the wavelet transform, is recovered) Tj T* -0.043 Tc 1.1573 Tw (with the inclusion of an additional dissimilarity measure,) Tj T* -0.0453 Tc 5.2396 Tw (directly extracted from the graphic of the warping) Tj T* -0.0524 Tc 5.5324 Tw (function between zero-crossings, given by the area) Tj T* -0.0367 Tc 2.3767 Tw (between this function and the diagonal in the dynamic) Tj T* -0.0537 Tc 0.8037 Tw (programming diagram. It is similar to the second pseudo-) Tj T* -0.0557 Tc 2.0957 Tw (distance of Sato and) Tj 0 Tc -0.12 Tw ( ) Tj 91.2 0 TD -0.0724 Tc 2.1724 Tw (Kogure, but including the wavelet) Tj -91.2 -12 TD -0.057 Tc 6.337 Tw (transform and represents a good measure because) Tj 0 -12 TD -0.0581 Tc 4.2581 Tw (forgeries tend to produce warping functions stronger) Tj T* -0.0436 Tc 1.9036 Tw (deviated from the diagonal than original samples of the) Tj T* -0.0477 Tc 0.1677 Tw (same signature.) Tj 19.92 -18 TD -0.0588 Tc 3.6455 Tw (Finally, in order to confirm the need of such ) Tj 3.6845 Tc 0 Tw (a) Tj -19.92 -12 TD -0.0364 Tc 6.8422 Tw (sophisticated tool as a wavelet transform in the) Tj 0 -12 TD -0.058 Tc 0.5208 Tw (verification process, we implemented a second method, in) Tj T* -0.0468 Tc 0.1934 Tw (which the features are simply the coordinates x\(t\) and y\(t\),) Tj T* -0.0575 Tc 1.3089 Tw (normalized but not transformed. Similarly to the wavelet) Tj T* -0.0441 Tc 3.9241 Tw (approach, the main tool in this case is the warping) Tj T* -0.0511 Tc 4.9445 Tw (function that results after the use of the DTW to) Tj ET endstream endobj 16 0 obj 9934 endobj 14 0 obj << /Type /Page /Parent 5 0 R /Resources << /Font << /F1 8 0 R >> /ProcSet 2 0 R >> /Contents 15 0 R >> endobj 20 0 obj << /Length 21 0 R >> stream BT 59.52 710.4 TD 0 0 0 rg /F1 10.08 Tf -0.0546 Tc 4.4146 Tw (dynamically align features. Besides the distance that) Tj 0 -12 TD -0.0571 Tc 2.7571 Tw (naturally comes out of the alignment process, we also) Tj T* -0.0353 Tc 1.7753 Tw (included the area between the warping function and the) Tj T* -0.0231 Tc 2.0231 Tw (corresponding diagonal as a dissimilarity measure. This) Tj T* -0.0286 Tc 5.4886 Tw (should take into account, in an indirect way, the) Tj T* -0.0341 Tc 2.9312 Tw (information associated with the writing motion in this) Tj T* -0.0753 Tc 0 Tw (analysis.) Tj 0 -29.76 TD /F0 10.08 Tf 0.06 Tc (2.) Tj 7.68 0 TD /F2 10.08 Tf 0 Tc 0.0778 Tw ( ) Tj 10.32 0 TD /F0 10.08 Tf -0.0699 Tc 0.1899 Tw (Data acquisition) Tj -18 -15.36 TD /F1 10.08 Tf -0.0527 Tc 2.2642 Tw (Data acquisition is accomplished with a graphics tablet) Tj 0 -12 TD -0.0383 Tc 1.5983 Tw (Graphire from) Tj 0 Tc 0.12 Tw ( ) Tj 63.12 0 TD -0.0539 Tc 1.5339 Tw (Wacom [14], with 12.76) Tj 102.24 0 TD /F3 10.08 Tf -0.0139 Tc 0 Tw (\264) Tj 5.52 0 TD /F1 10.08 Tf -0.113 Tc 1.673 Tw (9.28 cm) Tj 33.6 4.56 TD /F1 6.48 Tf 0.12 Tc 0 Tw (2) Tj 3.12 -4.56 TD /F1 10.08 Tf -0.0918 Tc 1.6518 Tw ( active) Tj -207.6 -12 TD -0.0421 Tc 1.7821 Tw (area and maximum data transmission rate of 100 points) Tj 0 -12 TD -0.0353 Tc 1.081 Tw (per second. Budget restrictions prevented us from testing) Tj T* -0.0764 Tc 2.2604 Tw (with a LCD pad, which would allow the same kind of) Tj T* -0.0471 Tc 4.4528 Tw (feedback provided by usual media \(paper and pen\).) Tj T* -0.0559 Tc 1.7187 Tw (However, the effectiveness of the proposed system does) Tj T* -0.0532 Tc 0.3172 Tw (not depend on this factor and the only influence that could) Tj T* -0.0561 Tc 1.3161 Tw (be expected from a better quality data acquisition device) Tj T* -0.0333 Tc 2.9 Tw (would be the acquirement of better error taxes in the) Tj T* -0.0463 Tc 0.1663 Tw (experimental phase of this work.) Tj 19.92 -18 TD -0.0553 Tc 3.5696 Tw (The data consisted of original signatures from ) Tj 3.84 Tc 0 Tw (4) Tj -19.92 -12 TD -0.0457 Tc 0.9457 Tw (people \(2 right-handed and two left-handed\). We took 30) Tj 0 -12 TD -0.061 Tc 3.601 Tw (samples from each person and we generated also 30) Tj T* -0.0392 Tc 1.5992 Tw (trained forgeries to each signature. These forgeries were) Tj T* -0.0545 Tc 0.8345 Tw (created with free access to all available information, such) Tj T* -0.0651 Tc 4.9251 Tw (as shape and sequence of writing of each original) Tj T* -0.0462 Tc 0.4329 Tw (signature and with no limitation in time for training. False) Tj T* -0.0547 Tc 5.7747 Tw (acceptation rates were computed only with trained) Tj T* -0.055 Tc 1.1007 Tw (forgeries. We used random forgeries in preliminary tests,) Tj T* -0.0541 Tc 0.4408 Tw (just to be sure that our system was correctly implemented,) Tj T* -0.0523 Tc 0.4923 Tw (but we did not include these results in the ) Tj 173.04 0 TD -0.0456 Tc 0.6456 Tw (FARs reported.) Tj -173.04 -12 TD -0.0382 Tc 0.8782 Tw (Random forgeries are not representative of real situations) Tj 0 -12 TD -0.066 Tc 2.466 Tw (and their inclusion would tend to dissimulate the error) Tj T* -0.0527 Tc 2.7784 Tw (taxes computed. Furthermore, a system that presents ) Tj 2.7245 Tc 0 Tw (a) Tj T* -0.0601 Tc 2.5115 Tw (good performance in preventing trained forgeries to be) Tj T* -0.0553 Tc 0.141 Tw (accepted must be effective with random forgeries too.) Tj 0 -29.52 TD /F0 10.08 Tf 0.06 Tc 0 Tw (3.) Tj 7.68 0 TD /F2 10.08 Tf 0 Tc 0.0778 Tw ( ) Tj 10.32 0 TD /F0 10.08 Tf -0.0491 Tc 0.1691 Tw (Overview of the system) Tj -18 -15.36 TD /F1 10.08 Tf -0.0496 Tc 1.1296 Tw (The signature to be tested is collected from an electronic) Tj 0 -12 TD -0.0306 Tc 0.6306 Tw (pad as two functions in time \(x\(t\),y\(t\)\) and is numerically) Tj T* -0.0339 Tc 0.8054 Tw (processed to generate numbers that represent the distance) Tj T* -0.0489 Tc 0.6146 Tw (between it and a reference signature \(standard\), computed) Tj T* -0.041 Tc 0.521 Tw (in a previous enrolment stage. If this distance lies inside a) Tj T* -0.0359 Tc 6.4759 Tw (statistically acceptable range, the test signature is) Tj T* -0.0338 Tc 3.1538 Tw (recognized as being original. The numerical treatment) Tj T* -0.0296 Tc -0.0904 Tw (includes ) Tj 38.88 0 TD -0.0565 Tc 3.4965 Tw (resampling to a uniform mesh, correction of) Tj -38.88 -12 TD -0.0482 Tc 1.8482 Tw (elementary distortions between curves \(such as spurious) Tj 0 -12 TD -0.034 Tc 0.49 Tw (displacements and rotations\), applying wavelet transforms) Tj T* -0.0524 Tc 1.9895 Tw (to produce features and finally nonlinear comparison in) Tj T* -0.0455 Tc 0.1655 Tw (time \(Dynamic Time Warping\).) Tj 258 612.24 TD /F0 10.08 Tf -0.0369 Tc 0.1569 Tw (3.1 Preprocessing) Tj 0 -15.36 TD /F1 10.08 Tf -0.0456 Tc 3.0456 Tw (Initially, raw coordinate functions ) Tj 3.12 Tc 0 Tw (x) Tj 155.04 -1.44 TD /F3 6.48 Tf 0.12 Tc (*) Tj 3.6 1.44 TD /F1 10.08 Tf -0.1994 Tc (\(t) Tj 5.76 -1.44 TD /F3 6.48 Tf 0.12 Tc (*) Tj 3.6 1.44 TD /F1 10.08 Tf -0.098 Tc 3.098 Tw (\) and ) Tj 3.36 Tc 0 Tw (y) Tj 33.12 -1.44 TD /F3 6.48 Tf 0.12 Tc (*) Tj 3.6 1.44 TD /F1 10.08 Tf 0.0406 Tc (\(t) Tj 6 -1.44 TD /F3 6.48 Tf 0.12 Tc (*) Tj 3.6 1.44 TD /F1 10.08 Tf 0.0439 Tc 3.1961 Tw (\) are) Tj -214.32 -12 TD -0.0418 Tc 0.8818 Tw (obtained as sequences over a non-uniform mesh in time,) Tj 0 -12 TD -0.0291 Tc 0.4491 Tw (presenting an average of 200 points each. These functions) Tj T* -0.0563 Tc 0.8963 Tw (are immediately) Tj 0 Tc -0.36 Tw ( ) Tj 68.64 0 TD -0.0493 Tc 1.0093 Tw (resampled to a uniform mesh with twice) Tj -68.64 -12 TD -0.0531 Tc 1.3045 Tw (the number of nodes in time. Then these) Tj 0 Tc -0.12 Tw ( ) Tj 173.28 0 TD -0.0479 Tc 1.6079 Tw (resampled data) Tj -173.28 -12 TD -0.0319 Tc 1.6819 Tw (are submitted to the same normalization to location and) Tj 0 -12 TD -0.0568 Tc 0.5608 Tw (rotation used by Sato and ) Tj 106.8 0 TD -0.062 Tc 0.542 Tw (Kogure [3], producing an effect) Tj -106.8 -12 TD -0.0473 Tc 0.1273 Tw (like the one showed in Figure 1.) Tj ET 0.24 w 1 J 1 j 0 0 0 RG 340.56 454.08 m 504.24 454.08 l S 340.56 477.84 m 504.24 477.84 l S 340.56 501.6 m 504.24 501.6 l S 340.56 548.88 m 504.24 548.88 l S 340.56 572.64 m 504.24 572.64 l S 340.56 596.4 m 504.24 596.4 l S 0.502 0.502 0.502 RG 340.56 596.4 m 504.24 596.4 l S q 504 591.36 0.72 5.28 re W n 504.24 596.4 m 504.24 454.08 l S Q q 504 580.08 0.72 11.28 re W n 504.24 596.4 m 504.24 454.08 l S Q q 504 453.6 0.72 126.48 re W n 504.24 596.4 m 504.24 454.08 l S Q 504.24 454.08 m 340.56 454.08 l S q 340.32 591.36 0.72 5.28 re W n 340.56 454.08 m 340.56 596.4 l S Q q 340.32 580.08 0.72 11.28 re W n 340.56 454.08 m 340.56 596.4 l S Q q 340.32 453.6 0.72 126.48 re W n 340.56 454.08 m 340.56 596.4 l S Q 0 0 0 RG 422.4 596.4 m 422.4 454.08 l S 421.2 454.08 m 422.4 454.08 l S 421.2 477.84 m 422.4 477.84 l S 421.2 501.6 m 422.4 501.6 l S 421.2 525.12 m 422.4 525.12 l S 421.2 548.88 m 422.4 548.88 l S 421.2 572.64 m 422.4 572.64 l S 421.2 596.4 m 422.4 596.4 l S 340.56 525.12 m 504.24 525.12 l S 340.56 523.92 m 340.56 525.12 l S 367.92 523.92 m 367.92 525.12 l S 395.04 523.92 m 395.04 525.12 l S 422.4 523.92 m 422.4 525.12 l S 449.52 523.92 m 449.52 525.12 l S 476.88 523.92 m 476.88 525.12 l S 504.24 523.92 m 504.24 525.12 l S 0.72 w 0 0.2 0 RG 368.4 529.44 m 368.4 529.44 l 368.4 528 l S 368.4 528 m 368.64 528 l 368.88 528 l 369.12 528 l S 369.12 528 m 369.36 528.24 l 369.36 529.2 l 369.6 529.68 l 369.6 530.16 l 369.84 530.88 l 370.08 532.08 l S 370.08 532.08 m 370.08 532.8 l 370.32 533.76 l 370.56 534.48 l 370.56 535.44 l 371.04 537.12 l 371.28 539.28 l S 371.28 539.28 m 371.28 540.24 l 371.52 541.2 l 371.76 543.36 l 371.76 547.44 l S 371.76 547.44 m 372 549.36 l 372 552.96 l 371.76 553.68 l 371.76 554.4 l S 371.76 554.4 m 371.76 555.84 l 371.76 557.04 l 371.52 558 l 371.52 558.72 l S 371.52 558.72 m 371.52 559.2 l 371.28 559.68 l 371.28 560.16 l S 371.28 560.16 m 371.28 559.92 l 371.04 559.44 l 371.04 558.96 l 370.56 558 l 370.56 557.28 l 370.32 556.56 l 370.32 555.84 l S 370.32 555.84 m 370.32 555.12 l 370.08 554.16 l 370.08 547.44 l S 370.08 547.44 m 370.08 544.8 l 369.84 543.36 l 369.84 538.32 l 370.08 534.96 l S 370.08 534.96 m 370.08 531.36 l 370.32 529.2 l 370.32 523.2 l 370.56 521.52 l 370.56 519.6 l S 370.56 519.6 m 370.56 517.92 l 370.8 516.24 l 370.8 514.56 l 371.04 513.12 l 371.04 510 l 371.28 507.12 l S 371.28 507.12 m 371.28 495.84 l S 371.28 495.84 m 371.04 493.44 l 371.04 491.28 l 370.8 490.32 l 370.8 488.4 l 370.56 487.44 l S 370.56 487.44 m 370.56 486.72 l 370.32 486 l 370.32 485.04 l 370.08 484.32 l 369.84 484.08 l 369.84 483.6 l 369.6 483.36 l S 369.6 483.36 m 369.6 483.12 l 369.36 483.12 l 369.36 482.88 l 368.88 482.88 l 368.4 483.36 l S 368.4 483.36 m 368.4 483.6 l 368.16 484.08 l 368.16 485.04 l 367.92 486.24 l 367.92 487.44 l S 367.92 487.44 m 367.92 488.88 l 367.92 490.08 l 367.92 491.52 l 367.92 493.2 l S 367.92 493.2 m 367.92 494.88 l 368.16 496.56 l 368.64 498.24 l 368.88 500.16 l S 368.88 500.16 m 369.12 502.08 l 369.6 504.24 l 369.84 506.4 l 370.32 508.56 l S 370.32 508.56 m 370.8 510.48 l 371.28 512.64 l 371.76 514.56 l 372.24 516.72 l S 372.24 516.72 m 372.48 517.92 l 372.72 519.36 l 373.2 521.76 l 373.44 523.2 l 373.68 524.4 l 373.68 525.6 l 373.92 526.56 l S 373.92 526.56 m 374.4 528.48 l 374.4 529.2 l 374.64 529.92 l 374.64 531.12 l 374.88 531.84 l 374.88 532.08 l S 374.88 532.08 m 374.88 533.76 l 374.88 533.52 l S 374.88 533.52 m 374.88 528 l 374.88 521.04 l S 374.88 521.04 m 375.12 519.6 l 375.12 517.92 l 375.36 517.44 l 375.36 516.72 l S 375.36 516.72 m 375.6 516.72 l 375.84 516.48 l 376.08 516.72 l 376.32 516.72 l S 376.32 516.72 m 376.8 517.68 l 377.76 520.56 l 378.24 522.48 l S 378.24 522.48 m 378.72 524.4 l 378.96 525.6 l 379.2 526.56 l 379.2 527.76 l 379.44 528.96 l 379.68 529.92 l 379.68 530.88 l S 379.68 530.88 m 379.92 531.6 l 379.92 532.32 l 380.16 532.8 l 380.16 534.48 l 380.4 534.72 l 380.4 534.96 l S 380.4 534.96 m 380.4 534.72 l 380.64 534.24 l 380.64 533.52 l S 380.64 533.52 m 380.64 529.44 l S 380.64 529.44 m 380.64 528 l 380.88 526.32 l 380.88 523.92 l S 380.88 523.92 m 381.12 523.2 l 381.12 522.96 l 381.36 522.72 l 381.36 522.48 l 381.6 522.48 l S 381.6 522.48 m 381.84 522.48 l 382.32 522.72 l 383.04 523.44 l 383.04 523.92 l S 383.04 523.92 m 383.28 524.4 l 383.76 525.84 l 383.76 526.56 l 384.24 528.48 l 384.48 529.68 l 384.48 530.88 l S 384.48 530.88 m 384.72 532.08 l 384.96 533.52 l 385.92 540.24 l 385.92 541.68 l 386.16 543.36 l S 386.16 543.36 m 386.64 549.12 l 386.64 554.4 l S 386.64 554.4 m 386.88 555.6 l 386.88 559.44 l 387.12 560.16 l 387.12 561.36 l S 387.12 561.36 m 386.88 562.08 l 386.88 563.04 l 386.64 562.8 l S 386.64 562.8 m 386.64 562.08 l 386.4 561.6 l 386.4 560.88 l 386.16 560.16 l 386.16 559.2 l 385.92 558.24 l 385.92 557.28 l S 385.92 557.28 m 385.68 556.08 l 385.68 554.88 l 385.44 553.68 l 385.2 552.24 l 385.2 549.12 l 384.96 546 l S 384.96 546 m 384.96 544.56 l 384.72 542.88 l 384.72 539.76 l 384.48 538.08 l 384.48 533.52 l S 384.48 533.52 m 384.48 532.32 l 384.72 531.12 l 384.72 528.72 l 384.96 527.76 l 384.96 526.8 l 385.2 525.84 l 385.2 525.12 l S 385.2 525.12 m 385.68 524.16 l 385.68 523.68 l 385.92 523.2 l 386.16 522.96 l 386.4 522.48 l 386.64 522.48 l S 386.64 522.48 m 387.12 522.48 l 387.36 522.96 l 387.6 523.2 l 387.6 523.68 l 388.32 525.12 l S 388.32 525.12 m 388.56 525.84 l 388.56 526.56 l 388.8 527.52 l 389.04 528.72 l 389.04 529.68 l 389.28 530.64 l 389.28 531.36 l 389.52 532.08 l S 389.52 532.08 m 389.76 533.52 l 389.76 534.24 l 390 534.96 l 390 536.4 l S 390 536.4 m 390 536.16 l 390.24 535.92 l 390.24 534.96 l 390 534.24 l 390 532.08 l S 390 532.08 m 390 525.12 l S 390 525.12 m 390.48 522.24 l 390.48 520.8 l 390.72 520.08 l 390.72 519.6 l S 390.72 519.6 m 390.96 518.64 l 390.96 518.16 l 391.2 517.68 l 391.44 517.44 l 391.44 516.96 l 391.68 516.72 l S 391.68 516.72 m 391.68 516.96 l 391.92 516.96 l 391.92 517.2 l 392.16 517.68 l 392.16 518.16 l S 392.16 518.16 m 392.16 544.56 l 391.92 545.52 l 391.92 550.32 l S 391.92 550.32 m 391.92 551.04 l 391.68 551.76 l 391.68 553.2 l 391.44 553.68 l 391.44 554.4 l S 391.44 554.4 m 391.2 554.4 l 391.2 554.64 l 390.96 554.64 l 390.96 554.4 l S 390.96 554.4 m 390.96 548.88 l 390.72 547.2 l 390.72 536.64 l 390.48 534.48 l 390.48 526.56 l S 390.48 526.56 m 390.48 522.48 l 390.72 521.76 l 390.72 521.04 l S 390.72 521.04 m 390.72 519.84 l 390.96 518.64 l 390.96 518.16 l 391.2 517.68 l 391.2 517.2 l 391.44 516.72 l S 391.44 516.72 m 391.68 516.24 l 391.92 515.76 l 392.4 515.52 l 392.64 515.52 l S 392.64 515.52 m 392.88 515.76 l 393.12 516.24 l 393.12 516.72 l S 393.12 516.72 m 393.36 517.2 l 393.36 518.16 l 393.6 518.64 l 394.08 521.04 l S 394.08 521.04 m 394.32 522.24 l 394.56 523.68 l 394.8 525.12 l 395.04 526.56 l S 395.04 526.56 m 395.28 528 l 395.52 529.44 l 395.76 530.88 l 396.24 532.08 l S 396.24 532.08 m 396.48 533.52 l 396.72 534.72 l 397.2 535.68 l 397.2 536.16 l 397.44 536.4 l S 397.44 536.4 m 397.44 536.4 l 397.68 536.4 l 397.92 536.4 l S 397.92 536.4 m 398.16 536.16 l 398.64 535.2 l 398.64 534.96 l S 398.64 534.96 m 398.64 534.96 l 398.88 534.96 l S 398.88 534.96 m 398.88 534.72 l 399.12 534 l 399.12 533.52 l S 399.12 533.52 m 399.12 535.92 l 398.88 536.16 l 398.88 536.4 l S 398.88 536.4 m 398.64 536.64 l 398.16 536.64 l 397.68 536.4 l S 397.68 536.4 m 396.72 535.44 l 396.72 535.2 l 396.48 534.96 l S 396.48 534.96 m 396.48 534.48 l 396.24 534 l 395.76 532.08 l 395.52 530.88 l S 395.52 530.88 m 395.52 529.44 l 395.28 528 l 395.28 525.12 l S 395.28 525.12 m 395.28 523.92 l 395.52 522.96 l 395.76 522 l 395.76 521.04 l S 395.76 521.04 m 396.24 520.08 l 396.24 519.6 l 396.48 519.12 l 396.48 518.88 l 396.72 518.4 l 396.96 518.4 l 397.2 518.16 l S 397.2 518.16 m 397.2 518.4 l 397.44 518.4 l 397.44 518.88 l 397.68 519.12 l 397.92 519.6 l 397.92 520.08 l 398.4 521.04 l S 398.4 521.04 m 398.4 521.52 l 398.64 522 l 398.88 523.2 l 399.36 524.16 l 399.36 524.64 l 399.6 525.12 l S 399.6 525.12 m 399.84 526.08 l 399.84 527.28 l 400.08 527.52 l 400.08 528 l S 400.08 528 m 400.32 528 l 400.32 528.24 l 400.32 528 l 400.56 528 l S 400.56 528 m 400.56 526.08 l 400.8 524.88 l 400.8 523.92 l S 400.8 523.92 m 400.8 522.96 l 400.8 522.24 l 401.04 521.76 l 401.04 521.04 l S 401.04 521.04 m 401.04 520.32 l 401.28 519.36 l 401.28 518.16 l S 401.28 518.16 m 401.52 518.16 l 401.52 518.64 l 402 519.6 l S 402 519.6 m 402 520.08 l 402.24 520.56 l 402.24 521.04 l 402.48 521.52 l 402.96 523.92 l S 402.96 523.92 m 403.2 524.88 l 403.44 526.08 l 403.68 527.04 l 403.92 528 l S 403.92 528 m 403.92 528.96 l 404.4 529.68 l 404.4 530.16 l 404.64 530.4 l 404.64 530.88 l S 404.64 530.88 m 404.88 530.88 l 405.12 530.64 l 405.12 530.4 l 405.6 529.44 l S 405.6 529.44 m 405.6 528.96 l 405.84 528.48 l 405.84 528 l 406.08 527.28 l 406.08 525.6 l 406.32 525.12 l S 406.32 525.12 m 406.32 524.4 l 406.56 523.68 l 406.8 522.96 l 406.8 522.48 l S 406.8 522.48 m 407.04 521.76 l 407.04 521.04 l S 407.04 521.04 m 407.28 521.04 l 407.28 522 l 407.76 523.92 l S 407.76 523.92 m 408 524.16 l 408 524.88 l 408.48 525.84 l 408.72 527.04 l 408.96 527.52 l 408.96 528 l S 408.96 528 m 409.2 528.96 l 409.44 529.68 l 409.68 530.16 l 409.68 530.4 l 409.92 530.64 l 409.92 530.88 l S 409.92 530.88 m 410.16 530.88 l 410.16 530.4 l 410.4 529.92 l 410.4 529.44 l S 410.4 529.44 m 410.64 528.72 l 410.88 528.24 l 411.12 527.52 l 411.12 526.56 l S 411.12 526.56 m 411.12 526.08 l 411.36 525.6 l 411.36 524.4 l 411.6 523.92 l 411.6 522.72 l 411.84 522.48 l S 411.84 522.48 m 411.84 521.76 l 412.08 521.52 l 412.08 521.28 l 412.32 521.04 l S 412.32 521.04 m 412.56 520.8 l 412.8 520.8 l 413.04 521.04 l S 413.04 521.04 m 413.04 521.52 l 413.28 521.76 l 413.28 522.96 l 413.52 523.92 l S 413.52 523.92 m 413.76 524.88 l 414 525.84 l 414.24 527.04 l 414.48 528 l S 414.48 528 m 414.72 529.2 l 414.96 530.16 l 415.2 531.36 l 415.44 532.08 l S 415.44 532.08 m 415.44 533.04 l 415.92 533.76 l 415.92 534.48 l 416.16 534.72 l 416.16 534.96 l S 416.16 534.96 m 416.4 535.2 l 416.88 535.2 l 417.36 534.96 l S 417.36 534.96 m 417.6 534.72 l 417.6 534.48 l 417.84 534 l 418.08 533.52 l S 418.08 533.52 m 418.32 533.28 l 418.56 532.8 l 418.8 532.32 l 419.04 532.08 l S 419.04 532.08 m 419.28 532.08 l S 419.28 532.08 m 419.28 534.96 l S 419.28 534.96 m 419.28 535.68 l 419.04 536.64 l 419.04 537.36 l 418.8 537.6 l 418.8 537.84 l S 418.8 537.84 m 418.56 537.84 l 418.32 537.6 l 418.08 537.6 l 417.84 537.12 l 417.84 536.88 l 417.6 536.4 l S 417.6 536.4 m 417.12 535.44 l 416.88 535.2 l 416.88 534.48 l 416.64 533.52 l 416.16 532.08 l S 416.16 532.08 m 416.16 530.88 l 415.92 529.44 l 415.92 528.48 l 415.68 527.76 l 415.68 526.56 l S 415.68 526.56 m 415.68 525.6 l 415.68 524.88 l 415.92 524.16 l 415.92 523.92 l S 415.92 523.92 m 416.16 523.68 l 416.64 523.44 l 416.88 523.44 l 417.36 523.92 l S 417.36 523.92 m 417.36 524.16 l 417.84 525.12 l 418.08 525.84 l 418.56 527.04 l 419.04 528 l S 419.04 528 m 419.52 528.96 l 419.76 529.68 l 420 530.16 l 420 530.4 l 420.24 530.64 l 420.24 530.88 l S 420.24 530.88 m 420.48 530.88 l 420.48 529.44 l S 420.48 529.44 m 420.72 528.72 l 420.72 528.24 l 420.72 527.52 l 420.96 526.56 l S 420.96 526.56 m 420.96 523.44 l 421.2 522.96 l 421.2 522.48 l S 421.2 522.48 m 421.44 521.52 l 421.68 520.8 l 422.16 520.32 l 422.4 519.6 l S 422.4 519.6 m 422.64 518.88 l 423.12 518.16 l 423.36 517.44 l 423.6 516.72 l S 423.6 516.72 m 423.84 516.48 l 424.08 516 l 424.32 515.76 l 424.56 515.52 l S 424.56 515.52 m 424.56 515.28 l 425.04 515.28 l 425.04 515.52 l S 425.04 515.52 m 425.52 516.24 l 425.76 516.96 l 426.24 517.92 l 427.2 520.32 l 427.92 521.52 l 428.4 522.72 l 429.84 525.6 l 430.32 527.28 l 433.2 533.52 l 434.64 536.88 l 436.32 540.24 l 437.76 543.6 l 438.96 546.72 l 439.68 548.4 l 441.12 551.28 l 441.6 552.48 l 442.08 553.92 l 442.8 554.88 l 443.04 556.08 l 444 558 l 444.24 558.72 l S 444.24 558.72 m 444.72 559.68 l 444.72 559.92 l 444.96 559.92 l 444.96 560.16 l S 444.96 560.16 m 444.96 560.4 l 445.2 560.88 l 445.2 561.84 l 445.44 563.04 l 445.44 564.24 l S 445.44 564.24 m 445.44 568.56 l 445.2 569.28 l 445.2 569.76 l S 445.2 569.76 m 444.96 570.72 l 444.96 571.2 l 444.72 571.68 l 444.72 571.92 l 444.48 572.4 l 444.24 572.64 l S 444.24 572.64 m 444 572.64 l 443.76 572.4 l 443.52 572.4 l 443.52 572.16 l 443.28 571.92 l 442.8 571.2 l S 442.8 571.2 m 442.32 570.48 l 442.08 569.52 l 441.6 568.32 l 441.36 567.12 l S 441.36 567.12 m 441.12 566.16 l 441.12 565.44 l 440.88 564.48 l 440.88 563.52 l 440.64 561.84 l 440.64 560.16 l S 440.64 560.16 m 440.64 558.48 l 440.64 557.04 l 440.64 555.6 l 440.64 554.4 l S 440.64 554.4 m 440.64 553.2 l 440.88 552 l 440.88 550.32 l S 440.88 550.32 m 441.12 550.32 l 441.36 550.32 l S 441.36 550.32 m 441.36 550.08 l 441.12 549.6 l 441.12 548.64 l 440.88 547.44 l 440.64 546 l S 440.64 546 m 440.4 544.8 l 440.4 543.6 l 440.16 541.92 l 440.16 540.48 l S 440.16 540.48 m 439.92 539.76 l 439.92 534.24 l 440.16 533.52 l S 440.16 533.52 m 440.16 532.56 l 440.4 532.08 l 440.4 531.84 l 440.64 531.36 l 440.64 531.12 l 440.88 530.88 l S 440.88 530.88 m 441.12 530.64 l 441.6 530.64 l 441.84 530.88 l S 441.84 530.88 0.96 0.72 re S 443.04 532.08 m 443.28 532.56 l 443.28 533.04 l 443.52 533.52 l 443.52 534.24 l 443.76 535.44 l 444 535.92 l 444 536.4 l S 444 536.4 m 444 536.88 l 444.24 537.36 l 444.24 539.28 l S 444.24 539.28 m 444.24 537.12 l 444 536.4 l 444 534.96 l S 444 534.96 m 444 531.6 l 444.24 530.64 l 444.24 528 l S 444.24 528 m 444.48 526.56 l 444.48 526.08 l 444.72 525.6 l 444.72 524.88 l 444.96 524.64 l 445.2 524.16 l 445.2 523.92 l S 445.2 523.92 m 445.44 523.68 l 445.44 523.44 l 446.4 523.44 l 446.88 523.92 l S 446.88 523.92 m 446.88 524.16 l 447.12 524.64 l 447.6 525.12 l 447.84 525.6 l 448.32 526.8 l 448.32 527.52 l 448.56 528 l S 448.56 528 m 448.8 529.2 l 449.04 530.16 l 449.28 531.36 l 449.52 532.08 l S 449.52 532.08 m 449.52 533.04 l 449.76 533.52 l 449.76 534.96 l S 449.76 534.96 m 449.76 532.08 l S 449.76 532.08 m 449.76 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475.2 501.6 l 475.44 502.08 l 475.44 502.56 l 475.68 502.8 l S 475.68 502.8 m 475.68 503.04 l 476.4 503.04 l 476.64 502.8 l S 476.64 502.8 m 476.88 502.8 l S 0 0.2 0 rg 385.68 507.84 m 385.92 506.4 l 386.64 506.4 l 386.4 507.84 l 385.68 507.84 l f* 385.92 507.12 m 386.16 505.68 l 386.88 505.44 l 386.64 507.12 l 385.92 507.12 l f* 386.16 506.4 m 386.4 505.2 l 387.12 505.2 l 386.88 506.4 l 386.16 506.4 l f* 386.4 506.16 m 386.4 504.96 l 387.12 504.72 l 387.12 505.92 l 386.4 506.16 l f* 386.4 505.44 0.72 0.24 re f 386.64 504.24 0.72 0.96 re f 386.64 504.24 m 386.64 505.2 l 387.6 505.2 l 387.36 504.24 l 386.64 504.24 l f* 386.64 504.48 m 386.88 505.44 l 387.6 505.2 l 387.6 504.24 l 386.64 504.48 l f* 386.88 504.48 0.72 0.96 re f 386.88 504.48 0.72 0.96 re f 386.88 504.72 0.72 1.2 re f 386.88 505.2 0.72 0.96 re f 386.88 505.44 m 386.64 506.88 l 387.6 506.88 l 387.6 505.44 l 386.88 505.44 l f* 386.64 506.16 m 386.64 507.6 l 387.36 507.6 l 387.6 505.92 l 386.64 506.16 l f* 386.64 506.88 m 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378.72 524.64 l 378.72 524.4 l 378 524.64 l f* 376.8 527.52 m 376.8 527.52 l 377.52 527.52 l 376.8 527.52 l f* 376.8 526.8 m 376.08 528.72 l 376.8 528.72 l 377.52 526.56 l 376.8 526.8 l f* 376.08 527.76 m 375.36 529.92 l 376.08 529.92 l 376.8 527.76 l 376.08 527.76 l f* 375.36 528.96 m 374.88 530.16 l 375.6 530.16 l 376.08 528.96 l 375.36 528.96 l f* 373.68 532.08 m 373.2 533.28 l 373.92 533.28 l 374.4 532.08 l 373.68 532.08 l f* 373.2 532.32 0.72 0.48 re f 372 534.72 m 372 535.2 l 372.72 535.2 l 372.96 534.72 l 372 534.72 l f* 372 534.48 m 371.76 535.44 l 372.48 535.44 l 372.72 534.24 l 372 534.48 l f* 371.28 535.2 m 370.8 536.88 l 371.76 536.88 l 372.24 535.2 l 371.28 535.2 l f* 370.8 536.16 m 370.32 537.6 l 371.04 537.6 l 371.76 535.92 l 370.8 536.16 l f* 370.32 536.88 m 369.84 538.32 l 370.8 538.32 l 371.04 536.64 l 370.32 536.88 l f* 369.84 537.36 m 369.84 537.84 l 370.56 537.84 l 370.8 537.36 l 369.84 537.36 l f* 368.88 539.04 0.72 0.96 re f 368.64 539.04 m 368.4 539.76 l 369.36 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398.64 491.52 l 399.6 491.52 l 399.12 492.48 l 398.16 492.48 l f* 400.32 489.84 m 400.8 488.4 l 401.76 488.4 l 401.04 489.6 l 400.32 489.84 l f* 402.24 486.48 m 402.96 485.04 l 403.92 485.04 l 403.2 486.24 l 402.24 486.48 l f* 403.68 484.8 m 405.12 481.44 l 406.08 481.44 l 404.4 484.8 l 403.68 484.8 l f* 405.12 482.4 m 406.08 480.72 l 406.8 480.72 l 406.08 482.4 l 405.12 482.4 l f* 407.28 478.8 m 407.76 477.36 l 408.72 477.12 l 408 478.8 l 407.28 478.8 l f* 407.76 478.08 m 408.96 475.44 l 409.68 475.2 l 408.72 478.08 l 407.76 478.08 l f* 408.96 476.16 m 410.16 473.52 l 410.88 473.52 l 409.68 476.16 l 408.96 476.16 l f* 410.16 474.48 m 410.88 472.08 l 411.6 471.84 l 410.88 474.48 l 410.16 474.48 l f* 411.6 470.4 m 411.84 470.4 l 412.56 470.16 l 412.56 470.4 l 411.6 470.4 l f* 411.84 471.12 m 412.08 469.68 l 412.8 469.68 l 412.56 470.88 l 411.84 471.12 l f* 412.32 469.68 m 412.8 468 l 413.52 468 l 413.04 469.68 l 412.32 469.68 l f* 412.8 467.52 0.72 1.2 re f 412.8 468.24 m 412.8 467.28 l 413.76 467.04 l 413.52 468.24 l 412.8 468.24 l f* 412.8 468 m 413.04 466.8 l 413.76 466.8 l 413.76 468 l 412.8 468 l f* 413.04 467.28 0.72 0.24 re f 413.04 467.04 m 412.8 466.08 l 413.76 465.84 l 413.76 466.8 l 413.04 467.04 l f* 413.52 466.08 m 412.56 465.84 l 412.8 466.8 l 413.76 466.8 l 413.52 466.08 l f* 413.52 466.8 m 412.56 466.8 l 412.56 466.08 l 413.52 465.84 l 413.52 466.8 l f* 412.32 466.08 0.96 0.72 re f 413.04 466.8 m 411.84 467.28 l 411.84 466.32 l 413.04 466.08 l 413.04 466.8 l f* 412.56 467.28 m 412.32 467.28 l 412.32 466.56 l 412.56 466.32 l 412.56 467.28 l f* 411.36 466.8 m 411.12 468 l 411.84 468 l 412.08 466.8 l 411.36 466.8 l f* 411.12 467.28 m 410.64 468.48 l 411.36 468.24 l 411.84 467.04 l 411.12 467.28 l f* 410.64 467.52 m 410.4 468.72 l 411.12 468.72 l 411.36 467.52 l 410.64 467.52 l f* 410.4 468 m 410.16 469.2 l 410.88 469.2 l 411.12 467.76 l 410.4 468 l f* 410.16 468.24 m 409.92 468.72 l 410.64 468.48 l 410.88 468.24 l 410.16 468.24 l f* 408.96 470.64 0.48 0.72 re f 408.72 470.4 m 408 472.32 l 408.72 472.32 l 409.44 470.4 l 408.72 470.4 l f* 408 471.6 m 407.28 473.76 l 408 473.52 l 408.72 471.36 l 408 471.6 l f* 407.28 472.8 m 407.04 473.76 l 407.76 473.76 l 408 472.8 l 407.28 472.8 l f* 406.08 475.92 m 405.84 476.4 l 406.8 476.16 l 406.8 475.92 l 406.08 475.92 l f* 405.84 475.44 m 405.12 477.84 l 406.08 477.6 l 406.8 475.44 l 405.84 475.44 l f* 405.12 476.88 m 404.4 479.28 l 405.36 479.28 l 406.08 476.88 l 405.12 476.88 l f* 404.4 478.56 m 404.4 479.28 l 405.12 479.28 l 405.36 478.32 l 404.4 478.56 l f* 403.44 481.44 m 403.2 481.92 l 404.16 481.68 l 404.16 481.44 l 403.44 481.44 l f* 403.2 480.96 m 402.96 482.16 l 403.92 482.16 l 404.16 480.96 l 403.2 480.96 l f* 402.96 481.92 m 402.48 483.84 l 403.2 483.84 l 403.68 481.92 l 402.96 481.92 l f* 402.48 483.12 m 402 485.04 l 402.72 484.8 l 403.2 482.88 l 402.48 483.12 l f* 402 484.08 m 401.52 485.76 l 402.24 485.76 l 402.72 484.08 l 402 484.08 l f* 400.8 487.44 m 400.32 488.88 l 401.04 488.88 l 401.52 487.2 l 400.8 487.44 l f* 399.36 491.04 m 399.12 492 l 399.84 492 l 400.08 491.04 l 399.36 491.04 l f* 399.12 491.28 m 398.16 494.4 l 398.88 494.4 l 399.84 491.28 l 399.12 491.28 l f* 398.16 493.68 m 397.44 495.84 l 398.4 495.6 l 398.88 493.44 l 398.16 493.68 l f* 396.72 498 m 396.48 499.2 l 397.2 498.96 l 397.44 498 l 396.72 498 l f* 396.48 498.24 m 396.24 498.72 l 396.96 498.72 l 397.2 498.24 l 396.48 498.24 l f* 395.52 500.64 m 394.8 502.56 l 395.76 502.56 l 396.24 500.64 l 395.52 500.64 l f* 394.8 501.84 m 394.32 504 l 395.04 503.76 l 395.76 501.6 l 394.8 501.84 l f* 394.32 503.04 m 393.84 504.24 l 394.56 504.24 l 395.04 503.04 l 394.32 503.04 l f* 392.64 506.4 m 392.4 507.6 l 393.12 507.36 l 393.6 506.4 l 392.64 506.4 l f* 392.4 506.64 0.72 0.48 re f 391.44 509.28 m 391.44 509.52 l 392.16 509.52 l 392.16 509.04 l 391.44 509.28 l f* 391.44 508.8 m 390.96 510 l 391.68 509.76 l 392.16 508.8 l 391.44 508.8 l f* 390.96 509.76 m 390.48 511.2 l 391.44 511.2 l 391.68 509.52 l 390.96 509.76 l f* 390.48 510.48 m 390.24 511.68 l 390.96 511.68 l 391.44 510.24 l 390.48 510.48 l f* 390.24 510.96 m 390 512.4 l 390.72 512.16 l 390.96 510.96 l 390.24 510.96 l f* 390 511.68 m 389.76 512.88 l 390.72 512.64 l 390.72 511.44 l 390 511.68 l f* 389.28 513.6 m 389.28 514.08 l 390 514.08 l 390.24 513.6 l 389.28 513.6 l f* 389.28 513.36 0.72 0.96 re f 389.28 513.6 m 389.04 515.04 l 389.76 514.8 l 390 513.6 l 389.28 513.6 l f* 389.04 514.08 m 388.56 515.28 l 389.52 515.28 l 389.76 514.08 l 389.04 514.08 l f* 388.56 514.56 m 388.56 515.52 l 389.28 515.52 l 389.52 514.32 l 388.56 514.56 l f* 388.56 514.56 0.72 0.96 re f 388.56 514.8 0.72 0.72 re f 388.32 515.52 m 388.56 514.56 l 389.28 514.56 l 389.28 515.52 l 388.32 515.52 l f* 388.56 515.52 m 388.56 514.56 l 389.28 514.32 l 389.28 515.28 l 388.56 515.52 l f* 388.56 515.28 m 388.56 514.08 l 389.52 514.08 l 389.28 515.28 l 388.56 515.28 l f* 388.56 515.04 m 388.8 513.84 l 389.52 513.84 l 389.52 514.8 l 388.56 515.04 l f* 388.8 514.56 m 389.04 513.36 l 390 513.12 l 389.52 514.56 l 388.8 514.56 l f* 389.76 513.12 m 390 511.44 l 390.96 511.2 l 390.48 513.12 l 389.76 513.12 l f* 390 512.16 m 390.72 510.48 l 391.44 510.48 l 390.96 512.16 l 390 512.16 l f* 390.72 511.44 m 391.2 509.52 l 392.16 509.52 l 391.44 511.44 l 390.72 511.44 l f* 391.92 509.52 m 392.4 507.84 l 393.12 507.84 l 392.64 509.28 l 391.92 509.52 l f* 392.4 508.8 m 392.64 507.36 l 393.6 507.12 l 393.12 508.8 l 392.4 508.8 l f* 392.64 508.08 m 393.84 505.92 l 394.56 505.92 l 393.6 508.08 l 392.64 508.08 l f* 394.56 504.72 m 395.52 504.72 l 395.28 504.72 l 394.56 504.72 l f* 394.56 505.68 m 395.04 504.24 l 395.76 504 l 395.52 505.44 l 394.56 505.68 l f* 395.28 503.76 m 396.48 503.28 l 396.72 504 l 395.28 504.48 l 395.28 503.76 l f* 395.76 503.28 m 396.72 503.04 l 396.96 504 l 395.76 504 l 395.76 503.28 l f* 396 503.04 1.2 0.72 re f 396.24 503.04 m 397.2 502.8 l 397.44 503.76 l 396.48 503.76 l 396.24 503.04 l f* 396.48 502.8 m 397.44 502.8 l 397.44 503.52 l 396.48 503.76 l 396.48 502.8 l f* 396.72 503.52 m 396.72 502.8 l 396.72 503.52 l f* 396.96 503.04 0.72 0.96 re f 396.96 503.28 0.72 1.2 re f 396.96 503.76 m 396.72 504.96 l 397.44 504.96 l 397.68 503.52 l 396.96 503.76 l f* 396.72 504.24 m 396.48 505.44 l 397.44 505.44 l 397.44 504 l 396.72 504.24 l f* 396.48 504.72 m 396.48 505.44 l 397.2 505.2 l 397.44 504.72 l 396.48 504.72 l f* 396 506.88 m 395.76 508.08 l 396.48 507.84 l 396.72 506.88 l 396 506.88 l f* 395.76 507.12 m 395.52 508.56 l 396.48 508.56 l 396.48 507.12 l 395.76 507.12 l f* 395.52 507.84 m 395.52 509.28 l 396.24 509.28 l 396.48 507.84 l 395.52 507.84 l f* 395.52 508.56 m 395.04 510.72 l 395.76 510.72 l 396.24 508.56 l 395.52 508.56 l f* 395.04 510 0.72 0.24 re f 394.56 512.64 m 394.32 512.88 l 395.04 512.88 l 395.28 512.64 l 394.56 512.64 l f* 394.32 512.16 m 394.08 513.36 l 395.04 513.36 l 395.04 512.16 l 394.32 512.16 l f* 394.08 512.88 m 393.84 514.08 l 394.8 514.08 l 395.04 512.64 l 394.08 512.88 l f* 393.84 513.36 m 393.6 514.8 l 394.56 514.8 l 394.8 513.36 l 393.84 513.36 l f* 393.6 514.08 m 393.36 515.52 l 394.08 515.28 l 394.56 514.08 l 393.6 514.08 l f* 393.36 514.56 m 393.12 516 l 393.84 515.76 l 394.08 514.56 l 393.36 514.56 l f* 392.64 516.72 m 392.64 517.44 l 393.36 517.2 l 393.36 516.72 l 392.64 516.72 l f* 392.64 516.48 m 392.4 517.44 l 393.36 517.44 l 393.36 516.48 l 392.64 516.48 l f* 392.4 516.72 0.96 0.72 re f 392.64 517.44 m 392.64 516.72 l 393.36 516.48 l 393.36 517.44 l 392.64 517.44 l f* 392.64 517.44 m 392.88 516.24 l 393.6 516.24 l 393.36 517.44 l 392.64 517.44 l f* 392.88 517.2 m 393.12 516 l 393.84 516 l 393.6 517.2 l 392.88 517.2 l f* 393.12 516.96 m 393.36 515.52 l 394.08 515.52 l 393.84 516.72 l 393.12 516.96 l f* 393.84 515.28 m 394.08 514.32 l 394.8 514.32 l 394.56 515.04 l 393.84 515.28 l f* 394.08 515.28 m 394.56 513.36 l 395.28 513.36 l 394.8 515.04 l 394.08 515.28 l f* 394.56 514.32 m 395.04 512.64 l 395.76 512.64 l 395.28 514.32 l 394.56 514.32 l f* 395.04 513.6 m 395.52 511.68 l 396.48 511.68 l 395.76 513.36 l 395.04 513.6 l f* 396.24 511.44 m 396.72 510 l 397.44 510 l 397.2 511.44 l 396.24 511.44 l f* 396.72 510.96 m 397.2 509.52 l 397.92 509.28 l 397.44 510.96 l 396.72 510.96 l f* 397.2 510.24 m 398.4 508.32 l 399.12 508.08 l 398.16 510.24 l 397.2 510.24 l f* 399.36 506.88 0.96 0.24 re f 399.36 507.84 m 399.84 506.4 l 400.56 506.4 l 400.32 507.84 l 399.36 507.84 l f* 400.32 506.16 m 401.52 505.68 l 401.52 506.4 l 400.32 506.88 l 400.32 506.16 l f* 400.8 505.68 m 402 505.44 l 402 506.16 l 400.8 506.4 l 400.8 505.68 l f* 401.28 505.44 m 402.48 505.2 l 402.48 506.16 l 401.28 506.16 l 401.28 505.44 l f* 401.76 505.2 0.96 0.96 re f 401.76 505.2 0.96 0.96 re f 402 505.2 0.72 0.96 re f 402 505.44 m 402 506.4 l 402.96 506.16 l 402.72 505.44 l 402 505.44 l f* 402 505.44 0.96 0.96 re f 402 505.68 m 402.24 506.64 l 402.96 506.64 l 402.96 505.68 l 402 505.68 l f* 402.24 505.92 0.72 1.2 re f 402.24 506.4 0.72 0.24 re f 402 507.12 m 401.76 508.32 l 402.72 508.32 l 402.72 506.88 l 402 507.12 l f* 401.76 507.6 m 401.52 509.04 l 402.48 509.04 l 402.72 507.6 l 401.76 507.6 l f* 401.52 508.32 m 401.28 509.76 l 402 509.76 l 402.48 508.08 l 401.52 508.32 l f* 401.28 509.04 m 401.04 510.24 l 401.76 510 l 402 509.04 l 401.28 509.04 l f* 400.56 511.68 0.48 0.72 re f 400.32 511.68 0.48 0.72 re f 399.36 513.6 m 398.88 515.52 l 399.6 515.52 l 400.08 513.6 l 399.36 513.6 l f* 398.88 514.8 m 398.4 516.72 l 399.12 516.72 l 399.6 514.8 l 398.88 514.8 l f* 398.4 516 m 397.92 517.44 l 398.64 517.44 l 399.12 516 l 398.4 516 l f* 396.96 518.88 m 396.48 520.32 l 397.2 520.32 l 397.92 518.88 l 396.96 518.88 l f* 395.28 522.48 m 395.04 523.44 l 395.76 523.44 l 396.24 522.48 l 395.28 522.48 l f* 395.04 522.72 m 394.8 523.2 l 395.76 523.2 l 395.76 522.72 l 395.04 522.72 l f* 394.32 523.92 m 393.6 526.08 l 394.56 526.08 l 395.04 523.92 l 394.32 523.92 l f* 393.6 525.12 m 392.88 527.52 l 393.84 527.28 l 394.56 525.12 l 393.6 525.12 l f* 392.88 526.56 m 392.64 527.28 l 393.36 527.28 l 393.84 526.56 l 392.88 526.56 l f* 391.44 529.44 m 390.72 530.88 l 391.68 530.64 l 392.16 529.2 l 391.44 529.44 l f* 389.76 532.08 m 389.28 533.52 l 390 533.52 l 390.72 531.84 l 389.76 532.08 l f* 388.56 534 m 388.08 535.92 l 388.8 535.68 l 389.28 533.76 l 388.56 534 l f* 388.08 534.96 m 387.36 536.88 l 388.08 536.64 l 388.8 534.72 l 388.08 534.96 l f* 387.36 535.92 m 386.88 537.36 l 387.6 537.36 l 388.08 535.92 l 387.36 535.92 l f* 385.92 538.56 m 385.92 539.28 l 386.64 539.04 l 386.88 538.56 l 385.92 538.56 l f* 385.92 538.32 m 385.68 539.28 l 386.4 539.04 l 386.64 538.32 l 385.92 538.32 l f* 384.72 540.48 m 384.72 540.96 l 385.44 540.96 l 385.68 540.48 l 384.72 540.48 l f* 384.72 540 m 384.24 541.44 l 385.2 541.2 l 385.44 540 l 384.72 540 l f* 384.24 540.48 m 384 541.68 l 384.72 541.68 l 385.2 540.48 l 384.24 540.48 l f* 383.76 540.96 0.96 0.72 re f 383.76 540.96 0.72 0.96 re f 383.52 541.2 0.96 0.72 re f 383.52 540.96 0.96 0.96 re f 383.52 541.92 m 383.76 540.96 l 384.48 540.72 l 384.48 541.68 l 383.52 541.92 l f* 383.76 540.48 0.72 1.2 re f 383.76 541.44 m 384 540.24 l 384.72 540.24 l 384.48 541.2 l 383.76 541.44 l f* 384 539.76 0.72 1.2 re f 384 540.24 0.72 0.24 re f 384.48 539.28 m 384.96 537.6 l 385.68 537.6 l 385.44 539.28 l 384.48 539.28 l f* 384.96 538.56 m 385.44 536.64 l 386.4 536.64 l 385.68 538.56 l 384.96 538.56 l f* 385.44 537.6 m 385.92 535.68 l 386.88 535.68 l 386.4 537.6 l 385.44 537.6 l f* 386.88 534.24 m 387.36 533.28 l 388.08 533.04 l 387.84 534.24 l 386.88 534.24 l f* 387.36 534 m 387.36 533.76 l 388.32 533.76 l 388.08 534 l 387.36 534 l f* 388.32 531.6 m 388.56 530.64 l 389.52 530.64 l 389.28 531.6 l 388.32 531.6 l f* 388.56 531.6 m 388.8 531.12 l 389.76 530.88 l 389.52 531.6 l 388.56 531.6 l f* 389.28 530.4 m 390 528.24 l 390.96 528.24 l 390.24 530.4 l 389.28 530.4 l f* 390 529.2 m 390.96 527.04 l 391.68 527.04 l 390.96 529.2 l 390 529.2 l f* 390.96 528 m 391.2 527.04 l 392.16 527.04 l 391.68 528 l 390.96 528 l f* 392.64 525.12 m 393.12 523.68 l 393.84 523.68 l 393.36 525.12 l 392.64 525.12 l f* 394.08 522.48 m 394.8 521.04 l 395.52 521.04 l 395.04 522.48 l 394.08 522.48 l f* 395.52 520.56 m 396.96 517.68 l 397.68 517.68 l 396.24 520.56 l 395.52 520.56 l f* 396.96 518.64 m 397.68 516.72 l 398.4 516.72 l 397.68 518.4 l 396.96 518.64 l f* 397.68 517.68 m 397.68 517.44 l 398.4 517.2 l 398.4 517.44 l 397.68 517.68 l f* 398.88 515.28 m 398.88 515.04 l 399.84 514.8 l 399.6 515.28 l 398.88 515.28 l f* 398.88 515.76 m 399.36 514.8 l 400.08 514.56 l 399.84 515.76 l 398.88 515.76 l f* 400.56 513.6 m 400.8 512.64 l 401.52 512.64 l 401.28 513.36 l 400.56 513.6 l f* 400.8 513.6 m 401.28 511.92 l 402 511.92 l 401.52 513.6 l 400.8 513.6 l f* 401.28 512.88 m 401.76 511.44 l 402.48 511.44 l 402 512.88 l 401.28 512.88 l f* 401.76 512.4 m 402.24 510.96 l 402.96 510.96 l 402.48 512.16 l 401.76 512.4 l f* 402.24 511.92 m 402.48 511.2 l 403.2 510.96 l 402.96 511.68 l 402.24 511.92 l f* 403.2 509.76 m 403.44 509.76 l 404.16 509.52 l 404.16 509.76 l 403.2 509.76 l f* 403.2 509.76 m 404.4 509.52 l 404.4 510.24 l 403.44 510.48 l 403.2 509.76 l f* 403.68 509.52 0.24 0.72 re f 403.92 510.24 m 404.64 510.24 l 404.88 509.52 l 403.92 509.52 l 403.92 510.24 l f* 403.92 509.52 m 404.16 510.48 l 404.88 510.48 l 404.88 509.52 l 403.92 509.52 l f* 404.16 509.76 m 404.16 510.96 l 405.12 510.72 l 404.88 509.76 l 404.16 509.76 l f* 404.16 510 0.96 1.2 re f 404.16 510.48 m 404.16 511.68 l 404.88 511.68 l 405.12 510.48 l 404.16 510.48 l f* 403.92 513.12 0.72 0.24 re f 403.92 512.64 m 403.68 514.08 l 404.4 514.08 l 404.64 512.64 l 403.92 512.64 l f* 403.68 513.36 m 403.2 514.8 l 404.16 514.8 l 404.4 513.12 l 403.68 513.36 l f* 403.2 514.08 m 402.96 515.76 l 403.68 515.76 l 404.16 514.08 l 403.2 514.08 l f* 402.96 515.04 m 402.72 515.76 l 403.68 515.76 l 403.68 514.8 l 402.96 515.04 l f* 402 517.92 m 401.76 518.4 l 402.72 518.4 l 402.72 517.92 l 402 517.92 l f* 401.76 517.68 m 401.52 518.64 l 402.24 518.64 l 402.72 517.44 l 401.76 517.68 l f* 401.04 519.36 m 400.8 520.8 l 401.52 520.8 l 402 519.12 l 401.04 519.36 l f* 400.8 520.08 m 400.32 521.76 l 401.28 521.52 l 401.52 520.08 l 400.8 520.08 l f* 400.32 520.8 m 400.08 522.48 l 400.8 522.48 l 401.28 520.8 l 400.32 520.8 l f* 400.08 521.76 m 399.84 522.48 l 400.8 522.24 l 400.8 521.76 l 400.08 521.76 l f* 399.12 523.92 m 399.12 524.64 l 399.84 524.64 l 400.08 523.92 l 399.12 523.92 l f* 399.12 523.92 0.72 0.72 re f 398.88 524.64 0.72 0.72 re f 398.88 524.64 0.96 0.72 re f 398.88 525.36 m 399.12 524.4 l 399.84 524.4 l 399.84 525.36 l 398.88 525.36 l f* 399.12 525.36 m 399.12 524.16 l 399.84 524.16 l 399.84 525.12 l 399.12 525.36 l f* 399.12 525.12 m 399.36 523.92 l 400.32 523.92 l 399.84 525.12 l 399.12 525.12 l f* 399.36 524.88 m 399.6 524.16 l 400.32 524.16 l 400.32 524.64 l 399.36 524.88 l f* 400.32 522.96 m 400.56 522.24 l 401.28 522 l 401.04 522.96 l 400.32 522.96 l f* 400.56 522.96 m 400.8 522.24 l 401.52 522.24 l 401.28 522.96 l 400.56 522.96 l f* 401.28 521.76 m 401.52 520.32 l 402.24 520.32 l 402 521.76 l 401.28 521.76 l f* 401.52 521.28 m 402 519.84 l 402.72 519.6 l 402.24 521.04 l 401.52 521.28 l f* 402 520.56 m 402.72 518.4 l 403.44 518.4 l 402.72 520.56 l 402 520.56 l f* 402.72 519.36 m 402.72 519.12 l 403.68 519.12 l 403.44 519.36 l 402.72 519.36 l f* 403.68 517.2 m 403.92 516.48 l 404.64 516.48 l 404.64 516.96 l 403.68 517.2 l f* 403.92 517.44 m 404.16 516.48 l 404.88 516.48 l 404.64 517.44 l 403.92 517.44 l f* 404.4 516.96 m 404.64 515.52 l 405.36 515.28 l 405.12 516.72 l 404.4 516.96 l f* 404.64 516.48 m 405.12 515.04 l 405.84 515.04 l 405.36 516.24 l 404.64 516.48 l f* 405.12 516 m 405.84 514.32 l 406.56 514.08 l 405.84 515.76 l 405.12 516 l f* 405.84 515.04 m 406.08 514.32 l 406.8 514.32 l 406.56 515.04 l 405.84 515.04 l f* 407.28 513.6 m 407.28 512.4 l 408 512.4 l 408 513.36 l 407.28 513.6 l f* 407.28 513.36 m 407.52 512.16 l 408.24 512.16 l 408 513.36 l 407.28 513.36 l f* 407.52 513.12 m 407.76 511.92 l 408.48 511.68 l 408.24 512.88 l 407.52 513.12 l f* 407.76 512.64 m 408 511.44 l 408.72 511.44 l 408.48 512.64 l 407.76 512.64 l f* 408 512.4 m 408.24 511.68 l 409.2 511.68 l 408.72 512.4 l 408 512.4 l f* 409.44 510.48 m 409.68 509.52 l 410.4 509.52 l 410.16 510.48 l 409.44 510.48 l f* 409.68 510.48 m 409.68 510 l 410.4 509.76 l 410.4 510.24 l 409.68 510.48 l f* 410.16 509.52 m 410.4 508.8 l 411.12 508.56 l 411.12 509.52 l 410.16 509.52 l f* 410.4 508.8 0.72 0.72 re f 410.16 509.28 m 409.92 510.48 l 410.64 510.24 l 410.88 509.04 l 410.16 509.28 l f* 409.92 509.52 m 409.68 510.72 l 410.4 510.72 l 410.64 509.52 l 409.92 509.52 l f* 409.68 510 m 409.44 511.2 l 410.16 511.2 l 410.4 509.76 l 409.68 510 l f* 409.44 510.24 m 409.2 511.68 l 409.92 511.68 l 410.16 510.24 l 409.44 510.24 l f* 409.2 510.96 m 409.2 511.2 l 409.92 510.96 l 409.92 510.72 l 409.2 510.96 l f* 408.24 512.4 m 407.76 513.84 l 408.48 513.84 l 409.2 512.4 l 408.24 512.4 l f* 406.8 515.04 m 406.08 516.48 l 406.8 516.48 l 407.52 515.04 l 406.8 515.04 l f* 405.12 518.4 m 404.88 519.12 l 405.6 518.88 l 405.84 518.4 l 405.12 518.4 l f* 404.88 518.16 m 403.68 520.8 l 404.4 520.56 l 405.6 518.16 l 404.88 518.16 l f* 403.68 519.84 m 402.96 521.76 l 403.68 521.76 l 404.4 519.84 l 403.68 519.84 l f* 401.76 523.68 m 401.52 524.16 l 402.48 524.16 l 402.72 523.68 l 401.76 523.68 l f* 401.52 523.2 m 401.28 524.4 l 402 524.16 l 402.48 523.2 l 401.52 523.2 l f* 400.08 526.32 m 399.6 527.52 l 400.32 527.28 l 400.8 526.32 l 400.08 526.32 l f* 399.6 526.56 m 399.6 527.04 l 400.32 526.8 l 400.32 526.56 l 399.6 526.56 l f* 398.4 528.96 m 397.92 530.16 l 398.64 530.16 l 399.12 528.96 l 398.4 528.96 l f* 397.92 529.44 m 397.44 530.88 l 398.16 530.64 l 398.64 529.2 l 397.92 529.44 l f* 397.44 529.92 m 397.2 531.36 l 397.92 531.36 l 398.16 529.92 l 397.44 529.92 l f* 397.2 530.4 m 396.96 531.6 l 397.68 531.6 l 397.92 530.4 l 397.2 530.4 l f* 396.48 531.36 m 396 533.04 l 396.72 532.8 l 397.44 531.36 l 396.48 531.36 l f* 396 532.08 m 395.52 533.52 l 396.24 533.52 l 396.72 532.08 l 396 532.08 l f* 395.52 532.56 m 395.04 534 l 395.76 534 l 396.24 532.56 l 395.52 532.56 l f* 395.28 533.52 0.48 0.48 re f 394.56 535.2 m 393.36 535.2 l 393.6 534.48 l 394.56 534.24 l 394.56 535.2 l f* 394.32 535.2 m 393.84 535.44 l 393.84 534.48 l 394.32 534.48 l 394.32 535.2 l f* 393.36 534.72 0.72 0.72 re f 394.08 534.72 m 393.12 534.48 l 393.12 535.44 l 394.08 535.44 l 394.08 534.72 l f* 393.12 534.48 0.72 0.96 re f 393.12 534.48 0.72 0.72 re f 393.12 535.44 m 393.36 534 l 394.08 534 l 393.84 535.2 l 393.12 535.44 l f* 393.36 534.96 m 393.6 533.76 l 394.32 533.76 l 394.08 534.96 l 393.36 534.96 l f* 393.6 534.72 m 394.08 532.8 l 395.04 532.8 l 394.32 534.48 l 393.6 534.72 l f* 394.08 533.76 m 394.56 532.8 l 395.28 532.8 l 395.04 533.76 l 394.08 533.76 l f* 395.76 530.64 m 396.48 530.64 l 395.76 530.64 l f* 395.76 531.6 m 396.48 530.16 l 397.2 530.16 l 396.48 531.6 l 395.76 531.6 l f* 397.68 528 0.72 0.24 re f 397.68 528.96 m 398.16 527.76 l 399.12 527.52 l 398.4 528.96 l 397.68 528.96 l f* 399.6 525.6 m 399.84 525.12 l 400.56 525.12 l 400.32 525.6 l 399.6 525.6 l f* 399.84 526.08 m 402 522.24 l 402.72 522.24 l 400.56 526.08 l 399.84 526.08 l f* 402 523.2 m 402.24 522.72 l 402.96 522.72 l 402.72 523.2 l 402 523.2 l f* 403.44 520.8 m 403.92 519.6 l 404.64 519.6 l 404.16 520.8 l 403.44 520.8 l f* 403.92 520.08 0.72 0.48 re f 405.12 518.16 m 405.6 517.44 l 406.32 517.2 l 406.08 518.16 l 405.12 518.16 l f* 405.6 518.16 m 405.84 517.68 l 406.56 517.68 l 406.32 518.16 l 405.6 518.16 l f* 406.8 516.48 m 407.28 515.04 l 408 514.8 l 407.52 516.48 l 406.8 516.48 l f* 407.28 515.76 m 407.76 514.32 l 408.48 514.32 l 408 515.76 l 407.28 515.76 l f* 407.76 515.28 m 408 513.84 l 408.96 513.6 l 408.48 515.28 l 407.76 515.28 l f* 408 514.56 m 408.24 513.84 l 409.2 513.84 l 408.96 514.56 l 408 514.56 l f* 409.2 512.4 0.72 0.24 re f 409.2 513.36 m 409.2 512.16 l 410.16 512.16 l 409.92 513.36 l 409.2 513.36 l f* 409.2 512.88 0.96 0.24 re f 409.44 512.88 m 409.68 511.92 l 410.4 511.68 l 410.16 512.88 l 409.44 512.88 l f* 409.68 512.64 m 409.68 511.68 l 410.64 511.68 l 410.4 512.64 l 409.68 512.64 l f* 409.68 511.68 m 410.88 511.44 l 410.88 512.16 l 409.68 512.4 l 409.68 511.68 l f* 410.16 511.44 m 411.12 511.2 l 411.12 511.92 l 410.16 512.16 l 410.16 511.44 l f* 410.4 511.2 0.96 0.72 re f 410.64 511.2 m 411.6 510.96 l 411.84 511.68 l 410.88 511.92 l 410.64 511.2 l f* 410.88 510.96 m 411.84 510.72 l 412.08 511.68 l 410.88 511.68 l 410.88 510.96 l f* 411.12 510.72 m 412.56 510.48 l 412.56 511.2 l 411.12 511.68 l 411.12 510.72 l f* 411.6 510.48 m 412.8 510.24 l 412.8 511.2 l 411.84 511.2 l 411.6 510.48 l f* 411.84 510.24 m 412.8 510.24 l 413.04 510.96 l 412.08 511.2 l 411.84 510.24 l f* 412.08 510.24 0.24 0.72 re f 412.56 510.24 0.72 0.96 re f 412.56 510.48 0.72 0.96 re f 412.56 510.72 m 412.32 511.68 l 413.04 511.68 l 413.28 510.72 l 412.56 510.72 l f* 412.32 510.96 m 412.08 512.16 l 413.04 511.92 l 413.04 510.96 l 412.32 510.96 l f* 412.08 511.2 m 411.84 512.64 l 412.8 512.64 l 413.04 511.2 l 412.08 511.2 l f* 411.36 513.12 m 411.36 514.32 l 412.08 514.32 l 412.32 512.88 l 411.36 513.12 l f* 411.36 513.6 m 411.12 515.04 l 411.84 515.04 l 412.08 513.6 l 411.36 513.6 l f* 411.12 514.32 m 410.88 515.76 l 411.6 515.52 l 411.84 514.08 l 411.12 514.32 l f* 410.88 514.8 m 410.4 516.24 l 411.36 516 l 411.6 514.8 l 410.88 514.8 l f* 409.68 517.68 m 409.2 519.12 l 410.16 519.12 l 410.4 517.68 l 409.68 517.68 l f* 409.2 518.4 m 408.72 520.56 l 409.44 520.56 l 410.16 518.4 l 409.2 518.4 l f* 408.72 519.84 m 408 521.76 l 408.72 521.76 l 409.44 519.6 l 408.72 519.84 l f* 408 521.04 m 407.76 522 l 408.48 522 l 408.72 521.04 l 408 521.04 l f* 406.8 523.44 m 406.32 525.6 l 407.04 525.36 l 407.52 523.44 l 406.8 523.44 l f* 406.32 524.64 m 405.84 526.56 l 406.8 526.56 l 407.04 524.64 l 406.32 524.64 l f* 405.84 525.84 m 405.6 527.52 l 406.32 527.28 l 406.8 525.84 l 405.84 525.84 l f* 405.36 527.52 m 405.12 528.96 l 406.08 528.96 l 406.08 527.52 l 405.36 527.52 l f* 405.12 528.24 0.96 1.2 re f 405.12 528.72 0.96 0.96 re f 405.12 528.96 m 405.36 529.92 l 406.08 529.92 l 406.08 528.96 l 405.12 528.96 l f* 405.36 529.2 0.72 0.72 re f 405.36 529.2 0.96 0.72 re f 405.6 529.2 m 406.56 528.96 l 406.8 529.68 l 405.6 529.92 l 405.6 529.2 l f* 405.84 529.92 m 406.08 528.72 l 407.04 528.72 l 406.8 529.92 l 405.84 529.92 l f* 406.08 528.72 m 407.28 528.48 l 407.28 529.2 l 406.08 529.44 l 406.08 528.72 l f* 406.56 529.44 m 407.04 528.24 l 407.76 528.24 l 407.28 529.44 l 406.56 529.44 l f* 407.76 528 m 408.48 526.56 l 409.2 526.56 l 408.72 528 l 407.76 528 l f* 408.48 526.56 m 409.68 526.08 l 409.68 526.8 l 408.48 527.28 l 408.48 526.56 l f* 408.96 527.04 m 409.44 525.6 l 410.4 525.36 l 409.68 527.04 l 408.96 527.04 l f* 409.44 526.32 m 409.68 525.6 l 410.64 525.6 l 410.4 526.32 l 409.44 526.32 l f* 409.92 525.84 m 410.4 524.64 l 411.12 524.64 l 410.88 525.84 l 409.92 525.84 l f* 410.4 525.6 m 410.64 524.16 l 411.36 524.16 l 411.12 525.36 l 410.4 525.6 l f* 410.64 525.12 m 410.88 523.92 l 411.6 523.92 l 411.36 524.88 l 410.64 525.12 l f* 410.88 523.92 0.72 0.96 re f 410.88 523.92 0.72 0.72 re f 410.88 523.92 m 410.64 524.88 l 411.36 524.88 l 411.6 523.68 l 410.88 523.92 l f* 410.64 523.92 m 410.4 525.12 l 411.12 524.88 l 411.36 523.92 l 410.64 523.92 l f* 410.4 524.16 m 410.16 525.36 l 410.88 525.36 l 411.12 524.16 l 410.4 524.16 l f* 410.16 524.4 m 409.92 525.6 l 410.64 525.6 l 410.88 524.4 l 410.16 524.4 l f* 409.92 524.88 m 409.44 525.6 l 410.4 525.6 l 410.64 524.64 l 409.92 524.88 l f* 409.44 526.8 m 408 527.04 l 408 526.32 l 409.44 525.84 l 409.44 526.8 l f* 408.72 527.04 m 407.52 527.28 l 407.52 526.56 l 408.96 526.32 l 408.72 527.04 l f* 408.24 527.28 m 407.04 527.52 l 407.04 526.8 l 408.48 526.56 l 408.24 527.28 l f* 406.8 526.8 0.96 0.72 re f 407.52 526.8 m 407.04 526.56 l 407.04 527.52 l 407.76 527.52 l 407.52 526.8 l f* 406.56 526.56 0.72 0.72 re f 406.56 527.52 m 406.32 526.32 l 407.28 526.32 l 407.28 527.52 l 406.56 527.52 l f* 406.32 527.28 m 406.08 526.08 l 407.04 525.84 l 407.28 527.28 l 406.32 527.28 l f* 406.08 526.8 m 406.08 525.84 l 406.8 525.84 l 407.04 526.8 l 406.08 526.8 l f* 406.08 526.56 m 406.08 525.6 l 406.8 525.36 l 406.8 526.56 l 406.08 526.56 l f* 406.08 525.6 m 406.08 524.16 l 407.04 524.16 l 406.8 525.6 l 406.08 525.6 l f* 406.08 525.12 m 406.32 523.68 l 407.28 523.68 l 407.04 524.88 l 406.08 525.12 l f* 406.32 524.4 m 406.8 523.2 l 407.52 522.96 l 407.28 524.4 l 406.32 524.4 l f* 406.8 523.92 m 407.04 522.48 l 407.76 522.48 l 407.52 523.92 l 406.8 523.92 l f* 408 521.04 m 408.24 520.08 l 408.96 520.08 l 408.72 521.04 l 408 521.04 l f* 408.24 521.04 m 408.24 520.56 l 409.2 520.32 l 408.96 521.04 l 408.24 521.04 l f* 408.48 520.32 m 409.2 518.4 l 409.92 518.16 l 409.2 520.32 l 408.48 520.32 l f* 409.2 519.12 m 409.92 516.96 l 410.64 516.96 l 409.92 519.12 l 409.2 519.12 l f* 409.92 517.92 m 410.16 516.72 l 410.88 516.72 l 410.64 517.68 l 409.92 517.92 l f* 411.12 514.8 m 411.36 514.56 l 412.08 514.56 l 411.12 514.8 l f* 411.36 515.52 m 412.08 513.6 l 412.8 513.36 l 412.08 515.28 l 411.36 515.52 l f* 412.08 514.32 m 412.8 512.4 l 413.52 512.4 l 412.8 514.32 l 412.08 514.32 l f* 412.8 513.36 m 413.28 512.16 l 414 511.92 l 413.52 513.36 l 412.8 513.36 l f* 414.24 511.2 m 414.96 511.2 l 414.96 511.92 l 414.48 511.92 l 414.24 511.2 l f* 414.24 511.2 m 415.2 510.96 l 415.2 511.68 l 414.24 511.92 l 414.24 511.2 l f* 414.48 510.96 0.96 0.72 re f 414.72 510.96 0.96 0.72 re f 414.96 511.68 m 415.92 511.92 l 415.92 510.96 l 414.96 510.96 l 414.96 511.68 l f* 414.96 511.92 m 415.92 511.92 l 416.16 511.2 l 415.2 510.96 l 414.96 511.92 l f* 415.2 511.2 0.48 0.72 re f 415.68 511.92 m 415.44 513.12 l 416.4 513.12 l 416.4 511.92 l 415.68 511.92 l f* 415.44 512.4 m 415.44 513.84 l 416.16 513.6 l 416.4 512.16 l 415.44 512.4 l f* 415.44 512.88 m 415.2 514.56 l 416.16 514.32 l 416.16 512.88 l 415.44 512.88 l f* 415.2 513.6 m 415.2 515.04 l 415.92 515.04 l 416.16 513.6 l 415.2 513.6 l f* 414.48 516.48 m 414.48 517.68 l 415.2 517.68 l 415.44 516.48 l 414.48 516.48 l f* 414.48 516.96 m 414.48 517.44 l 415.2 517.2 l 415.2 516.72 l 414.48 516.96 l f* 414.24 517.68 m 414 519.6 l 414.96 519.6 l 415.2 517.44 l 414.24 517.68 l f* 414 518.88 m 413.76 520.8 l 414.48 520.8 l 414.96 518.64 l 414 518.88 l f* 413.76 520.08 m 413.76 521.52 l 414.48 521.28 l 414.48 520.08 l 413.76 520.08 l f* 413.76 520.56 m 414.48 520.56 l 413.76 520.56 l f* 413.52 522.24 0.72 0.48 re f 413.52 522 m 413.28 523.44 l 414.24 523.2 l 414.24 522 l 413.52 522 l f* 413.28 522.48 m 413.28 523.92 l 414 523.68 l 414.24 522.48 l 413.28 522.48 l f* 413.28 522.96 0.72 0.96 re f 413.28 523.2 0.72 0.96 re f 413.28 523.44 0.72 0.72 re f 413.28 524.16 m 413.28 523.44 l 413.28 524.16 l f* 413.28 524.4 m 413.52 523.2 l 414.24 523.2 l 414 524.16 l 413.28 524.4 l f* 413.28 523.2 m 414.24 523.2 l 414.48 523.92 l 413.52 524.16 l 413.28 523.2 l f* 413.52 524.16 m 413.76 522.96 l 414.48 522.96 l 414.48 523.92 l 413.52 524.16 l f* 413.76 523.92 m 414 522.48 l 414.72 522.48 l 414.48 523.68 l 413.76 523.92 l f* 414 523.44 m 414.24 522.48 l 415.2 522.48 l 414.72 523.44 l 414 523.44 l f* 415.2 522 m 415.68 520.32 l 416.4 520.32 l 415.92 522 l 415.2 522 l f* 415.68 521.28 m 416.4 519.36 l 417.12 519.36 l 416.4 521.04 l 415.68 521.28 l f* 416.4 520.32 m 416.88 518.64 l 417.84 518.4 l 417.12 520.32 l 416.4 520.32 l f* 417.6 518.4 m 418.08 517.2 l 418.8 516.96 l 418.56 518.4 l 417.6 518.4 l f* 418.08 518.16 m 418.56 516.72 l 419.28 516.48 l 418.8 517.92 l 418.08 518.16 l f* 418.56 517.44 m 419.28 515.76 l 420 515.52 l 419.28 517.44 l 418.56 517.44 l f* 419.28 516.48 m 419.52 516 l 420.24 515.76 l 420 516.48 l 419.28 516.48 l f* 420.24 514.56 m 420.24 514.32 l 421.2 514.32 l 420.96 514.56 l 420.24 514.56 l f* 420.24 515.28 m 420.72 514.08 l 421.44 514.08 l 421.2 515.28 l 420.24 515.28 l f* 420.72 514.08 0.72 0.96 re f 420.72 514.08 0.96 0.72 re f 420.72 514.8 m 421.68 515.04 l 421.68 514.32 l 420.72 514.08 l 420.72 514.8 l f* 420.96 514.32 m 421.2 515.28 l 421.92 515.28 l 421.68 514.08 l 420.96 514.32 l f* 421.2 514.32 0.72 0.96 re f 421.2 514.56 0.72 0.96 re f 421.2 514.8 0.72 0.96 re f 421.2 515.04 0.72 1.2 re f 421.2 515.52 m 420.96 516.72 l 421.68 516.72 l 421.92 515.52 l 421.2 515.52 l f* 420.96 516 0.72 1.2 re f 420.96 516.48 m 420.72 517.68 l 421.44 517.68 l 421.68 516.48 l 420.96 516.48 l f* 420.72 516.96 m 420.48 518.16 l 421.44 518.16 l 421.44 516.72 l 420.72 516.96 l f* 420.48 517.44 m 420.24 518.64 l 421.2 518.64 l 421.44 517.44 l 420.48 517.44 l f* 420.24 517.92 m 420.24 518.4 l 420.96 518.4 l 421.2 517.92 l 420.24 517.92 l f* 419.52 520.8 m 420.24 520.8 l 420.48 520.56 l 419.52 520.8 l f* 419.52 520.08 m 419.28 522 l 420 522 l 420.24 520.08 l 419.52 520.08 l f* 419.28 521.28 m 418.8 523.2 l 419.52 522.96 l 420 521.04 l 419.28 521.28 l f* 418.8 522.24 m 418.32 523.92 l 419.28 523.92 l 419.52 522.24 l 418.8 522.24 l f* 418.08 524.16 m 418.08 525.6 l 418.8 525.6 l 419.04 524.16 l 418.08 524.16 l f* 418.08 524.64 0.72 1.44 re f 418.08 525.12 0.72 1.2 re f 418.08 525.6 0.72 0.72 re f 418.08 525.6 m 418.08 526.56 l 419.04 526.32 l 418.8 525.6 l 418.08 525.6 l f* 418.08 525.84 m 419.04 525.6 l 419.04 526.56 l 418.32 526.56 l 418.08 525.84 l f* 418.32 525.6 m 419.28 525.6 l 419.28 526.32 l 418.32 526.56 l 418.32 525.6 l f* 418.56 526.32 m 418.8 525.36 l 419.52 525.12 l 419.28 526.32 l 418.56 526.32 l f* 418.8 526.32 m 419.04 524.88 l 420 524.88 l 419.52 526.08 l 418.8 526.32 l f* 419.04 525.84 m 419.52 524.88 l 420.24 524.64 l 420 525.84 l 419.04 525.84 l f* 420.24 524.64 m 420.72 523.2 l 421.44 523.2 l 421.2 524.4 l 420.24 524.64 l f* 420.72 524.16 m 420.96 522.96 l 421.92 522.72 l 421.44 524.16 l 420.72 524.16 l f* 420.96 523.68 m 421.68 522 l 422.64 521.76 l 421.92 523.68 l 420.96 523.68 l f* 421.68 522.96 m 422.16 522 l 422.88 522 l 422.64 522.72 l 421.68 522.96 l f* 423.12 520.8 m 423.36 520.08 l 424.08 520.08 l 423.84 520.8 l 423.12 520.8 l f* 423.36 521.04 m 423.84 519.36 l 424.8 519.36 l 424.08 521.04 l 423.36 521.04 l f* 423.84 520.32 m 424.56 518.88 l 425.28 518.88 l 424.8 520.32 l 423.84 520.32 l f* 424.56 519.84 m 425.04 518.4 l 425.76 518.4 l 425.28 519.84 l 424.56 519.84 l f* 425.04 519.36 m 425.04 518.64 l 426 518.4 l 425.76 519.12 l 425.04 519.36 l f* 425.28 518.16 m 426.24 517.92 l 426.48 518.64 l 425.52 518.88 l 425.28 518.16 l f* 425.52 517.92 0.96 0.72 re f 425.76 517.92 m 426 519.12 l 426.72 518.88 l 426.48 517.92 l 425.76 517.92 l f* 426 518.16 0.72 0.96 re f 426 518.4 0.72 0.96 re f 426 518.64 0.72 0.96 re f 425.76 518.88 m 425.52 520.32 l 426.48 520.32 l 426.72 518.88 l 425.76 518.88 l f* 425.52 519.6 m 425.28 521.04 l 426 521.04 l 426.48 519.36 l 425.52 519.6 l f* 425.28 520.32 m 425.28 520.8 l 426 520.56 l 426 520.32 l 425.28 520.32 l f* 425.04 521.04 m 424.8 522.72 l 425.52 522.48 l 425.76 521.04 l 425.04 521.04 l f* 424.8 521.76 m 424.56 523.44 l 425.28 523.44 l 425.52 521.76 l 424.8 521.76 l f* 424.56 522.72 m 424.56 523.92 l 425.28 523.68 l 425.28 522.48 l 424.56 522.72 l f* 424.56 522.96 m 424.32 524.16 l 425.28 524.16 l 425.28 522.96 l 424.56 522.96 l f* 424.32 523.92 m 424.32 524.88 l 425.28 524.88 l 425.04 523.92 l 424.32 523.92 l f* 424.32 524.16 m 424.56 525.12 l 425.28 525.12 l 425.28 523.92 l 424.32 524.16 l f* 424.56 524.88 m 425.52 525.12 l 425.52 524.16 l 424.56 524.16 l 424.56 524.88 l f* 424.8 524.16 0.96 0.96 re f 424.8 525.12 m 425.04 524.16 l 425.76 524.16 l 425.76 525.12 l 424.8 525.12 l f* 425.04 525.12 m 425.28 523.92 l 426 523.92 l 425.76 525.12 l 425.04 525.12 l f* 425.28 524.88 m 425.52 523.44 l 426.24 523.44 l 426 524.88 l 425.28 524.88 l f* 425.52 524.4 m 425.76 523.2 l 426.48 522.96 l 426.24 524.4 l 425.52 524.4 l f* 425.76 523.92 m 426.24 522.48 l 426.96 522.48 l 426.48 523.92 l 425.76 523.92 l f* 426.24 523.2 0.72 0.24 re f 427.2 521.04 m 427.92 521.04 l 427.2 521.04 l f* 427.2 522 m 427.44 520.56 l 428.4 520.56 l 427.92 521.76 l 427.2 522 l f* 427.44 521.52 m 428.16 520.08 l 428.88 519.84 l 428.4 521.52 l 427.44 521.52 l f* 428.16 520.8 m 428.64 519.36 l 429.36 519.36 l 428.88 520.8 l 428.16 520.8 l f* 428.64 519.36 m 429.84 518.88 l 429.84 519.84 l 428.64 520.08 l 428.64 519.36 l f* 429.12 519.84 m 429.36 519.12 l 430.08 518.88 l 429.84 519.84 l 429.12 519.84 l f* 429.6 519.36 m 430.08 518.16 l 430.8 518.16 l 430.32 519.36 l 429.6 519.36 l f* 430.08 519.12 m 430.32 517.68 l 431.04 517.68 l 430.8 518.88 l 430.08 519.12 l f* 430.32 518.64 m 430.32 517.68 l 431.28 517.44 l 431.04 518.64 l 430.32 518.64 l f* 430.32 518.4 m 430.56 517.44 l 431.28 517.44 l 431.28 518.4 l 430.32 518.4 l f* 430.56 517.44 0.72 0.72 re f 430.8 517.44 0.72 0.96 re f 430.8 517.44 0.72 0.96 re f 430.8 517.68 0.72 0.72 re f 430.8 517.68 m 430.8 518.64 l 431.76 518.64 l 431.52 517.68 l 430.8 517.68 l f* 430.8 517.92 0.96 1.2 re f 430.8 518.4 m 430.8 518.88 l 431.52 518.88 l 431.76 518.4 l 430.8 518.4 l f* 430.8 519.12 m 430.56 520.32 l 431.28 520.32 l 431.52 519.12 l 430.8 519.12 l f* 430.56 519.6 m 430.32 521.04 l 431.04 520.8 l 431.28 519.36 l 430.56 519.6 l f* 430.32 520.08 m 430.08 521.52 l 430.8 521.52 l 431.04 520.08 l 430.32 520.08 l f* 430.08 520.8 m 429.6 522.24 l 430.56 522 l 430.8 520.8 l 430.08 520.8 l f* 428.88 523.44 m 428.64 524.4 l 429.36 524.4 l 429.6 523.44 l 428.88 523.44 l f* 428.64 523.68 0.48 0.48 re f 428.4 524.16 m 427.92 526.08 l 428.64 526.08 l 429.12 524.16 l 428.4 524.16 l f* 427.92 525.36 m 427.44 527.28 l 428.16 527.28 l 428.64 525.36 l 427.92 525.36 l f* 427.44 526.56 m 427.2 528.24 l 427.92 528 l 428.16 526.32 l 427.44 526.56 l f* 426.96 528.24 m 426.72 529.92 l 427.44 529.92 l 427.68 528.24 l 426.96 528.24 l f* 426.72 529.2 m 426.48 530.88 l 427.44 530.64 l 427.44 529.2 l 426.72 529.2 l f* 426.48 529.92 m 426.48 531.6 l 427.2 531.6 l 427.44 529.92 l 426.48 529.92 l f* 426.48 530.64 0.72 0.72 re f 426.48 531.36 m 426.48 532.32 l 427.44 532.32 l 427.2 531.36 l 426.48 531.36 l f* 426.48 531.36 m 426.72 532.56 l 427.44 532.32 l 427.44 531.36 l 426.48 531.36 l f* 426.72 532.32 m 427.68 532.56 l 427.68 531.84 l 426.72 531.6 l 426.72 532.32 l f* 426.96 532.56 m 427.92 532.56 l 428.16 531.84 l 426.96 531.84 l 426.96 532.56 l f* 427.2 531.84 1.2 0.72 re f 427.68 531.84 1.2 0.72 re f 428.16 531.84 m 429.36 531.6 l 429.36 532.32 l 428.16 532.56 l 428.16 531.84 l f* 428.64 531.6 m 429.84 531.36 l 429.84 532.08 l 428.64 532.32 l 428.64 531.6 l f* 429.12 531.36 m 430.32 531.12 l 430.32 532.08 l 429.12 532.08 l 429.12 531.36 l f* 429.6 531.12 m 430.56 531.12 l 430.56 531.84 l 429.6 532.08 l 429.6 531.12 l f* 429.84 531.12 m 430.8 530.88 l 430.8 531.6 l 429.84 531.84 l 429.84 531.12 l f* 430.08 530.88 m 431.28 530.64 l 431.28 531.36 l 430.08 531.6 l 430.08 530.88 l f* 430.56 531.36 m 430.8 530.4 l 431.52 530.4 l 431.28 531.36 l 430.56 531.36 l f* 430.8 531.36 m 430.8 530.16 l 431.52 530.16 l 431.52 531.12 l 430.8 531.36 l f* 430.8 531.12 m 430.8 530.16 l 430.8 531.12 l f* 431.04 530.4 m 430.8 531.12 l 431.76 531.12 l 431.76 530.16 l 431.04 530.4 l f* 430.8 530.4 m 430.8 531.36 l 431.52 531.36 l 431.76 530.4 l 430.8 530.4 l f* 430.8 530.64 m 430.56 531.84 l 431.52 531.84 l 431.52 530.64 l 430.8 530.64 l f* 430.56 530.88 m 430.32 532.08 l 431.28 532.08 l 431.52 530.88 l 430.56 530.88 l f* 430.32 531.36 m 430.08 532.32 l 430.8 532.32 l 431.28 531.12 l 430.32 531.36 l f* 429.36 532.8 m 428.88 534.24 l 429.6 534.24 l 430.08 532.56 l 429.36 532.8 l f* 428.88 533.28 m 428.4 534.72 l 429.12 534.72 l 429.6 533.28 l 428.88 533.28 l f* 428.4 534 m 428.16 535.2 l 428.88 535.2 l 429.12 533.76 l 428.4 534 l f* 428.88 534.96 m 427.68 535.2 l 427.92 534.48 l 428.88 534.24 l 428.88 534.96 l f* 427.92 535.68 m 426.72 535.68 l 426.96 534.96 l 428.16 534.72 l 427.92 535.68 l f* 426.48 534.96 1.2 0.72 re f 427.2 534.96 m 426.24 534.72 l 426.24 535.44 l 427.44 535.68 l 427.2 534.96 l f* 426.24 534.48 0.72 0.96 re f 426.24 535.44 m 426 534.48 l 426.96 534.24 l 426.96 535.2 l 426.24 535.44 l f* 426 534 0.96 1.2 re f 426 534.72 m 426.24 533.52 l 426.96 533.52 l 426.96 534.72 l 426 534.72 l f* 426.24 534.48 m 426.24 533.04 l 426.96 533.04 l 426.96 534.24 l 426.24 534.48 l f* 426.24 533.76 m 426.24 532.56 l 427.2 532.56 l 426.96 533.76 l 426.24 533.76 l f* 426.24 533.28 m 426.48 532.8 l 427.2 532.8 l 427.2 533.28 l 426.24 533.28 l f* 426.96 530.4 m 426.96 529.92 l 427.92 529.92 l 427.68 530.4 l 426.96 530.4 l f* 426.96 530.64 m 427.2 529.2 l 428.16 529.2 l 427.92 530.64 l 426.96 530.64 l f* 427.2 529.92 m 427.44 528.48 l 428.4 528.24 l 428.16 529.92 l 427.2 529.92 l f* 427.44 529.2 m 427.92 527.52 l 428.64 527.52 l 428.4 529.2 l 427.44 529.2 l f* 427.92 528.24 m 428.16 527.52 l 428.88 527.52 l 428.64 528.24 l 427.92 528.24 l f* 428.64 526.08 m 429.12 524.88 l 429.84 524.64 l 429.6 526.08 l 428.64 526.08 l f* 429.12 525.6 m 429.12 525.36 l 429.84 525.12 l 429.84 525.6 l 429.12 525.6 l f* 429.6 524.16 m 430.08 522.72 l 430.8 522.48 l 430.56 523.92 l 429.6 524.16 l f* 430.08 523.44 m 430.32 522.24 l 431.04 522 l 430.8 523.44 l 430.08 523.44 l f* 430.32 522.96 m 430.56 521.52 l 431.28 521.52 l 431.04 522.96 l 430.32 522.96 l f* 430.56 522.48 m 430.8 521.04 l 431.52 521.04 l 431.28 522.24 l 430.56 522.48 l f* 432 519.6 0.72 0.24 re f 432 519.6 m 433.2 519.12 l 433.2 519.84 l 432 520.32 l 432 519.6 l f* 432.48 520.08 m 432.72 518.88 l 433.44 518.88 l 433.2 520.08 l 432.48 520.08 l f* 432.48 518.88 m 433.68 518.64 l 433.68 519.6 l 432.72 519.84 l 432.48 518.88 l f* 432.96 518.64 m 433.92 518.64 l 433.92 519.36 l 432.96 519.6 l 432.96 518.64 l f* 433.2 518.64 m 433.92 518.64 l 434.16 519.36 l 433.2 519.36 l 433.2 518.64 l f* 433.68 518.88 m 433.68 519.84 l 434.4 519.84 l 434.4 518.64 l 433.68 518.88 l f* 433.68 519.12 0.96 0.96 re f 433.68 519.12 0.96 1.2 re f 433.68 519.6 0.96 1.2 re f 433.68 520.08 m 433.68 521.04 l 434.4 521.04 l 434.64 520.08 l 433.68 520.08 l f* 433.68 522 m 433.44 523.2 l 434.16 523.2 l 434.4 522 l 433.68 522 l f* 433.44 522.48 0.72 1.44 re f 433.44 523.2 m 433.2 525.12 l 434.16 525.12 l 434.16 522.96 l 433.44 523.2 l f* 433.2 524.4 m 433.2 525.12 l 433.92 525.12 l 434.16 524.16 l 433.2 524.4 l f* 432.96 526.56 0.96 0.24 re f 432.96 526.08 m 432.96 527.28 l 433.68 527.28 l 433.92 525.84 l 432.96 526.08 l f* 432.96 526.56 m 432.96 527.76 l 433.68 527.76 l 433.68 526.32 l 432.96 526.56 l f* 432.96 527.04 m 432.72 528.24 l 433.68 528.24 l 433.68 527.04 l 432.96 527.04 l f* 432.72 527.52 m 432.72 528.48 l 433.44 528.48 l 433.68 527.52 l 432.72 527.52 l f* 432.72 527.52 0.72 1.2 re f 432.72 527.76 0.72 0.96 re f 432.72 528.72 m 432.72 528 l 432.72 528.72 l f* 432.72 528 m 433.68 527.76 l 433.68 528.72 l 432.72 528.72 l 432.72 528 l f* 432.96 528.72 m 432.96 527.52 l 433.92 527.52 l 433.68 528.72 l 432.96 528.72 l f* 432.96 528.48 m 433.2 527.28 l 433.92 527.28 l 433.92 528.48 l 432.96 528.48 l f* 433.2 528.24 m 433.44 527.04 l 434.16 527.04 l 433.92 528.24 l 433.2 528.24 l f* 433.44 528 m 433.92 527.04 l 434.64 527.04 l 434.16 528 l 433.44 528 l f* 434.64 526.56 m 434.88 525.12 l 435.6 525.12 l 435.36 526.56 l 434.64 526.56 l f* 434.88 526.08 m 435.36 524.88 l 436.08 524.88 l 435.6 526.08 l 434.88 526.08 l f* 435.36 525.84 m 436.08 523.92 l 436.8 523.92 l 436.08 525.6 l 435.36 525.84 l f* 436.08 524.88 m 436.32 523.92 l 437.04 523.92 l 436.8 524.64 l 436.08 524.88 l f* 437.28 522.72 m 437.52 522.24 l 438.24 522.24 l 438.24 522.72 l 437.28 522.72 l f* 437.52 522.24 m 438.96 521.52 l 438.96 522.48 l 437.52 522.96 l 437.52 522.24 l f* 438 521.52 m 439.44 521.04 l 439.44 521.76 l 438.24 522.48 l 438 521.52 l f* 438.72 521.04 m 440.16 520.56 l 440.16 521.52 l 438.72 521.76 l 438.72 521.04 l f* 439.2 520.56 m 440.4 520.32 l 440.4 521.04 l 439.44 521.52 l 439.2 520.56 l f* 439.92 520.08 m 441.36 519.6 l 441.36 520.56 l 439.92 521.04 l 439.92 520.08 l f* 440.64 519.6 m 442.08 519.12 l 442.08 519.84 l 440.64 520.56 l 440.64 519.6 l f* 441.36 519.12 m 442.8 518.64 l 442.8 519.36 l 441.36 519.84 l 441.36 519.12 l f* 442.08 518.64 m 442.8 518.4 l 442.8 519.36 l 442.08 519.36 l 442.08 518.64 l f* 442.56 518.4 m 443.76 517.92 l 444 518.64 l 442.56 519.12 l 442.56 518.4 l f* 443.04 517.92 m 444.24 517.68 l 444.48 518.4 l 443.04 518.64 l 443.04 517.92 l f* 443.52 517.68 1.2 0.72 re f 443.76 517.68 m 444.96 517.44 l 444.96 518.16 l 444 518.4 l 443.76 517.68 l f* 444.24 517.44 0.72 0.72 re f 444.24 517.44 0.96 0.72 re f 444.24 518.16 m 445.2 518.4 l 445.44 517.44 l 444.48 517.44 l 444.24 518.16 l f* 444.48 518.4 m 445.44 518.4 l 445.44 517.68 l 444.48 517.44 l 444.48 518.4 l f* 444.72 517.68 m 444.72 518.64 l 445.68 518.4 l 445.44 517.44 l 444.72 517.68 l f* 444.72 517.68 0.96 0.72 re f 444.72 517.92 m 444.72 519.6 l 445.44 519.36 l 445.68 517.68 l 444.72 517.92 l f* 444.72 518.64 m 444.48 520.56 l 445.2 520.56 l 445.44 518.64 l 444.72 518.64 l f* 444.48 519.84 m 444.24 521.76 l 444.96 521.52 l 445.2 519.6 l 444.48 519.84 l f* 444.24 520.8 m 444.96 520.8 l 444.24 520.8 l f* 443.76 523.2 m 443.52 524.4 l 444.24 524.16 l 444.48 523.2 l 443.76 523.2 l f* 443.52 523.44 m 443.52 524.16 l 444.24 523.92 l 444.24 523.44 l 443.52 523.44 l f* 443.04 526.32 m 442.8 527.52 l 443.52 527.28 l 443.76 526.32 l 443.04 526.32 l f* 442.8 526.56 m 442.8 527.28 l 443.52 527.04 l 443.52 526.56 l 442.8 526.56 l f* 442.32 529.44 m 442.08 530.88 l 442.8 530.64 l 443.04 529.44 l 442.32 529.44 l f* 442.08 529.92 m 441.6 532.56 l 442.32 532.56 l 442.8 529.92 l 442.08 529.92 l f* 441.6 531.84 m 441.36 533.52 l 442.08 533.28 l 442.32 531.84 l 441.6 531.84 l f* 440.88 535.68 m 440.64 536.4 l 441.6 536.4 l 441.6 535.68 l 440.88 535.68 l f* 440.64 535.68 m 440.64 536.4 l 441.36 536.4 l 441.6 535.44 l 440.64 535.68 l f* 439.92 539.52 0.72 0.72 re f 439.92 539.52 0.48 0.72 re f 438.96 543.36 m 438.96 544.32 l 439.68 544.32 l 439.92 543.36 l 438.96 543.36 l f* 438.96 543.6 m 438 547.92 l 438.72 547.92 l 439.68 543.36 l 438.96 543.6 l f* 437.52 550.32 m 437.04 551.76 l 438 551.76 l 438.24 550.08 l 437.52 550.32 l f* 436.56 553.44 m 436.32 554.88 l 437.04 554.88 l 437.28 553.2 l 436.56 553.44 l f* 435.84 557.28 0.72 0.48 re f 435.84 557.04 m 435.36 559.68 l 436.08 559.44 l 436.56 557.04 l 435.84 557.04 l f* 435.36 558.72 m 434.88 561.12 l 435.6 561.12 l 436.08 558.72 l 435.36 558.72 l f* 434.4 562.8 m 434.16 564.24 l 434.88 564.24 l 435.36 562.56 l 434.4 562.8 l f* 433.68 565.92 m 433.68 567.12 l 434.4 566.88 l 434.64 565.68 l 433.68 565.92 l f* 433.68 566.16 0.72 0.48 re f 433.2 569.04 m 433.2 569.28 l 433.92 569.28 l 433.92 568.8 l 433.2 569.04 l f* 433.2 568.56 m 432.96 570.24 l 433.68 570 l 433.92 568.32 l 433.2 568.56 l f* 432.96 569.28 0.72 1.44 re f 432.96 570 0.72 1.2 re f 432.96 570.48 m 432.96 571.68 l 433.68 571.44 l 433.68 570.48 l 432.96 570.48 l f* 432.96 570.72 m 432.96 571.68 l 433.92 571.68 l 433.68 570.72 l 432.96 570.72 l f* 432.96 570.96 0.96 0.72 re f 432.96 570.96 m 432.96 572.16 l 433.68 572.16 l 433.92 570.96 l 432.96 570.96 l f* 432.96 571.44 m 432.72 572.64 l 433.68 572.4 l 433.68 571.2 l 432.96 571.44 l f* 432.72 571.68 m 432.48 573.6 l 433.2 573.36 l 433.68 571.68 l 432.72 571.68 l f* 432.48 572.64 m 432 574.08 l 432.72 574.08 l 433.2 572.64 l 432.48 572.64 l f* 431.28 574.8 m 431.04 576.48 l 431.76 576.24 l 432 574.8 l 431.28 574.8 l f* 431.04 575.52 m 430.56 576.96 l 431.28 576.96 l 431.76 575.52 l 431.04 575.52 l f* 430.56 576 m 429.6 578.4 l 430.32 578.16 l 431.28 576 l 430.56 576 l f* 428.88 579.6 m 428.64 579.6 l 429.6 579.6 l 429.6 579.36 l 428.88 579.6 l f* 428.64 578.88 m 428.4 580.08 l 429.12 580.08 l 429.6 578.64 l 428.64 578.88 l f* 427.92 579.6 m 427.44 581.04 l 428.16 581.04 l 428.64 579.6 l 427.92 579.6 l f* 428.16 580.8 m 426.96 581.28 l 426.96 580.32 l 428.16 580.08 l 428.16 580.8 l f* 427.68 581.28 m 426.48 581.28 l 426.72 580.56 l 427.92 580.32 l 427.68 581.28 l f* 426.24 580.56 1.2 0.72 re f 426.96 580.56 m 426 580.32 l 426.24 581.28 l 427.2 581.28 l 426.96 580.56 l f* 426.24 581.28 m 426 580.08 l 426.72 580.08 l 426.96 581.28 l 426.24 581.28 l f* 426 581.04 m 425.76 580.08 l 426.48 579.84 l 426.72 581.04 l 426 581.04 l f* 425.76 579.84 0.72 0.96 re f 425.76 580.8 m 425.52 579.6 l 426.24 579.36 l 426.48 580.56 l 425.76 580.8 l f* 425.28 578.4 0.72 0.24 re f 425.28 579.12 m 425.52 577.68 l 426.24 577.68 l 426 579.12 l 425.28 579.12 l f* 425.52 576.96 0.96 1.68 re f 425.52 577.68 m 425.76 576.24 l 426.72 576 l 426.48 577.68 l 425.52 577.68 l f* 425.76 576.96 m 426 576 l 426.72 576 l 426.72 576.96 l 425.76 576.96 l f* 426.72 573.36 0.72 0.48 re f 426.72 574.08 m 426.96 573.12 l 427.68 573.12 l 427.44 574.08 l 426.72 574.08 l f* 427.44 572.4 m 428.16 569.76 l 428.88 569.76 l 428.16 572.16 l 427.44 572.4 l f* 428.16 570.72 m 428.88 568.32 l 429.6 568.08 l 428.88 570.48 l 428.16 570.72 l f* 428.88 568.56 0.72 0.48 re f 429.84 566.4 m 430.32 564.96 l 431.28 564.72 l 430.56 566.4 l 429.84 566.4 l f* 430.32 565.92 m 430.8 564.24 l 431.52 564 l 431.28 565.68 l 430.32 565.92 l f* 430.8 564.96 m 431.28 563.28 l 432.24 563.28 l 431.52 564.96 l 430.8 564.96 l f* 431.28 564.24 m 432 562.32 l 432.96 562.32 l 432.24 564.24 l 431.28 564.24 l f* 432.96 561.12 m 433.44 560.16 l 434.16 559.92 l 433.92 561.12 l 432.96 561.12 l f* 433.44 560.88 m 433.44 560.64 l 434.16 560.4 l 434.16 560.88 l 433.44 560.88 l f* 434.16 559.68 m 434.64 558.24 l 435.36 558.24 l 434.88 559.68 l 434.16 559.68 l f* 434.64 559.2 m 434.88 558 l 435.6 558 l 435.36 559.2 l 434.64 559.2 l f* 434.88 558.96 m 435.36 557.28 l 436.08 557.28 l 435.6 558.72 l 434.88 558.96 l f* 435.36 558.24 m 435.6 557.04 l 436.32 557.04 l 436.08 558.24 l 435.36 558.24 l f* 436.08 557.28 m 436.56 556.08 l 437.28 556.08 l 436.8 557.28 l 436.08 557.28 l f* 436.32 556.08 m 437.76 555.84 l 437.76 556.56 l 436.56 556.8 l 436.32 556.08 l f* 436.8 555.84 m 438 555.6 l 438 556.32 l 437.04 556.56 l 436.8 555.84 l f* 437.28 555.6 m 438 555.6 l 438.24 556.32 l 437.28 556.32 l 437.28 555.6 l f* 437.28 555.6 0.96 0.72 re f 437.52 555.6 0.72 0.72 re f 437.52 555.6 0.72 0.96 re f 437.52 555.84 m 437.28 556.8 l 438.24 556.8 l 438.24 555.84 l 437.52 555.84 l f* 437.28 556.08 m 437.28 557.04 l 438 557.04 l 438.24 556.08 l 437.28 556.08 l f* 437.28 556.32 m 437.04 557.28 l 438 557.28 l 438 556.32 l 437.28 556.32 l f* 437.04 556.56 m 437.04 557.28 l 437.76 557.04 l 438 556.56 l 437.04 556.56 l f* 437.04 556.8 0.72 0.96 re f 437.04 556.8 0.72 0.96 re f 437.04 556.56 0.72 0.96 re f 437.04 556.32 0.72 0.96 re f 437.04 555.84 0.72 1.44 re f 437.04 556.8 m 437.04 556.32 l 437.76 556.08 l 437.76 556.56 l 437.04 556.8 l f* 437.04 556.32 m 437.28 555.12 l 438 554.88 l 438 556.08 l 437.04 556.32 l f* 437.28 555.84 m 437.52 554.64 l 438.24 554.64 l 438 555.84 l 437.28 555.84 l f* 437.52 555.36 m 437.76 553.68 l 438.72 553.68 l 438.24 555.36 l 437.52 555.36 l f* 437.76 554.4 m 438.24 553.2 l 438.96 553.2 l 438.72 554.4 l 437.76 554.4 l f* 438.96 552.48 m 439.2 550.8 l 439.92 550.8 l 439.68 552.24 l 438.96 552.48 l f* 439.2 551.76 m 439.44 550.32 l 440.4 550.32 l 439.92 551.76 l 439.2 551.76 l f* 439.44 551.04 m 440.16 549.12 l 440.88 548.88 l 440.4 551.04 l 439.44 551.04 l f* 440.16 549.84 m 440.4 549.36 l 441.12 549.36 l 440.88 549.84 l 440.16 549.84 l f* 441.12 547.44 m 441.36 546.96 l 442.08 546.96 l 442.08 547.44 l 441.12 547.44 l f* 441.36 547.92 m 441.6 546.72 l 442.32 546.72 l 442.08 547.92 l 441.36 547.92 l f* 441.6 547.44 m 442.32 545.28 l 443.04 545.28 l 442.32 547.2 l 441.6 547.44 l f* 442.32 546.24 m 443.04 544.56 l 443.76 544.32 l 443.04 546.24 l 442.32 546.24 l f* 443.04 545.28 m 443.76 544.08 l 444.48 544.08 l 443.76 545.28 l 443.04 545.28 l f* 444.48 542.88 m 445.92 542.4 l 446.16 543.12 l 444.48 543.84 l 444.48 542.88 l f* 445.2 542.4 m 446.88 541.92 l 446.88 542.64 l 445.2 543.12 l 445.2 542.4 l f* 446.16 541.92 m 447.6 541.44 l 447.6 542.4 l 446.16 542.64 l 446.16 541.92 l f* 446.88 541.44 m 447.36 541.44 l 447.6 542.16 l 446.88 542.4 l 446.88 541.44 l f* 447.36 541.2 m 448.32 541.2 l 448.56 541.92 l 447.6 541.92 l 447.36 541.2 l f* 447.6 541.92 m 448.56 541.92 l 448.8 541.2 l 447.6 541.2 l 447.6 541.92 l f* 447.84 541.92 m 449.04 542.16 l 449.04 541.44 l 447.84 541.2 l 447.84 541.92 l f* 448.32 542.16 m 449.28 542.4 l 449.28 541.68 l 448.32 541.44 l 448.32 542.16 l f* 448.56 541.68 m 448.56 542.64 l 449.52 542.64 l 449.28 541.68 l 448.56 541.68 l f* 448.56 541.92 m 448.8 542.88 l 449.52 542.88 l 449.52 541.92 l 448.56 541.92 l f* 448.8 542.16 0.72 0.96 re f 448.8 542.4 m 448.56 543.6 l 449.52 543.6 l 449.52 542.4 l 448.8 542.4 l f* 448.56 542.88 m 448.56 544.08 l 449.28 544.08 l 449.52 542.88 l 448.56 542.88 l f* 448.56 543.36 m 448.32 544.56 l 449.28 544.56 l 449.28 543.36 l 448.56 543.36 l f* 448.32 543.84 m 448.08 545.04 l 448.8 545.04 l 449.28 543.6 l 448.32 543.84 l f* 448.08 544.32 m 447.84 545.76 l 448.56 545.76 l 448.8 544.32 l 448.08 544.32 l f* 447.84 545.04 m 447.6 546.24 l 448.32 546.24 l 448.56 544.8 l 447.84 545.04 l f* 447.6 545.52 0.72 0.24 re f 446.88 547.2 m 446.88 547.92 l 447.6 547.68 l 447.84 547.2 l 446.88 547.2 l f* 446.88 547.2 m 446.88 547.92 l 447.6 547.92 l 447.6 546.96 l 446.88 547.2 l f* 446.88 547.2 m 447.6 547.2 l 446.88 547.2 l f* 446.88 547.2 m 446.64 548.16 l 447.6 548.16 l 447.6 547.2 l 446.88 547.2 l f* 446.64 548.16 m 446.64 547.2 l 447.36 547.2 l 447.6 548.16 l 446.64 548.16 l f* 446.64 547.2 0.72 0.96 re f 446.64 546.96 0.72 0.96 re f 446.64 547.68 m 446.88 546.48 l 447.6 546.48 l 447.36 547.68 l 446.64 547.68 l f* 446.88 546.96 0.72 0.24 re f 446.88 546.72 m 447.12 545.52 l 447.84 545.28 l 447.84 546.48 l 446.88 546.72 l f* 447.12 546.24 m 447.36 545.04 l 448.08 545.04 l 447.84 546.24 l 447.12 546.24 l f* 447.36 546 m 447.84 544.08 l 448.8 544.08 l 448.08 545.76 l 447.36 546 l f* 447.84 545.04 m 448.32 543.84 l 449.04 543.84 l 448.8 544.8 l 447.84 545.04 l f* 449.28 542.88 m 450 541.2 l 450.72 541.2 l 450 542.88 l 449.28 542.88 l f* 450 542.16 m 450.72 540.24 l 451.44 540.24 l 450.72 541.92 l 450 542.16 l f* 450.72 541.2 m 451.2 539.76 l 452.16 539.76 l 451.44 541.2 l 450.72 541.2 l f* 452.16 539.52 m 452.88 538.08 l 453.6 537.84 l 452.88 539.52 l 452.16 539.52 l f* 452.88 538.8 m 453.36 537.36 l 454.08 537.12 l 453.6 538.8 l 452.88 538.8 l f* 453.36 538.32 m 453.6 536.88 l 454.32 536.88 l 454.08 538.08 l 453.36 538.32 l f* 453.6 536.88 m 454.32 536.88 l 454.56 537.6 l 453.6 537.84 l 453.6 536.88 l f* 454.32 537.36 m 455.04 537.36 l 455.28 536.64 l 454.32 536.4 l 454.32 537.36 l f* 454.32 536.64 0.96 0.72 re f 454.56 536.64 m 454.8 537.84 l 455.52 537.6 l 455.28 536.64 l 454.56 536.64 l f* 454.8 536.88 0.72 0.96 re f 454.8 537.12 m 454.8 538.32 l 455.76 538.08 l 455.52 537.12 l 454.8 537.12 l f* 454.8 537.36 0.96 0.48 re f 455.04 538.56 m 454.8 539.76 l 455.76 539.76 l 455.76 538.56 l 455.04 538.56 l f* 454.8 539.04 m 454.8 540.48 l 455.52 540.48 l 455.76 539.04 l 454.8 539.04 l f* 454.8 539.76 m 454.56 541.2 l 455.28 540.96 l 455.52 539.52 l 454.8 539.76 l f* 454.56 540.24 m 454.32 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362.88 m 373.44 365.04 l 374.16 364.8 l 373.68 362.64 l 372.96 362.88 l f* 373.44 364.08 m 373.92 369.12 l 374.64 369.12 l 374.16 364.08 l 373.44 364.08 l f* 373.92 368.4 m 373.92 373.92 l 374.88 373.68 l 374.64 368.4 l 373.92 368.4 l f* 373.92 376.8 0.96 0.72 re f 373.92 376.8 m 373.92 382.32 l 374.64 382.32 l 374.88 376.8 l 373.92 376.8 l f* 373.68 385.44 m 373.68 386.88 l 374.4 386.88 l 374.4 385.2 l 373.68 385.44 l f* 373.68 386.64 m 372.96 392.16 l 373.92 391.92 l 374.4 386.64 l 373.68 386.64 l f* 372.72 395.28 m 372.72 396.72 l 373.44 396.72 l 373.44 395.04 l 372.72 395.28 l f* 372.48 396.24 m 371.76 401.76 l 372.48 401.76 l 373.44 396.24 l 372.48 396.24 l f* 371.52 401.76 m 370.32 405.36 l 371.04 405.36 l 372.24 401.76 l 371.52 401.76 l f* 370.32 405.36 m 369.84 403.2 l 370.56 402.96 l 371.04 405.36 l 370.32 405.36 l f* 369.84 398.4 0.72 5.52 re f 370.08 394.56 0.72 0.72 re f 370.08 395.52 m 370.8 390 l 371.52 390 l 370.8 395.52 l 370.08 395.52 l f* 371.04 387.12 m 371.28 385.44 l 372.24 385.44 l 372 386.88 l 371.04 387.12 l f* 371.76 382.32 m 372.48 382.32 l 371.76 382.32 l f* 371.76 383.04 m 372.48 377.76 l 373.44 377.52 l 372.48 383.04 l 371.76 383.04 l f* 372.96 374.64 m 373.2 372.96 l 373.92 372.96 l 373.68 374.4 l 372.96 374.64 l f* 373.68 369.84 m 373.92 368.4 l 374.64 368.4 l 374.4 369.84 l 373.68 369.84 l f* 374.16 366.48 m 375.12 361.2 l 375.84 360.96 l 375.12 366.48 l 374.16 366.48 l f* 375.6 358.08 m 375.84 356.4 l 376.8 356.4 l 376.32 358.08 l 375.6 358.08 l f* 376.32 353.28 m 376.8 351.84 l 377.52 351.84 l 377.28 353.28 l 376.32 353.28 l f* 377.04 351.12 m 377.76 345.84 l 378.48 345.84 l 377.76 351.12 l 377.04 351.12 l f* 378.24 342.72 m 378.48 341.28 l 379.2 341.28 l 378.96 342.72 l 378.24 342.72 l f* 378.96 337.92 0.72 0.24 re f 378.96 338.88 m 379.44 333.36 l 380.4 333.36 l 379.68 338.64 l 378.96 338.88 l f* 379.92 330.24 m 379.92 328.56 l 380.88 328.56 l 380.64 330.24 l 379.92 330.24 l f* 380.16 323.52 0.72 5.52 re f 380.16 322.08 m 379.44 318.48 l 380.16 318.48 l 380.88 322.08 l 380.16 322.08 l f* 379.44 318.48 m 378.24 320.64 l 379.2 320.4 l 380.4 318.24 l 379.44 318.48 l f* 378.24 319.68 m 377.52 324.72 l 378.24 324.48 l 379.2 319.68 l 378.24 319.68 l f* 377.52 324 m 377.28 329.28 l 378 329.28 l 378.24 323.76 l 377.52 324 l f* 377.28 329.52 m 377.52 334.8 l 378.24 334.8 l 378 329.28 l 377.28 329.52 l f* 377.52 336.48 m 377.76 342 l 378.48 342 l 378.24 336.48 l 377.52 336.48 l f* 378 345.12 0.72 1.44 re f 378 346.32 m 378.48 351.84 l 379.44 351.84 l 378.72 346.32 l 378 346.32 l f* 378.72 354.96 m 378.96 356.4 l 379.68 356.4 l 379.68 354.96 l 378.72 354.96 l f* 378.96 356.16 m 378.96 361.68 l 379.68 361.68 l 379.92 356.16 l 378.96 356.16 l f* 378.96 364.8 0.72 1.44 re f 378.96 366 m 379.2 371.04 l 379.92 371.04 l 379.68 366 l 378.96 366 l f* 379.2 370.32 m 378.96 372.48 l 379.68 372.24 l 379.92 370.32 l 379.2 370.32 l f* 378.96 368.88 0.72 3.36 re f 378.96 369.6 m 379.44 364.8 l 380.16 364.56 l 379.68 369.6 l 378.96 369.6 l f* 379.44 365.52 m 380.16 360 l 381.12 360 l 380.16 365.52 l 379.44 365.52 l f* 380.4 360 m 381.6 357.84 l 382.32 357.6 l 381.12 360 l 380.4 360 l f* 381.6 357.84 m 382.32 362.88 l 383.28 362.88 l 382.32 357.84 l 381.6 357.84 l f* 382.32 362.16 m 383.28 367.44 l 384 367.44 l 383.28 362.16 l 382.32 362.16 l f* 383.52 367.92 m 383.76 372.72 l 384.48 372.72 l 384.24 367.68 l 383.52 367.92 l f* 383.76 372.72 m 384 369.36 l 384.72 369.12 l 384.48 372.72 l 383.76 372.72 l f* 384 370.08 m 384.48 365.04 l 385.2 365.04 l 384.72 369.84 l 384 370.08 l f* 384.48 365.76 m 385.68 360.72 l 386.64 360.48 l 385.2 365.76 l 384.48 365.76 l f* 385.92 360.48 m 387.12 358.32 l 388.08 358.08 l 386.88 360.48 l 385.92 360.48 l f* 387.12 358.32 m 388.08 360.72 l 388.8 360.48 l 388.08 358.08 l 387.12 358.32 l f* 388.08 359.76 m 388.32 365.28 l 389.28 365.28 l 388.8 359.76 l 388.08 359.76 l f* 388.56 366.96 0.96 5.28 re f 388.56 375.36 m 388.8 377.04 l 389.52 376.8 l 389.52 375.36 l 388.56 375.36 l f* 388.8 378 m 388.32 383.52 l 389.04 383.52 l 389.52 378 l 388.8 378 l f* 388.08 386.64 0.72 1.44 re f 387.84 389.28 m 387.36 394.56 l 388.08 394.56 l 388.56 389.04 l 387.84 389.28 l f* 387.12 396.24 m 386.64 398.4 l 387.36 398.16 l 387.84 396 l 387.12 396.24 l f* 386.64 398.4 m 386.16 394.56 l 386.88 394.56 l 387.36 398.16 l 386.64 398.4 l f* 386.16 395.52 m 386.4 390 l 387.12 390 l 386.88 395.28 l 386.16 395.52 l f* 386.64 385.2 0.72 1.68 re f 386.64 385.68 m 387.12 380.16 l 388.08 380.16 l 387.36 385.68 l 386.64 385.68 l f* 387.6 377.04 m 387.6 375.6 l 388.32 375.36 l 388.32 377.04 l 387.6 377.04 l f* 387.84 374.64 m 388.8 369.12 l 389.52 369.12 l 388.56 374.4 l 387.84 374.64 l f* 389.28 366.24 m 389.52 365.52 l 390.24 365.52 l 390 366 l 389.28 366.24 l f* 389.52 366.24 m 390.96 361.44 l 391.68 361.44 l 390.24 366.24 l 389.52 366.24 l f* 390.96 361.44 m 392.16 365.04 l 393.12 365.04 l 391.68 361.44 l 390.96 361.44 l f* 392.16 364.32 m 392.64 369.84 l 393.36 369.6 l 393.12 364.32 l 392.16 364.32 l f* 392.88 371.28 m 393.12 376.8 l 393.84 376.8 l 393.6 371.28 l 392.88 371.28 l f* 393.12 377.76 m 393.6 372.96 l 394.56 372.72 l 394.08 377.76 l 393.12 377.76 l f* 393.6 373.68 m 394.32 368.16 l 395.04 368.16 l 394.56 373.68 l 393.6 373.68 l f* 394.32 368.16 m 395.52 363.12 l 396.24 363.12 l 395.04 367.92 l 394.32 368.16 l f* 395.52 364.08 m 396.48 359.04 l 397.44 359.04 l 396.24 363.84 l 395.52 364.08 l f* 396.48 359.04 m 396 364.56 l 396.72 364.56 l 397.44 359.04 l 396.48 359.04 l f* 395.76 367.68 m 395.52 369.12 l 396.48 369.12 l 396.48 367.68 l 395.76 367.68 l f* 395.28 372.24 m 395.04 373.68 l 396 373.68 l 396.24 372.24 l 395.28 372.24 l f* 394.8 376.8 m 394.32 382.32 l 395.04 382.32 l 395.76 376.8 l 394.8 376.8 l f* 394.08 384 m 392.64 389.04 l 393.36 388.8 l 394.8 384 l 394.08 384 l f* 392.4 388.08 0.96 0.72 re f 392.4 389.04 m 393.36 383.52 l 394.08 383.52 l 393.12 388.8 l 392.4 389.04 l f* 393.84 380.64 m 394.08 378.96 l 394.8 378.96 l 394.56 380.4 l 393.84 380.64 l f* 394.56 375.84 m 395.04 374.4 l 395.76 374.4 l 395.52 375.84 l 394.56 375.84 l f* 395.52 371.28 m 396.48 366 l 397.2 366 l 396.24 371.28 l 395.52 371.28 l f* 396.48 366.96 m 397.2 361.92 l 397.92 361.92 l 397.2 366.72 l 396.48 366.96 l f* 397.2 362.88 m 398.16 360.48 l 398.88 360.48 l 397.92 362.64 l 397.2 362.88 l f* 398.16 361.44 m 399.12 359.28 l 400.08 359.04 l 398.88 361.44 l 398.16 361.44 l f* 399.12 359.28 m 399.6 362.88 l 400.32 362.88 l 400.08 359.28 l 399.12 359.28 l f* 399.6 362.16 m 399.84 367.68 l 400.56 367.44 l 400.32 362.16 l 399.6 362.16 l f* 399.84 367.68 m 400.08 373.2 l 400.8 373.2 l 400.8 367.68 l 399.84 367.68 l f* 400.08 373.44 m 400.56 378.48 l 401.28 378.24 l 400.8 373.44 l 400.08 373.44 l f* 400.56 377.52 m 401.52 379.92 l 402.24 379.92 l 401.28 377.52 l 400.56 377.52 l f* 401.52 379.92 m 402.72 376.32 l 403.44 376.32 l 402.24 379.92 l 401.52 379.92 l f* 402.72 377.04 m 403.68 373.68 l 404.4 373.68 l 403.44 377.04 l 402.72 377.04 l f* 403.68 374.4 m 403.92 372.24 l 404.64 372.24 l 404.4 374.4 l 403.68 374.4 l f* 403.92 372.24 m 402.96 375.84 l 403.68 375.84 l 404.64 372.24 l 403.92 372.24 l f* 403.68 375.84 m 401.28 377.04 l 401.28 376.08 l 403.68 374.88 l 403.68 375.84 l f* 401.28 377.04 m 399.84 374.64 l 400.8 374.64 l 402.24 377.04 l 401.28 377.04 l f* 399.84 375.6 m 399.84 370.08 l 400.56 370.08 l 400.56 375.36 l 399.84 375.6 l f* 399.84 369.84 m 400.08 364.56 l 400.8 364.56 l 400.56 369.84 l 399.84 369.84 l f* 400.08 364.32 m 401.28 359.52 l 402 359.28 l 400.8 364.32 l 400.08 364.32 l f* 401.28 360.24 m 403.68 360.24 l 403.68 359.52 l 401.28 359.28 l 401.28 360.24 l f* 402.96 359.52 m 403.92 364.8 l 404.88 364.8 l 403.68 359.52 l 402.96 359.52 l f* 404.4 365.28 m 405.6 370.32 l 406.32 370.32 l 405.12 365.28 l 404.4 365.28 l f* 405.6 369.6 m 406.08 371.76 l 406.8 371.76 l 406.32 369.6 l 405.6 369.6 l f* 406.08 371.76 m 406.8 368.4 l 407.52 368.16 l 406.8 371.76 l 406.08 371.76 l f* 406.8 369.12 m 407.52 364.08 l 408.24 364.08 l 407.52 369.12 l 406.8 369.12 l f* 407.52 365.04 m 408.48 360 l 409.44 360 l 408.24 364.8 l 407.52 365.04 l f* 408.48 360.72 m 409.92 360.72 l 410.16 360 l 408.48 360 l 408.48 360.72 l f* 409.2 360 m 409.68 362.4 l 410.64 362.16 l 410.16 360 l 409.2 360 l f* 409.68 361.44 m 410.4 366.48 l 411.12 366.48 l 410.64 361.44 l 409.68 361.44 l f* 410.4 365.76 m 410.88 370.8 l 411.6 370.8 l 411.12 365.76 l 410.4 365.76 l f* 410.88 369.84 m 411.6 372.24 l 412.56 372.24 l 411.6 369.84 l 410.88 369.84 l f* 411.6 372.24 m 412.56 368.88 l 413.52 368.64 l 412.56 372.24 l 411.6 372.24 l f* 412.56 369.6 m 413.76 364.8 l 414.48 364.56 l 413.52 369.6 l 412.56 369.6 l f* 413.76 365.52 m 414.72 361.92 l 415.44 361.92 l 414.48 365.52 l 413.76 365.52 l f* 414.72 362.64 m 416.16 362.88 l 416.16 361.92 l 414.72 361.92 l 414.72 362.64 l f* 415.44 362.16 m 415.92 365.52 l 416.64 365.52 l 416.16 361.92 l 415.44 362.16 l f* 415.92 364.8 m 416.64 368.4 l 417.36 368.4 l 416.64 364.8 l 415.92 364.8 l f* 416.4 368.4 m 417.84 368.4 l 417.84 367.68 l 416.64 367.68 l 416.4 368.4 l f* 417.12 368.64 m 417.84 363.6 l 418.8 363.6 l 417.84 368.4 l 417.12 368.64 l f* 417.84 364.32 m 419.04 360.96 l 419.76 360.72 l 418.8 364.32 l 417.84 364.32 l f* 419.04 361.68 m 419.52 359.52 l 420.24 359.52 l 419.76 361.68 l 419.04 361.68 l f* 419.52 359.52 m 420.24 361.92 l 420.96 361.68 l 420.24 359.28 l 419.52 359.52 l f* 420.24 360.96 m 420.24 366.48 l 421.2 366.48 l 420.96 360.96 l 420.24 360.96 l f* 420.24 366.72 m 420.96 371.76 l 421.68 371.52 l 421.2 366.48 l 420.24 366.72 l f* 420.96 370.8 m 421.92 374.64 l 422.64 374.4 l 421.68 370.8 l 420.96 370.8 l f* 421.92 374.4 m 424.08 374.64 l 424.08 373.68 l 421.92 373.68 l 421.92 374.4 l f* 423.12 373.68 m 425.52 372.48 l 425.52 373.44 l 423.36 374.64 l 423.12 373.68 l f* 424.8 373.44 m 425.52 371.28 l 426.24 371.04 l 425.52 373.44 l 424.8 373.44 l f* 425.52 371.28 m 425.28 374.88 l 426 374.64 l 426.24 371.28 l 425.52 371.28 l f* 425.28 374.16 m 424.32 377.52 l 425.04 377.52 l 426 373.92 l 425.28 374.16 l f* 425.04 376.8 m 422.88 376.56 l 422.88 377.28 l 425.04 377.52 l 425.04 376.8 l f* 422.88 377.52 m 421.68 372.24 l 422.4 372.24 l 423.6 377.28 l 422.88 377.52 l f* 421.68 373.2 m 421.44 367.68 l 422.16 367.68 l 422.4 372.96 l 421.68 373.2 l f* 421.2 366 m 421.68 361.2 l 422.4 361.2 l 421.92 366 l 421.2 366 l f* 421.68 361.92 m 422.64 359.76 l 423.6 359.76 l 422.4 361.92 l 421.68 361.92 l f* 422.64 359.76 m 424.08 363.6 l 424.8 363.36 l 423.6 359.76 l 422.64 359.76 l f* 424.08 362.88 m 425.76 367.92 l 426.48 367.68 l 424.8 362.64 l 424.08 362.88 l f* 425.76 366.96 m 426.24 369.36 l 426.96 369.36 l 426.48 366.96 l 425.76 366.96 l f* 426.24 369.36 m 426.72 365.76 l 427.68 365.76 l 426.96 369.36 l 426.24 369.36 l f* 426.72 366.48 m 427.92 361.68 l 428.64 361.68 l 427.68 366.48 l 426.72 366.48 l f* 427.92 362.4 m 429.36 359.04 l 430.08 358.8 l 428.64 362.4 l 427.92 362.4 l f* 429.36 359.76 m 430.8 356.16 l 431.76 356.16 l 430.08 359.76 l 429.36 359.76 l f* 430.8 357.12 m 432 354.96 l 432.96 354.96 l 431.76 357.12 l 430.8 357.12 l f* 432 354.96 1.44 0.72 re f 432.72 354.96 m 433.92 360.48 l 434.88 360.24 l 433.44 354.96 l 432.72 354.96 l f* 434.64 363.36 m 435.12 364.8 l 435.84 364.8 l 435.6 363.36 l 434.64 363.36 l f* 435.84 367.92 m 436.08 369.36 l 437.04 369.36 l 436.56 367.92 l 435.84 367.92 l f* 436.8 372.48 m 438.24 377.76 l 438.96 377.76 l 437.76 372.48 l 436.8 372.48 l f* 438.96 380.88 m 439.2 382.32 l 440.16 382.32 l 439.68 380.64 l 438.96 380.88 l f* 439.92 385.2 m 440.4 386.88 l 441.12 386.88 l 440.64 385.2 l 439.92 385.2 l f* 441.12 389.76 m 442.32 395.28 l 443.04 395.04 l 441.84 389.76 l 441.12 389.76 l f* 443.04 398.16 m 443.52 399.6 l 444.24 399.6 l 443.76 398.16 l 443.04 398.16 l f* 444.24 402.72 m 444.48 404.16 l 445.2 404.16 l 444.96 402.72 l 444.24 402.72 l f* 445.2 406.56 m 446.16 408.72 l 446.88 408.72 l 445.92 406.32 l 445.2 406.56 l f* 446.16 408 m 446.4 413.04 l 447.12 413.04 l 446.88 407.76 l 446.16 408 l f* 446.4 412.32 m 445.44 417.6 l 446.16 417.6 l 447.12 412.08 l 446.4 412.32 l f* 445.44 417.6 m 444.24 419.76 l 444.96 419.76 l 446.16 417.6 l 445.44 417.6 l f* 444.96 418.8 m 442.32 417.36 l 442.32 418.08 l 444.96 419.76 l 444.96 418.8 l f* 442.32 418.32 m 441.6 412.8 l 442.32 412.8 l 443.04 418.08 l 442.32 418.32 l f* 441.12 411.12 m 440.88 405.6 l 441.84 405.6 l 441.84 411.12 l 441.12 411.12 l f* 440.88 404.16 m 441.36 398.64 l 442.08 398.64 l 441.6 404.16 l 440.88 404.16 l f* 441.6 397.2 m 442.32 393.6 l 443.04 393.6 l 442.32 397.2 l 441.6 397.2 l f* 442.32 394.56 m 443.04 392.16 l 443.76 392.16 l 443.04 394.56 l 442.32 394.56 l f* 443.04 392.4 m 443.28 394.56 l 444 394.56 l 443.76 392.16 l 443.04 392.4 l f* 443.28 394.56 m 442.8 392.4 l 443.52 392.16 l 444 394.56 l 443.28 394.56 l f* 442.8 393.12 m 442.56 388.08 l 443.28 388.08 l 443.52 393.12 l 442.8 393.12 l f* 442.56 388.8 m 442.8 383.28 l 443.52 383.28 l 443.28 388.8 l 442.56 388.8 l f* 442.8 383.28 m 444 378.48 l 444.72 378.24 l 443.52 383.28 l 442.8 383.28 l f* 444 379.2 m 445.92 375.6 l 446.88 375.6 l 444.72 379.2 l 444 379.2 l f* 445.92 376.56 m 448.08 376.56 l 448.08 375.84 l 445.92 375.6 l 445.92 376.56 l f* 447.36 375.84 m 447.84 378 l 448.56 378 l 448.08 375.84 l 447.36 375.84 l f* 447.84 377.28 m 448.08 382.32 l 448.8 382.32 l 448.56 377.28 l 447.84 377.28 l f* 448.08 382.32 m 447.6 380.16 l 448.32 379.92 l 448.8 382.32 l 448.08 382.32 l f* 447.6 380.88 m 447.84 375.84 l 448.8 375.84 l 448.32 380.88 l 447.6 380.88 l f* 447.84 376.8 m 449.04 371.76 l 450 371.76 l 448.8 376.56 l 447.84 376.8 l f* 449.04 372.48 m 450 369.12 l 450.96 368.88 l 450 372.48 l 449.04 372.48 l f* 450 368.88 m 451.68 371.52 l 452.4 371.28 l 450.96 368.88 l 450 368.88 l f* 451.68 370.56 m 452.4 376.08 l 453.12 375.84 l 452.4 370.56 l 451.68 370.56 l f* 452.64 376.32 m 452.88 381.84 l 453.6 381.6 l 453.36 376.32 l 452.64 376.32 l f* 452.88 381.84 m 453.12 384 l 454.08 384 l 453.84 381.84 l 452.88 381.84 l f* 453.12 384 m 453.36 379.2 l 454.08 379.2 l 454.08 384 l 453.12 384 l f* 453.36 379.92 m 454.08 374.64 l 455.04 374.4 l 454.08 379.92 l 453.36 379.92 l f* 454.32 374.4 m 456 370.8 l 456.72 370.8 l 455.04 374.4 l 454.32 374.4 l f* 455.76 371.76 m 458.4 371.76 l 458.4 371.04 l 456 370.8 l 455.76 371.76 l f* 457.68 371.04 m 459.12 376.08 l 459.84 376.08 l 458.4 371.04 l 457.68 371.04 l f* 459.12 375.36 m 459.36 380.88 l 460.32 380.88 l 459.84 375.36 l 459.12 375.36 l f* 459.6 381.12 m 459.12 385.92 l 459.84 385.92 l 460.32 380.88 l 459.6 381.12 l f* 459.12 385.2 m 458.88 387.36 l 459.6 387.36 l 459.84 385.2 l 459.12 385.2 l f* 458.88 383.76 0.72 3.6 re f 458.88 384.72 m 459.36 379.2 l 460.08 379.2 l 459.6 384.48 l 458.88 384.72 l f* 459.6 377.52 m 460.56 372.24 l 461.28 372.24 l 460.56 377.52 l 459.6 377.52 l f* 461.04 369.12 m 461.28 367.68 l 462 367.68 l 461.76 369.12 l 461.04 369.12 l f* 461.52 366.48 m 462.48 361.2 l 463.2 361.2 l 462.24 366.48 l 461.52 366.48 l f* 462.96 358.08 m 463.2 356.64 l 464.16 356.64 l 463.92 358.08 l 462.96 358.08 l f* 463.92 353.52 m 464.16 352.08 l 464.88 351.84 l 464.64 353.52 l 463.92 353.52 l f* 464.16 352.8 m 464.88 347.52 l 465.6 347.28 l 464.88 352.8 l 464.16 352.8 l f* 465.36 344.4 m 465.6 342.72 l 466.32 342.72 l 466.32 344.16 l 465.36 344.4 l f* 466.08 339.6 m 467.04 339.6 l 466.08 339.6 l f* 466.08 340.32 m 466.8 335.04 l 467.52 334.8 l 467.04 340.32 l 466.08 340.32 l f* 467.28 331.2 0.96 0.72 re f 467.28 332.16 m 467.76 327.12 l 468.72 327.12 l 468.24 331.92 l 467.28 332.16 l f* 467.76 328.08 m 467.04 325.68 l 467.76 325.44 l 468.72 327.84 l 467.76 328.08 l f* 467.76 325.68 m 466.32 325.44 l 466.32 326.16 l 467.76 326.4 l 467.76 325.68 l f* 466.32 325.68 m 465.36 329.04 l 466.08 329.04 l 467.04 325.44 l 466.32 325.68 l f* 465.36 328.32 m 464.64 331.68 l 465.6 331.68 l 466.08 328.32 l 465.36 328.32 l f* 464.64 330.96 m 464.4 336.48 l 465.12 336.48 l 465.6 330.96 l 464.64 330.96 l f* 464.16 337.92 m 464.16 343.44 l 464.88 343.44 l 465.12 337.92 l 464.16 337.92 l f* 463.92 346.56 m 463.92 348 l 464.64 348 l 464.88 346.56 l 463.92 346.56 l f* 463.92 351.12 0.72 0.24 re f 463.92 350.64 m 463.92 355.92 l 464.64 355.92 l 464.64 350.4 l 463.92 350.64 l f* 463.92 359.04 m 463.92 360.72 l 464.88 360.72 l 464.64 359.04 l 463.92 359.04 l f* 463.92 361.68 m 464.16 367.2 l 465.12 367.2 l 464.88 361.68 l 463.92 361.68 l f* 464.4 370.32 0.72 0.72 re f 464.4 370.32 m 465.12 375.6 l 465.84 375.6 l 465.12 370.08 l 464.4 370.32 l f* 465.12 375.84 m 466.08 378.24 l 466.8 378.24 l 465.84 375.84 l 465.12 375.84 l f* 466.08 378.24 m 467.04 374.64 l 467.76 374.64 l 466.8 378 l 466.08 378.24 l f* 467.04 375.36 m 468.24 370.08 l 468.96 370.08 l 467.76 375.36 l 467.04 375.36 l f* 468.72 368.64 m 469.44 363.6 l 470.4 363.6 l 469.44 368.64 l 468.72 368.64 l f* 469.44 363.6 m 469.92 365.76 l 470.88 365.76 l 470.4 363.6 l 469.44 363.6 l f* 469.92 365.04 m 470.16 370.56 l 471.12 370.56 l 470.88 365.04 l 469.92 365.04 l f* 470.4 372 m 470.4 377.52 l 471.36 377.52 l 471.12 372 l 470.4 372 l f* 470.64 379.2 m 470.88 382.8 l 471.6 382.56 l 471.36 379.2 l 470.64 379.2 l f* 470.88 382.56 m 472.32 382.8 l 472.32 381.84 l 470.88 381.84 l 470.88 382.56 l f* 471.6 382.8 m 472.8 378 l 473.52 377.76 l 472.32 382.8 l 471.6 382.8 l f* 472.8 378.72 m 474 373.44 l 474.72 373.44 l 473.52 378.72 l 472.8 378.72 l f* 474.24 373.2 m 475.2 368.4 l 475.92 368.16 l 475.2 373.2 l 474.24 373.2 l f* 475.2 368.16 0.96 0.96 re f 475.44 368.4 m 475.68 372 l 476.64 372 l 476.16 368.16 l 475.44 368.4 l f* 475.68 371.28 m 475.92 376.08 l 476.88 376.08 l 476.64 371.04 l 475.68 371.28 l f* 475.92 375.36 m 476.4 380.4 l 477.36 380.4 l 476.88 375.36 l 475.92 375.36 l f* 476.4 379.44 m 477.36 381.84 l 478.08 381.84 l 477.36 379.44 l 476.4 379.44 l f* 477.36 381.84 m 479.04 381.84 l 479.28 381.12 l 477.36 381.12 l 477.36 381.84 l f* 478.32 382.08 m 479.28 379.92 l 480 379.68 l 479.28 381.84 l 478.32 382.08 l f* 479.28 380.64 m 479.76 378.48 l 480.48 378.48 l 480 380.64 l 479.28 380.64 l f* 479.76 378.48 m 479.28 380.64 l 480 380.64 l 480.48 378.48 l 479.76 378.48 l f* 479.28 379.92 m 478.08 382.08 l 478.8 381.84 l 480 379.68 l 479.28 379.92 l f* 478.08 381.84 m 476.64 378.24 l 477.6 378.24 l 478.8 381.84 l 478.08 381.84 l f* 476.64 378.96 m 476.16 373.92 l 476.88 373.92 l 477.6 378.96 l 476.64 378.96 l f* 476.16 374.64 m 476.64 369.36 l 477.6 369.36 l 476.88 374.64 l 476.16 374.64 l f* 476.88 369.36 m 478.08 365.76 l 478.8 365.76 l 477.6 369.12 l 476.88 369.36 l f* 478.08 365.76 m 479.52 368.16 l 480.48 368.16 l 478.8 365.52 l 478.08 365.76 l f* 479.52 367.2 m 480.48 369.6 l 481.2 369.6 l 480.24 367.2 l 479.52 367.2 l f* 480.48 369.6 m 480.96 367.44 l 481.68 367.2 l 481.2 369.36 l 480.48 369.6 l f* 480.96 368.16 m 481.68 362.88 l 482.64 362.64 l 481.68 368.16 l 480.96 368.16 l f* 481.92 362.64 m 482.64 357.36 l 483.6 357.12 l 482.64 362.64 l 481.92 362.64 l f* 483.36 354.24 m 483.6 352.56 l 484.32 352.56 l 484.08 354 l 483.36 354.24 l f* 483.84 351.6 m 484.32 346.08 l 485.04 346.08 l 484.56 351.6 l 483.84 351.6 l f* 484.56 342.96 m 484.8 341.52 l 485.52 341.52 l 485.52 342.96 l 484.56 342.96 l f* 484.8 342 m 485.28 336.48 l 486 336.48 l 485.76 341.76 l 484.8 342 l f* 485.28 333.36 m 485.52 332.88 l 486.24 332.64 l 486.24 333.36 l 485.28 333.36 l f* 485.52 333.6 m 484.32 329.76 l 485.28 329.76 l 486.24 333.36 l 485.52 333.6 l f* 485.04 330.48 m 482.64 331.68 l 482.64 330.96 l 485.28 329.76 l 485.04 330.48 l f* 482.64 330.96 m 481.2 334.56 l 481.92 334.56 l 483.36 330.96 l 482.64 330.96 l f* 481.2 333.84 m 480.96 339.36 l 481.92 339.12 l 481.92 333.84 l 481.2 333.84 l f* 480.96 339.36 m 481.2 344.88 l 482.16 344.64 l 481.68 339.36 l 480.96 339.36 l f* 481.44 344.88 m 483.12 348.72 l 483.84 348.72 l 482.16 344.88 l 481.44 344.88 l f* 483.12 347.76 m 483.84 350.16 l 484.56 350.16 l 483.84 347.76 l 483.12 347.76 l f* 483.84 349.44 1.2 0.72 re f 484.32 349.44 0.96 0.72 re f 484.32 349.44 0.96 0.72 re f 484.32 350.16 m 484.32 348 l 485.28 348 l 485.04 350.16 l 484.32 350.16 l f* BT 412.8 297.12 TD 0 0 0 rg -0.0008 Tc 0 Tw (-1.5) Tj 3.36 23.76 TD -0 Tc (-1) Tj -3.36 23.76 TD -0.0008 Tc (-0.5) Tj 4.8 23.52 TD -0.0019 Tc (0) Tj -3.36 23.76 TD -0.0016 Tc (0.5) Tj 3.36 23.76 TD -0.0019 Tc (1) Tj -3.36 23.76 TD -0.0016 Tc (1.5) Tj -77.28 -77.28 TD -0.0008 Tc (-1.5) Tj 29.28 0 TD -0 Tc (-1) Tj 25.92 0 TD -0.0008 Tc (-0.5) Tj 29.76 0 TD -0.0019 Tc (0) Tj 25.92 0 TD -0.0016 Tc (0.5) Tj 29.28 0 TD -0.0019 Tc (1) Tj 25.68 0 TD -0.0016 Tc (1.5) Tj -161.76 -90.24 TD /F0 10.08 Tf 0 Tc 0.1195 Tw (Figure 1) Tj 36 0 TD /F1 10.08 Tf -0.057 Tc 0.129 Tw ( Effect of preprocessing over spurious) Tj 5.04 -11.52 TD -0.0144 Tc 0.0144 Tw (displacement and rotation.) Tj -44.64 -23.52 TD -0.0454 Tc 0.3454 Tw (Specifically, time is changed to the unit interval [0;1]) Tj -19.92 -12 TD -0.0542 Tc 0.3542 Tw (and x\(t\) and y\(t\) are changed to [-1;1]. In the next step, an) Tj 0 -12 TD -0.0438 Tc 5.5038 Tw (auxiliary complex valued function z\(t\)) Tj 175.44 0 TD /F3 10.08 Tf -0.0139 Tc 0 Tw (=) Tj 5.52 0 TD /F1 10.08 Tf -0.0389 Tc (x\(t\)) Tj 14.4 0 TD /F3 10.08 Tf -0.0139 Tc (+) Tj 5.28 0 TD /F1 10.08 Tf 0.0049 Tc 5.6351 Tw (i.y\(t\) is) Tj -200.64 -12 TD -0.0424 Tc 2.0138 Tw (defined, whose origin is then situated over the) Tj 0 Tc -0.12 Tw ( ) Tj 202.56 0 TD -0.049 Tc 0 Tw (centroid) Tj -202.56 -12 TD -0.0406 Tc 0.1606 Tw (with ) Tj ET 0.48 w 0 0 0 RG 339.6 196.32 m 344.88 196.32 l S q 337.68 185.52 34.08 15.36 re W n BT 0.75 0 0 1 345.36 188.88 Tm /F3 15.84 Tf -0.1547 Tc 0 Tw (\() Tj ET Q q 340.56 185.52 39.6 15.36 re W n BT 0.75 0 0 1 353.76 188.88 Tm /F3 15.84 Tf -0.1547 Tc 0 Tw (\)) Tj ET Q q 361.92 185.52 39.6 15.36 re W n BT 0.75 0 0 1 375.12 188.88 Tm /F3 15.84 Tf -0.1547 Tc 0 Tw (\() Tj ET Q q 370.32 185.52 39.6 15.36 re W n BT 0.75 0 0 1 383.52 188.88 Tm /F3 15.84 Tf -0.1547 Tc 0 Tw (\)) Tj ET Q BT 404.16 186 TD /F1 6.96 Tf -0.0823 Tc 0 Tw (C) Tj -6.48 2.88 TD /F1 12 Tf -0.048 Tc (z) Tj -18.48 0 TD 0.024 Tc (t) Tj -9.6 0 TD -0.048 Tc (z) Tj -20.16 0 TD 0.024 Tc (t) Tj -9.84 0 TD -0.048 Tc (z) Tj 49.2 0 TD /F3 12 Tf -0.108 Tc (-) Tj -29.04 0 TD (=) Tj 50.88 0 TD /F1 10.08 Tf -0.0442 Tc -0.0758 Tw (, where ) Tj 32.16 0 TD 0.0845 Tc 0 Tw (z) Tj 4.56 -1.44 TD /F1 6.48 Tf -0.0022 Tc (C) Tj 4.08 1.44 TD /F1 10.08 Tf -0.0327 Tc -0.0073 Tw ( is defined as:) Tj ET BT 0.75 0 0 1 439.44 158.4 Tm /F3 15.84 Tf -0.1547 Tc 0 Tw (\() Tj 10.56 0 TD (\)) Tj ET BT 426.72 154.08 TD /F3 18 Tf 0.108 Tc (\362) Tj -9.84 4.08 TD /F3 12 Tf -0.108 Tc (=) Tj 10.56 13.92 TD /F1 6.96 Tf 0.12 Tc (1) Tj 0 -26.88 TD (0) Tj 23.28 12.96 TD /F5 12 Tf 0.012 Tc (dt) Tj -7.92 0 TD 0.024 Tc (t) Tj -8.64 0 TD -0.108 Tc (z) Tj -32.4 0 TD (z) Tj 5.28 -2.88 TD /F5 6.96 Tf -0.0823 Tc (C) Tj 133.92 3.12 TD /F1 10.08 Tf 0.0022 Tc (\(1\)) Tj -223.44 -36.48 TD -0.0395 Tc 2.4795 Tw (The signature is then aligned with one of its principal) Tj 0 -11.52 TD -0.0357 Tc 0.1557 Tw (axes, with:) Tj ET q 399.36 81.36 30.72 15.12 re W n BT 0.75 0 0 1 406.08 84.72 Tm /F3 14.4 Tf 0.0048 Tc 0 Tw (\() Tj ET Q q 401.52 81.36 36 15.12 re W n BT 0.75 0 0 1 413.52 84.72 Tm /F3 14.4 Tf 0.0048 Tc 0 Tw (\)) Tj ET Q 427.92 91.44 m 432.72 91.44 l S q 421.2 81.36 36 15.12 re W n BT 0.75 0 0 1 433.2 84.72 Tm /F3 14.4 Tf 0.0048 Tc 0 Tw (\() Tj ET Q q 428.64 81.36 36 15.12 re W n BT 0.75 0 0 1 440.64 84.72 Tm /F3 14.4 Tf 0.0048 Tc 0 Tw (\)) Tj ET Q BT 475.2 89.52 TD /F3 6.24 Tf -0.0974 Tc 0 Tw (a) Tj -24.48 0 TD -0.0658 Tc (-) Tj -31.68 -4.8 TD /F3 10.8 Tf 0.0708 Tc (=) Tj 39.6 4.8 TD /F1 6.24 Tf 0.0593 Tc (arctan) Tj -2.16 0 TD 0.12 Tc (.) Tj -1.92 0 TD -0.0547 Tc (i) Tj -9.36 -4.8 TD /F1 10.8 Tf 0.0048 Tc (e) Tj -2.16 0 TD -0.06 Tc (.) Tj -6.24 0 TD 0.1176 Tc (t) Tj -8.88 0 TD 0.0048 Tc (z) Tj -18.24 0 TD 0.1176 Tc (t) Tj -8.64 0 TD 0.0048 Tc (z) Tj 0.48 0.48 TD 0.0036 Tc (\210) Tj 139.44 0 TD /F1 10.08 Tf 0.0022 Tc (\(2\)) Tj ET endstream endobj 21 0 obj 143916 endobj 17 0 obj << /Type /Page /Parent 5 0 R /Resources << /Font 26 0 R /ProcSet 2 0 R >> /Contents 20 0 R >> endobj 26 0 obj << /F0 6 0 R /F1 8 0 R /F2 12 0 R /F3 18 0 R /F4 22 0 R /F5 24 0 R >> endobj 28 0 obj << /Length 29 0 R >> stream BT 59.52 707.52 TD 0 0 0 rg /F1 10.08 Tf -0.0291 Tc -0.0909 Tw (where ) Tj ET 0.48 w 1 J 1 j 0 0 0 RG 128.16 708.24 m 129.36 708.96 l S 0.72 w 129.36 708.72 m 131.28 704.16 l S 0.48 w 131.52 704.16 m 133.92 717.36 l 157.68 717.36 l S BT 152.88 711.12 TD /F1 6 Tf 0.12 Tc 0 Tw (2) Tj -19.44 -4.56 TD /F1 10.08 Tf 0 Tc (1) Tj 13.44 0 TD /F3 10.08 Tf -0.0139 Tc (b) Tj -7.2 0 TD (+) Tj -19.68 0 TD (+) Tj -7.2 0 TD (b) Tj -5.52 0 TD (-) Tj -7.92 0 TD (=) Tj -9.12 0 TD 0.1195 Tc (a) Tj 69.6 0.96 TD /F1 10.08 Tf -0.0212 Tc 2.7012 Tw ( is the inclination angle of the) Tj -100.32 -16.08 TD -0.0677 Tc 0.1477 Tw (principal axis, for a value of ) Tj 115.2 0 TD /F3 10.08 Tf -0.0139 Tc 0 Tw (b) Tj 5.52 0 TD /F1 10.08 Tf -0.15 Tc 0.27 Tw ( given by:) Tj ET BT 0.75 0 0 1 192.24 656.88 Tm /F3 14.4 Tf 0.0048 Tc 0 Tw (\() Tj 9.92 0 TD (\)) Tj -21.1199 0 TD (\() Tj 25.2799 0 TD (\)) Tj -14.0799 -34.32 TD (\() Tj 9.92 0 TD (\)) Tj -21.1199 0 TD (\() Tj 25.2799 0 TD (\)) Tj ET 160.08 642.24 m 230.16 642.24 l S BT 225.12 620.4 TD /F3 10.8 Tf -0.0672 Tc (\372) Tj 0 -9.6 TD (\373) Tj 0 19.92 TD (\371) Tj -51.84 -10.32 TD (\352) Tj 0 -9.6 TD (\353) Tj 0 19.92 TD (\351) Tj 51.84 23.76 TD (\372) Tj 0 -9.6 TD (\373) Tj 0 19.92 TD (\371) Tj -51.84 -10.32 TD (\352) Tj 0 -9.6 TD (\353) Tj 0 19.92 TD (\351) Tj -22.08 -25.2 TD 0.0708 Tc (=) Tj -8.64 0 TD (b) Tj 35.28 -20.88 TD /F3 16.32 Tf 0.0883 Tc (\362) Tj 0 34.08 TD (\362) Tj 0.48 -17.76 TD /F1 6.24 Tf 0 Tc (1) Tj 0 -24.24 TD (0) Tj 42.24 9.12 TD (*) Tj -14.16 8.16 TD (2) Tj -28.08 41.04 TD (1) Tj 0.24 -24 TD (0) Tj 42 8.88 TD (*) Tj -14.16 8.4 TD (2) Tj 4.8 -39.84 TD /F1 10.8 Tf -0.1212 Tc (dt) Tj -15.36 0 TD 0.1176 Tc (t) Tj -8.64 0 TD 0.0048 Tc (z) Tj 0.48 0.48 TD 0.0036 Tc (\210) Tj -26.88 -0.48 TD -0.2394 Tc (Im) Tj 50.4 34.32 TD -0.1212 Tc (dt) Tj -15.36 0 TD 0.1176 Tc (t) Tj -8.64 0 TD 0.0048 Tc (z) Tj 0.72 0.48 TD 0.0036 Tc (\210) Tj -27.12 -0.48 TD 0 Tc (Re) Tj 122.16 -13.68 TD /F1 10.08 Tf 0.0022 Tc (\(3\)) Tj -223.44 -57.12 TD /F0 10.08 Tf -0.0607 Tc 0.1807 Tw (3.2 Wavelet-based feature extraction) Tj 0 -15.36 TD /F1 10.08 Tf -0.0618 Tc 0.5018 Tw (Considering the good results presented by ) Tj 173.28 0 TD -0.0479 Tc 0.5679 Tw (Deng et al. [9],) Tj -173.28 -12 TD -0.0686 Tc 0.9806 Tw (we decided to use the wavelet transform as the main tool) Tj 0 -12 TD -0.057 Tc 2.727 Tw (for feature extraction. The wavelet transform is also ) Tj 2.7245 Tc 0 Tw (a) Tj T* -0.057 Tc 0.597 Tw (good choice because of its capability to allow hierarchical) Tj T* -0.0608 Tc 7.2208 Tw (decomposition of functions in different levels of) Tj T* -0.0441 Tc 2.8727 Tw (resolution, separating in each level a an approximated) Tj T* -0.0567 Tc 4.87 Tw (shape from the details that complement it. It is ) Tj 4.8845 Tc 0 Tw (a) Tj T* -0.0358 Tc 5.1958 Tw (reasonable assumption to suppose that an authentic) Tj T* -0.0411 Tc 0.5078 Tw (signature must be consistent with a standard pattern in the) Tj T* -0.0547 Tc 2.1847 Tw (details, at a suitable level of resolution. We considered) Tj T* -0.0609 Tc 1.9942 Tw (also to use Fourier Transform in place of wavelets, but) Tj T* -0.0538 Tc 2.2804 Tw (this option was discarded in view of the remarks from) Tj T* -0.0419 Tc 2.5619 Tw (Sundaresan and) Tj 0 Tc -0.12 Tw ( ) Tj 70.56 0 TD -0.0549 Tc 2.5749 Tw (Keerthi [6]. Fourier coefficients would) Tj -70.56 -12 TD -0.0439 Tc 1.0039 Tw (tend to increase the \(false\) acceptation of forgeries, since) Tj 0 -12 TD -0.0527 Tc 0.5807 Tw (they would not be able to indicate changes of style during) Tj T* -0.0591 Tc 0.7191 Tw (the signing process, while these changes can be identified) Tj T* -0.066 Tc 3.186 Tw (in a natural way in the detail functions of a wavelet) Tj T* -0.0431 Tc 0 Tw (transform.) Tj 19.92 -18 TD -0.0581 Tc 0.4181 Tw (The decomposition of the functions x\(t\) and y\(t\) with) Tj -19.92 -12 TD -0.035 Tc 2.555 Tw (wavelet transform generates approximations and details) Tj 0 -12 TD -0.0617 Tc 1.5737 Tw (like those showed in Figure 2 to an original example of) Tj T* -0.0511 Tc 1.6591 Tw (x\(t\). To each zero-crossing of the detail curve at the ) Tj 1.92 Tc 0 Tw (4) Tj 230.16 4.56 TD /F1 6.48 Tf -0.1207 Tc (th) Tj -230.16 -16.56 TD /F1 10.08 Tf -0.0466 Tc 1.2766 Tw (level of resolution \(this level was chosen empirically, by) Tj 0 -12 TD -0.0271 Tc 5.3242 Tw (trial and error\), three parameters are extracted: its) Tj T* -0.0396 Tc 1.3596 Tw (abscissa, the integral between consecutive zero-crossings) Tj T* -0.0392 Tc 0.0992 Tw (\(WD4 is the wavelet detail function at the 4) Tj 174.96 4.56 TD /F1 6.48 Tf 0.1193 Tc 0 Tw (th) Tj 5.04 -4.56 TD /F1 10.08 Tf -0.0449 Tc 0.1649 Tw ( level\):) Tj -66.72 -46.32 TD /F3 18 Tf 0.108 Tc 0 Tw (\362) Tj 6 -10.56 TD /F3 5.04 Tf 0.113 Tc (-) Tj -22.08 14.88 TD /F3 12 Tf -0.108 Tc (=) Tj 21.6 12.72 TD /F1 5.04 Tf 0.12 Tc (k) Tj 3.12 -27.6 TD (1) Tj -6 0 TD (k) Tj -6.48 29.52 TD /F1 6.96 Tf -0.1274 Tc (ZC) Tj -2.88 -27.6 TD (ZC) Tj -17.76 10.08 TD 0.12 Tc (k) Tj 70.56 2.88 TD /F1 12 Tf 0.012 Tc (dt) Tj -4.08 0 TD 0.084 Tc (\)) Tj -3.84 0 TD 0.024 Tc (t) Tj -4.56 0 TD 0.084 Tc (\() Tj -6 0 TD 0 Tc (4) Tj -20.16 0 TD -0.276 Tc (WD) Tj -42.48 0 TD -0.228 Tc (vi) Tj 139.68 0 TD /F1 10.08 Tf 0.0022 Tc (\(4\)) Tj -217.92 -38.16 TD -0.0453 Tc 1.3053 Tw (and the corresponding amplitude to the same abscissa in) Tj 0 -12 TD -0.0312 Tc 0.4212 Tw (the approximation function one resolution up \(WA3 is the) Tj T* -0.037 Tc 0.109 Tw (wavelet approximation function at the 3) Tj 159.84 4.56 TD /F1 6.48 Tf 0.0611 Tc 0 Tw (rd) Tj 5.28 -4.56 TD /F1 10.08 Tf -0.0449 Tc 0.1649 Tw ( level\):) Tj ET q 180.96 130.08 39.6 15.36 re W n BT 0.75 0 0 1 194.16 133.44 Tm /F3 15.84 Tf -0.1547 Tc 0 Tw (\() Tj ET Q q 202.56 130.08 18.24 15.36 re W n BT 0.75 0 0 1 215.76 133.44 Tm /F3 15.84 Tf -0.1547 Tc 0 Tw (\)) Tj ET Q BT 209.76 130.32 TD /F1 6.96 Tf 0.12 Tc 0 Tw (k) Tj -59.04 0 TD (k) Tj 47.28 3.12 TD /F1 12 Tf -0.048 Tc (zc) Tj -9.36 0 TD 0 Tc (3) Tj -20.16 0 TD -0.276 Tc (WA) Tj -30.72 0 TD -0.264 Tc (va) Tj 21.36 0 TD /F3 12 Tf -0.108 Tc (=) Tj 118.32 0 TD /F1 10.08 Tf 0.0022 Tc (\(5\)) Tj -198 -26.16 TD -0.0606 Tc 2.7177 Tw (As it has been demonstrated that this information) Tj -19.92 -12 TD -0.0371 Tc 6.0543 Tw (suffices to a complete reconstruction of the non-) Tj 258 615.12 TD -0.0582 Tc 0.4782 Tw (transformed curve \(see ) Tj 98.64 0 TD -0.026 Tc 0.722 Tw (Deng et al. [9]\), these parameters) Tj -98.64 -12 TD -0.052 Tc 0.132 Tw (can be used as highly significant features.) Tj ET 0.24 w 1 1 1 rg 324.96 568.56 220.08 106.56 re b 348.96 643.44 m 348.96 581.28 l S 346.8 581.28 m 348.96 581.28 l S 346.8 591.6 m 348.96 591.6 l S 346.8 601.92 m 348.96 601.92 l S 346.8 612.24 m 348.96 612.24 l S 346.8 622.8 m 348.96 622.8 l S 346.8 633.12 m 348.96 633.12 l S 346.8 643.44 m 348.96 643.44 l S 348.96 612.24 m 538.8 612.24 l S 348.96 610.08 m 348.96 612.24 l S 354.24 610.08 m 354.24 612.24 l S 359.52 610.08 m 359.52 612.24 l S 364.8 610.08 m 364.8 612.24 l S 370.08 610.08 m 370.08 612.24 l S 375.36 610.08 m 375.36 612.24 l S 380.64 610.08 m 380.64 612.24 l S 385.92 610.08 m 385.92 612.24 l S 391.2 610.08 m 391.2 612.24 l S 396.48 610.08 m 396.48 612.24 l S 401.76 610.08 m 401.76 612.24 l S 407.04 610.08 m 407.04 612.24 l S 412.32 610.08 m 412.32 612.24 l S 417.6 610.08 m 417.6 612.24 l S 422.64 610.08 m 422.64 612.24 l S 428.16 610.08 m 428.16 612.24 l S 433.2 610.08 m 433.2 612.24 l S 438.72 610.08 m 438.72 612.24 l S 444 610.08 m 444 612.24 l S 449.28 610.08 m 449.28 612.24 l S 454.56 610.08 m 454.56 612.24 l S 459.6 610.08 m 459.6 612.24 l S 465.12 610.08 m 465.12 612.24 l S 470.16 610.08 m 470.16 612.24 l S 475.68 610.08 m 475.68 612.24 l S 480.72 610.08 m 480.72 612.24 l S 486.24 610.08 m 486.24 612.24 l S 491.28 610.08 m 491.28 612.24 l S 496.8 610.08 m 496.8 612.24 l S 501.84 610.08 m 501.84 612.24 l S 507.12 610.08 m 507.12 612.24 l S 512.4 610.08 m 512.4 612.24 l S 517.68 610.08 m 517.68 612.24 l S 522.96 610.08 m 522.96 612.24 l S 528.24 610.08 m 528.24 612.24 l S 533.52 610.08 m 533.52 612.24 l S 538.8 610.08 m 538.8 612.24 l S 0.72 w 0 0 0.502 RG 349.68 618 m 350.64 621.84 l 351.6 624.24 l 352.56 625.44 l 353.76 624 l 354.72 617.76 l 355.92 609.84 l 356.88 603.12 l 358.08 599.28 l 359.04 601.44 l 360 607.2 l 360.96 611.52 l 362.16 615.36 l 363.12 617.76 l 364.32 618.72 l 365.28 619.68 l 366.48 618.72 l 367.44 613.44 l 368.64 607.2 l 369.6 602.64 l 370.56 600.96 l 371.52 605.52 l 372.72 612.96 l 373.68 617.76 l 374.88 620.64 l 375.84 618.72 l 377.04 614.64 l 378 612.72 l 378.96 612 l 379.92 612.48 l 381.12 613.92 l 382.08 613.92 l 383.28 612.72 l 384.24 610.56 l 385.44 608.4 l 386.4 607.2 l 387.6 607.68 l 388.56 610.08 l 389.52 613.2 l 390.48 615.84 l 391.68 616.8 l 392.64 616.08 l 393.84 613.92 l 394.8 612.72 l 396 611.76 l 396.96 611.52 l 397.92 612 l 399.12 611.52 l 400.08 611.28 l 401.28 611.28 l 402.24 611.28 l 403.44 611.76 l 404.4 612.48 l 405.6 612.96 l 406.56 613.68 l 407.52 613.92 l 408.48 613.68 l 409.68 612.72 l 410.64 611.28 l 411.84 610.56 l 412.8 610.56 l 414 612 l 414.96 614.16 l 415.92 615.36 l 416.88 615.36 l 418.08 613.92 l 419.04 611.28 l 420.24 609.6 l 421.2 608.88 l 422.4 609.36 l 423.36 610.56 l 424.56 612 l 425.52 613.44 l 426.48 615.6 l 427.44 617.28 l 428.64 617.76 l 429.6 616.32 l 430.8 611.52 l 431.76 605.76 l 432.96 602.64 l 433.92 603.36 l 435.12 610.08 l 435.84 619.44 l 437.04 624.24 l 438 624.24 l 439.2 615.84 l 440.16 603.6 l 441.36 597.12 l 442.32 597.12 l 443.52 606.48 l 444.48 620.88 l 445.44 629.28 l 446.4 630.96 l 447.6 623.52 l 448.56 610.32 l 449.76 602.64 l 450.72 599.76 l 451.92 603.12 l 452.88 611.04 l 454.08 614.88 l 455.04 615.84 l 456 613.44 l 456.96 608.88 l 458.16 607.92 l 459.12 609.6 l 460.32 613.92 l 461.28 619.44 l 462.48 621.6 l 463.44 619.68 l 464.4 612.96 l 465.36 603.84 l 466.56 598.8 l 467.52 599.28 l 468.72 607.68 l 469.68 619.92 l 470.88 627.6 l 471.84 630 l 473.04 624.48 l 474 613.92 l 474.96 606.72 l 475.92 602.64 l 477.12 602.16 l 478.08 605.04 l 479.28 606.24 l 480.24 607.44 l 481.44 610.08 l 482.4 612.96 l 483.36 616.08 l 484.32 618.72 l 485.52 618.24 l 486.48 616.56 l 487.68 615.12 l 488.64 614.16 l 489.84 614.4 l 490.8 614.88 l 492 613.92 l 492.96 611.76 l 493.92 608.4 l 495.12 605.28 l 496.08 603.6 l 497.28 605.04 l 498.24 610.08 l 499.44 616.56 l 500.4 620.88 l 501.36 622.32 l 502.32 618.72 l 503.52 612.24 l 504.48 608.16 l 505.68 606.24 l 506.64 607.92 l 507.84 612 l 508.8 613.92 l 510 614.64 l 510.96 613.68 l 511.92 611.52 l 512.88 610.56 l 514.08 610.08 l 515.04 609.84 l 516.24 610.08 l 517.2 610.08 l 518.4 611.04 l 519.36 612.96 l 520.32 615.6 l 521.28 618 l 522.48 620.16 l 523.44 621.6 l 524.64 621.6 l 525.6 619.92 l 526.8 615.36 l 527.76 606.72 l 528.96 597.36 l 529.92 591.36 l 530.88 591.12 l 531.84 599.76 l 533.04 613.44 l 534 623.76 l 535.2 630 l 536.16 628.8 l 537.36 622.32 l 538.32 618 l S BT 382.32 662.64 TD 0 0 0 rg /F4 8.88 Tf 0.026 Tc -0.0467 Tw (WT detail function - level 4) Tj -49.92 -83.76 TD /F4 7.44 Tf 0.0964 Tc 0 Tw (-60) Tj 0 10.56 TD (-40) Tj 0 10.32 TD (-20) Tj 6.72 10.32 TD -0.0566 Tc (0) Tj -4.32 10.32 TD 0.1834 Tc (20) Tj 0 10.32 TD (40) Tj T* (60) Tj 12.72 -42 TD -0.0566 Tc (1) Tj 18.96 0 TD 0.1834 Tc (21) Tj 21.12 0 TD (41) Tj 20.88 0 TD (61) Tj 21.12 0 TD (81) Tj 18.96 0 TD 0.0234 Tc (101) Tj 21.12 0 TD (121) Tj 21.36 0 TD (141) Tj 20.88 0 TD (161) Tj ET 0.24 w 0 0 0 RG 324.96 568.56 220.08 106.56 re S 1 1 1 rg 324.96 444 220.08 106.56 re b 350.64 518.88 m 350.64 467.76 l S 348.48 467.76 m 350.64 467.76 l S 348.48 484.8 m 350.64 484.8 l S 348.48 501.84 m 350.64 501.84 l S 348.48 518.88 m 350.64 518.88 l S 350.64 467.76 m 538.8 467.76 l S 350.64 465.6 m 350.64 467.76 l S 355.92 465.6 m 355.92 467.76 l S 361.2 465.6 m 361.2 467.76 l S 366.48 465.6 m 366.48 467.76 l S 371.52 465.6 m 371.52 467.76 l S 376.8 465.6 m 376.8 467.76 l S 382.08 465.6 m 382.08 467.76 l S 387.36 465.6 m 387.36 467.76 l S 392.4 465.6 m 392.4 467.76 l S 397.92 465.6 m 397.92 467.76 l S 402.96 465.6 m 402.96 467.76 l S 408.24 465.6 m 408.24 467.76 l S 413.28 465.6 m 413.28 467.76 l S 418.8 465.6 m 418.8 467.76 l S 423.84 465.6 m 423.84 467.76 l S 429.12 465.6 m 429.12 467.76 l S 434.16 465.6 m 434.16 467.76 l S 439.68 465.6 m 439.68 467.76 l S 444.72 465.6 m 444.72 467.76 l S 450 465.6 m 450 467.76 l S 455.28 465.6 m 455.28 467.76 l S 460.56 465.6 m 460.56 467.76 l S 465.6 465.6 m 465.6 467.76 l S 470.88 465.6 m 470.88 467.76 l S 476.16 465.6 m 476.16 467.76 l S 481.44 465.6 m 481.44 467.76 l S 486.48 465.6 m 486.48 467.76 l S 492 465.6 m 492 467.76 l S 497.04 465.6 m 497.04 467.76 l S 502.32 465.6 m 502.32 467.76 l S 507.36 465.6 m 507.36 467.76 l S 512.88 465.6 m 512.88 467.76 l S 517.92 465.6 m 517.92 467.76 l S 523.2 465.6 m 523.2 467.76 l S 528.24 465.6 m 528.24 467.76 l S 533.76 465.6 m 533.76 467.76 l S 538.8 465.6 m 538.8 467.76 l S 0.72 w 0 0 0.502 RG 351.36 473.28 m 352.32 475.2 l 353.28 476.4 l 354.24 477.84 l 355.44 478.32 l 356.4 478.08 l 357.36 477.6 l 358.56 476.88 l 359.52 476.4 l 360.72 476.64 l 361.68 477.12 l 362.88 477.12 l 363.84 477.36 l 364.8 477.36 l 365.76 477.36 l 366.96 477.36 l 367.92 477.12 l 368.88 476.64 l 370.08 476.16 l 371.04 475.68 l 372.24 475.92 l 373.2 476.88 l 374.16 478.08 l 375.12 479.28 l 376.32 480 l 377.28 479.76 l 378.48 479.04 l 379.44 478.8 l 380.4 478.8 l 381.6 479.04 l 382.56 479.28 l 383.76 479.52 l 384.72 479.28 l 385.68 479.04 l 386.64 478.32 l 387.84 478.08 l 388.8 478.08 l 390 478.56 l 390.96 479.04 l 391.92 479.52 l 393.12 480 l 394.08 480 l 395.04 480 l 396 480 l 397.2 480.24 l 398.16 480.48 l 399.36 480.96 l 400.32 480.96 l 401.52 480.96 l 402.48 481.2 l 403.68 481.2 l 404.64 481.44 l 405.6 481.68 l 406.56 481.92 l 407.52 482.16 l 408.72 482.64 l 409.68 482.88 l 410.88 482.88 l 411.84 482.88 l 413.04 483.12 l 414 483.6 l 414.96 483.84 l 415.92 484.56 l 416.88 484.8 l 418.08 485.04 l 419.04 485.04 l 420.24 484.8 l 421.2 484.56 l 422.4 484.56 l 423.36 484.8 l 424.56 484.8 l 425.52 485.28 l 426.48 485.52 l 427.44 485.76 l 428.4 486.24 l 429.6 486.24 l 430.56 486 l 431.76 485.52 l 432.72 484.56 l 433.92 484.32 l 434.88 484.8 l 435.84 486 l 436.8 487.92 l 438 489.36 l 438.96 489.84 l 439.92 489.12 l 441.12 487.44 l 442.08 487.2 l 443.28 487.92 l 444.24 490.32 l 445.44 493.2 l 446.4 495.36 l 447.36 496.32 l 448.32 495.84 l 449.52 494.16 l 450.48 493.2 l 451.44 492.72 l 452.64 493.2 l 453.6 494.16 l 454.8 494.4 l 455.76 494.16 l 456.72 493.68 l 457.68 493.2 l 458.88 493.2 l 459.84 493.68 l 461.04 495.12 l 462 497.04 l 462.96 498.24 l 464.16 498.72 l 465.12 498.48 l 466.32 497.52 l 467.28 497.28 l 468.24 497.76 l 469.2 499.2 l 470.4 501.12 l 471.36 502.56 l 472.56 502.56 l 473.52 501.84 l 474.48 500.16 l 475.68 498.72 l 476.64 498 l 477.6 497.76 l 478.56 498.24 l 479.76 498.24 l 480.72 498.48 l 481.92 498.72 l 482.88 498.72 l 484.08 499.2 l 485.04 499.44 l 486 499.44 l 487.2 499.2 l 488.16 498.96 l 489.12 498.96 l 490.08 499.2 l 491.28 499.68 l 492.24 499.68 l 493.44 499.68 l 494.4 499.68 l 495.6 499.44 l 496.56 499.68 l 497.52 500.4 l 498.48 501.6 l 499.44 503.28 l 500.64 504.48 l 501.6 504.96 l 502.8 504.48 l 503.76 503.52 l 504.96 503.28 l 505.92 503.04 l 507.12 503.52 l 508.08 504.48 l 509.04 504.96 l 510 505.2 l 510.96 505.44 l 512.16 505.44 l 513.12 505.44 l 514.32 505.44 l 515.28 505.44 l 516.48 505.44 l 517.44 505.44 l 518.4 505.2 l 519.36 504.96 l 520.56 504.72 l 521.52 504.72 l 522.48 504.72 l 523.68 504.96 l 524.64 505.2 l 525.84 505.44 l 526.8 505.68 l 528 505.68 l 528.96 505.92 l 529.92 506.4 l 530.88 507.36 l 532.08 508.56 l 533.04 509.76 l 534 509.52 l 535.2 507.36 l 536.16 502.08 l 537.36 495.12 l 538.32 488.16 l S BT 365.04 538.08 TD 0 0 0 rg /F4 8.88 Tf 0.0205 Tc -0.0412 Tw (WT approximation function - level 3) Tj -24.24 -72.48 TD /F4 7.44 Tf -0.0566 Tc 0 Tw (0) Tj -8.4 17.04 TD 0.0234 Tc (200) Tj 0 17.04 TD (400) Tj 0 16.8 TD (600) Tj 16.8 -61.92 TD -0.0566 Tc (1) Tj 18.72 0 TD 0.1834 Tc (21) Tj 20.88 0 TD (41) Tj 20.88 0 TD (61) Tj 20.88 0 TD (81) Tj 18.72 0 TD 0.0234 Tc (101) Tj 20.88 0 TD (121) Tj 21.12 0 TD (141) Tj 20.88 0 TD (161) Tj ET 0.24 w 0 0 0 RG 324.96 444 220.08 106.56 re S BT 328.32 420.48 TD /F0 10.08 Tf 0 Tc 0.1195 Tw (Figure 2) Tj 36 0 TD /F1 10.08 Tf -0.0614 Tc 0.0914 Tw ( Example of a function x\(t\) after the wavelet) Tj 49.92 -11.52 TD -0.0431 Tc 0 Tw (transform.) Tj -96.72 -23.76 TD /F0 10.08 Tf -0.0429 Tc 0.1629 Tw (3.3 Calculation of the dissimilarity measures) Tj 0 -15.36 TD /F1 10.08 Tf -0.049 Tc 0.6927 Tw (The main goal of the feature extraction is to allow for the) Tj 0 -12 TD -0.0471 Tc 3.6872 Tw (dissimilarity between two signatures to be quantified.) Tj T* -0.056 Tc 6.3131 Tw (However, even for original samples, it is almost) Tj T* -0.0547 Tc 2.3004 Tw (impossible to have two original signatures with exactly) Tj T* -0.0362 Tc 0.1322 Tw (the same shape and velocity profiles, so that the right pairs) Tj T* -0.0396 Tc 1.0929 Tw (of zero-crossings to be associated will never occur at the) Tj T* -0.0632 Tc 1.4312 Tw (same time and sometimes they will not be even close to) Tj T* -0.0374 Tc 0.5474 Tw (each other. So, before measuring distances, it is necessary) Tj T* -0.0555 Tc 5.0555 Tw (to identify a suitable correspondence between zero-) Tj T* -0.0464 Tc 0.7149 Tw (crossings, which is accomplished with the Dynamic Time) Tj T* -0.0591 Tc 1.3791 Tw (Warping \(DTW\) algorithm from Sato and) Tj 0 Tc -0.12 Tw ( ) Tj 177.36 0 TD -0.0818 Tc 1.5218 Tw (Kogure [3]. It) Tj -177.36 -12 TD -0.0269 Tc 0.9869 Tw (consists of a linear programming technique, in which the) Tj 0 -12 TD -0.0474 Tc 1.5594 Tw (time axis of the reference curve is fixed, while the time) Tj T* -0.0491 Tc 2.5691 Tw (axis of the test curve is nonlinearly adjusted, so as to) Tj T* -0.0375 Tc 2.6175 Tw (minimize the norm of the global distance between the) Tj T* -0.0612 Tc 1.3812 Tw (curves. This optimization tool, described by) Tj 0 Tc -0.36 Tw ( ) Tj 185.52 0 TD -0.0533 Tc 1.6133 Tw (Rabiner [2],) Tj -185.52 -12 TD -0.0494 Tc 2.6594 Tw (is also used in speech recognition to identify different) Tj 0 -12 TD -0.0498 Tc 0.1098 Tw (utterances from the same phoneme.) Tj 19.92 -18 TD -0.0651 Tc 5.5051 Tw (Typically, this DTW is executed between two) Tj -19.92 -12 TD -0.0511 Tc 3.1711 Tw (discrete functions, having or not the same number of) Tj 0 -12 TD -0.0486 Tc 3.2543 Tw (points, to find the best correspondence between these) Tj T* -0.0482 Tc 1.0215 Tw (points. In our context, the best correspondence is the one) Tj T* -0.0663 Tc 3.7863 Tw (in which the sum of the) Tj 0 Tc -0.12 Tw ( ) Tj 118.56 0 TD -0.0652 Tc 3.7852 Tw (euclidean distance between) Tj -118.56 -12 TD -0.04 Tc 0.3658 Tw (selected points is minimum. This is accomplished through) Tj ET endstream endobj 29 0 obj 19814 endobj 27 0 obj << /Type /Page /Parent 5 0 R /Resources << /Font << /F0 6 0 R /F1 8 0 R /F3 18 0 R /F4 22 0 R >> /ProcSet 2 0 R >> /Contents 28 0 R >> endobj 31 0 obj << /Length 32 0 R >> stream BT 59.52 710.4 TD 0 0 0 rg /F1 10.08 Tf -0.0694 Tc 0.9694 Tw (the assignment of costs \(distance between points\) to each) Tj 0 -12 TD -0.0507 Tc 0.3078 Tw (association between points in different curves. These costs) Tj T* -0.0471 Tc 0.7671 Tw (are organized as a matrix [A], whose element ) Tj 190.32 0 TD 0.0845 Tc 0 Tw (a) Tj 4.56 -1.44 TD /F1 6.48 Tf -0.1214 Tc (ij) Tj 3.36 1.44 TD /F1 10.08 Tf 0.0304 Tc 1.0496 Tw ( contains) Tj -198.24 -12 TD -0.0666 Tc 2.5866 Tw (the value of the) Tj 0 Tc -0.12 Tw ( ) Tj 74.16 0 TD -0.0486 Tc 2.8086 Tw (euclidean distance between point) Tj 0 Tc 0.12 Tw ( ) Tj 145.44 0 TD -0.1082 Tc 2.6282 Tw (i in) Tj -219.6 -12 TD -0.0627 Tc 0.6627 Tw (some curve f\(x\) and point j in some g\(x\). This matrix can) Tj 0 -12 TD -0.0751 Tc 3.9871 Tw (be viewed as a diagram with) Tj 0 Tc 0.36 Tw ( ) Tj 139.2 0 TD 0.0811 Tc 0 Tw (T) Tj 6.24 -1.44 TD /F1 6.48 Tf 0.0022 Tc (f) Tj 1.92 0 TD 0 Tc 0.06 Tw ( ) Tj 5.52 1.44 TD /F3 10.08 Tf -0.0139 Tc 0 Tw (\264) Tj 5.52 0 TD /F1 10.08 Tf 0.0811 Tc (T) Tj 6.24 -1.44 TD /F1 6.48 Tf 0.12 Tc (g) Tj 2.88 1.44 TD /F1 10.08 Tf -0.0433 Tc 3.9233 Tw ( points and an) Tj -167.52 -12 TD -0.0548 Tc 0.9634 Tw (algorithm of linear programming indicates which pairs of) Tj 0 -12 TD -0.0634 Tc 3.1434 Tw (points compose the path that leads to the best global) Tj T* -0.0579 Tc 6.1779 Tw (correspondence. Typically, the optimization solution) Tj T* -0.0426 Tc 0.8226 Tw (deviates from the main diagonal of the diagram, meaning) Tj T* -0.0478 Tc 0.0878 Tw (that some "warping" had to be imposed.) Tj 19.92 -18 TD -0.0444 Tc 2.0044 Tw (A recursive algorithm that finds the best path in ) Tj 2.0045 Tc 0 Tw (a) Tj -19.92 -12 TD -0.0504 Tc 0.1704 Tw (diagram with ) Tj 55.68 0 TD 0.0811 Tc 0 Tw (T) Tj 6.24 -1.44 TD /F1 6.48 Tf 0.0022 Tc (f) Tj 1.92 1.44 TD /F1 10.08 Tf -0.0778 Tc 0.0778 Tw ( X ) Tj 12.24 0 TD 0.0811 Tc 0 Tw (T) Tj 6.24 -1.44 TD /F1 6.48 Tf 0.12 Tc (g) Tj 2.88 1.44 TD /F1 10.08 Tf -0.0281 Tc 0.3481 Tw ( points, starting at \(1,1\) and finishing) Tj -85.2 -12 TD -0.0389 Tc 1.3589 Tw (at ) Tj 1.2034 Tc 0 Tw (\() Tj 14.4 0 TD 0.0811 Tc (T) Tj 6.24 -1.44 TD /F1 6.48 Tf 0.0022 Tc (f) Tj 1.92 1.44 TD /F1 10.08 Tf 0.1006 Tc (,T) Tj 8.88 -1.44 TD /F1 6.48 Tf 0.12 Tc (g) Tj 2.88 1.44 TD /F1 10.08 Tf -0.0687 Tc 1.5754 Tw (\), can be described by the three steps below ) Tj 1.4434 Tc 0 Tw (\() Tj 192.48 0 TD 0 Tc (d) Tj 5.04 -1.44 TD /F1 6.48 Tf -0.1214 Tc (ij) Tj -231.84 -10.56 TD /F1 10.08 Tf -0.0467 Tc 2.5067 Tw (means local cost between points) Tj 0 Tc -0.36 Tw ( ) Tj 143.52 0 TD -0.0391 Tc 2.4631 Tw (i and j and D means) Tj -143.52 -12 TD -0.0581 Tc 2.8181 Tw (global cost from \(1,1\) until ) Tj 2.6434 Tc 0 Tw (\() Tj 127.2 0 TD -0.0488 Tc 2.8088 Tw (i,j\), following an optimal) Tj -127.2 -12 TD -0.0428 Tc 0.1628 Tw (path\), extracted from ) Tj 86.88 0 TD -0.079 Tc 0.199 Tw (Rabiner [2]:) Tj -69.12 -18 TD 0.06 Tc 0 Tw (1.) Tj 7.68 0 TD /F4 10.08 Tf 0 Tc 0.0778 Tw ( ) Tj 10.08 0 TD /F1 10.08 Tf -0.0214 Tc 5.7814 Tw (Initialization: ) Tj 5.9222 Tc 0 Tw (D) Tj 77.76 -1.44 TD /F1 6.48 Tf 0.0129 Tc (\(1,1\)) Tj 12.48 1.44 TD /F1 10.08 Tf 0.0749 Tc 5.6851 Tw ( = ) Tj 6 Tc 0 Tw (d) Tj 27.36 -1.44 TD /F1 6.48 Tf 0.0129 Tc (\(1,1\)) Tj 12.48 1.44 TD /F1 10.08 Tf -0.1411 Tc (.m) Tj 10.32 -1.44 TD /F1 6.48 Tf 0.0414 Tc (\(1\)) Tj 7.44 1.44 TD /F1 10.08 Tf -0.0442 Tc 6.0442 Tw (, where ) Tj 5.8378 Tc 0 Tw (m) Tj -165.6 -12 TD -0.0537 Tc 6.2217 Tw (contains weights that empirically impose some) Tj 0 -12 TD -0.0564 Tc 0.1764 Tw (preference among possible paths \(see Figure 3\).) Tj 0 -18 TD 0.06 Tc 0 Tw (2.) Tj 7.68 0 TD /F4 10.08 Tf 0 Tc 0.0778 Tw ( ) Tj 10.08 0 TD /F1 10.08 Tf -0.0558 Tc 0.2358 Tw (Recursive step: search on a tree of possible paths.) Tj -17.76 -12 TD -0.0439 Tc 7.5559 Tw (Starting by the last point ) Tj 7.4434 Tc 0 Tw (\() Tj 141.36 0 TD 0.0811 Tc (T) Tj 6.24 -1.44 TD /F1 6.48 Tf 0.0022 Tc (f) Tj 1.92 1.44 TD /F1 10.08 Tf 0.1006 Tc (,T) Tj 8.88 -1.44 TD /F1 6.48 Tf 0.12 Tc (g) Tj 2.88 1.44 TD /F1 10.08 Tf -0.0641 Tc 7.7441 Tw (\), for each) Tj -161.28 -12 TD -0.0378 Tc 7.8378 Tw (intermediary combination ) Tj 7.6834 Tc 0 Tw (\() Tj 124.8 0 TD 0.0778 Tc (i) Tj 2.88 -1.44 TD /F1 6.48 Tf 0.0022 Tc (f) Tj 1.92 1.44 TD /F1 10.08 Tf 0.0989 Tc (,i) Tj 5.52 -1.44 TD /F1 6.48 Tf 0.12 Tc (g) Tj 2.88 1.44 TD /F1 10.08 Tf -0.0014 Tc 7.9214 Tw (\), search among) Tj -138 -12 TD -0.0459 Tc 2.3259 Tw (allowed candidates ) Tj 2.1634 Tc 0 Tw (\() Tj 86.64 0 TD -0.1483 Tc (i') Tj 4.56 -1.44 TD /F1 6.48 Tf 0.0022 Tc (f) Tj 1.92 1.44 TD /F1 10.08 Tf 0.1011 Tc (,i') Tj 7.44 -1.44 TD /F1 6.48 Tf 0.12 Tc (g) Tj 2.88 1.44 TD /F1 10.08 Tf -0.0204 Tc 2.3484 Tw (\), the one which, after the) Tj -103.44 -12 TD -0.0599 Tc 1.9399 Tw (addition of the local cost between ) Tj 1.9234 Tc 0 Tw (\() Tj 151.2 0 TD 0.0778 Tc (i) Tj 2.88 -1.44 TD /F1 6.48 Tf 0.0022 Tc (f) Tj 1.92 1.44 TD /F1 10.08 Tf 0.0989 Tc (,i) Tj 5.52 -1.44 TD /F1 6.48 Tf 0.12 Tc (g) Tj 2.88 1.44 TD /F1 10.08 Tf -0.038 Tc 2.078 Tw (\) and ) Tj 1.9234 Tc 0 Tw (\() Tj 30.24 0 TD -0.1483 Tc (i') Tj 4.56 -1.44 TD /F1 6.48 Tf 0.0022 Tc (f) Tj 1.92 1.44 TD /F1 10.08 Tf 0.1011 Tc (,i') Tj 7.44 -1.44 TD /F1 6.48 Tf 0.12 Tc (g) Tj 2.88 1.44 TD /F1 10.08 Tf 0.0617 Tc (\),) Tj -211.44 -12 TD -0.0441 Tc 1.4241 Tw (leads to a global distance from \(1,1\) to ) Tj 1.4434 Tc 0 Tw (\() Tj 171.12 0 TD 0.0778 Tc (i) Tj 2.88 -1.44 TD /F1 6.48 Tf 0.0022 Tc (f) Tj 1.92 1.44 TD /F1 10.08 Tf 0.0989 Tc (,i) Tj 5.52 -1.44 TD /F1 6.48 Tf 0.12 Tc (g) Tj 2.88 1.44 TD /F1 10.08 Tf 0.0343 Tc 1.4057 Tw (\) that is) Tj -184.32 -12 TD -0.0502 Tc 2.2959 Tw (minimum. Since the alternative paths tend to grow) Tj 0 -12 TD -0.0397 Tc 2.0497 Tw (exponentially, only the 3 paths that conform to the) Tj T* -0.0436 Tc 2.4607 Tw (restriction rule showed in Figure 3 are considered.) Tj T* -0.0539 Tc 2.2996 Tw (Mathematically, this can be stated as: for 1> /ProcSet 2 0 R >> /Contents 31 0 R >> endobj 34 0 obj << /Length 35 0 R >> stream 0.48 w 1 J 1 j 0 0 0 RG 136.56 717.6 m 136.56 699.6 l S 135.12 717.6 m 135.12 699.6 l S 221.28 717.6 m 221.28 699.6 l S 219.84 717.6 m 219.84 699.6 l S BT 199.92 710.88 TD 0 0 0 rg /F1 6.72 Tf 0 Tc 0 Tw (2) Tj -2.16 0 TD (,) Tj -4.08 0 TD (x) Tj -0.24 -7.92 TD -0.1427 Tc (CAM) Tj -40.32 7.92 TD 0 Tc (1) Tj -1.44 0 TD (,) Tj -3.84 0 TD (x) Tj -0.24 -7.92 TD -0.1427 Tc (CAM) Tj -29.76 7.92 TD 0 Tc (x) Tj 96.24 -9.6 TD /F1 4.8 Tf (2) Tj -1.92 0 TD (,) Tj -2.88 0 TD (k) Tj -41.76 0 TD (1) Tj -1.2 0 TD (,) Tj -3.12 0 TD (k) Tj 20.64 4.56 TD /F1 11.52 Tf -0.2813 Tc (vi) Tj -46.08 0 TD (vi) Tj -30.24 0 TD -0.0413 Tc (di) Tj 67.2 0 TD /F3 11.52 Tf -0.0845 Tc (-) Tj -48.96 0 TD (=) Tj 157.2 0.48 TD /F1 10.08 Tf 0.0022 Tc (\(8\)) Tj ET 136.56 683.52 m 136.56 665.04 l S 134.88 683.52 m 134.88 665.04 l S 221.28 683.52 m 221.28 665.04 l S 219.6 683.52 m 219.6 665.04 l S BT 199.44 676.56 TD /F1 6.72 Tf 0 Tc (2) Tj -2.16 0 TD (,) Tj -3.6 0 TD (y) Tj -0.24 -8.16 TD -0.1427 Tc (CAM) Tj -40.56 8.16 TD 0 Tc (1) Tj -1.44 0 TD (,) Tj -3.84 0 TD (y) Tj -0.24 -8.16 TD -0.1427 Tc (CAM) Tj -29.52 8.16 TD 0 Tc (y) Tj 96 -9.84 TD /F1 4.8 Tf (2) Tj -1.68 0 TD (,) Tj -3.12 0 TD (k) Tj -41.76 0 TD (1) Tj -1.2 0 TD (,) Tj -3.12 0 TD (k) Tj 20.64 4.8 TD /F1 11.52 Tf -0.2813 Tc (vi) Tj -46.08 0 TD (vi) Tj -30 0 TD -0.0413 Tc (di) Tj 66.96 0 TD /F3 11.52 Tf -0.0845 Tc (-) Tj -48.96 0 TD (=) Tj 157.44 0.48 TD /F1 10.08 Tf 0.0022 Tc (\(9\)) Tj -202.08 -30.24 TD -0.0291 Tc 1.1091 Tw (where ) Tj 0.9634 Tc 0 Tw ([) Tj 31.44 0 TD -0.0541 Tc (CAM) Tj 22.8 -1.44 TD /F1 6.48 Tf 0.019 Tc (i,j) Tj 5.04 1.44 TD /F1 10.08 Tf -0.0449 Tc 1.1649 Tw (] is the matrix containing the optimal) Tj -59.28 -12 TD -0.0287 Tc 0.1487 Tw (path and [) Tj 40.32 0 TD -0.2011 Tc 0 Tw (vi) Tj 7.68 -1.44 TD /F1 6.48 Tf 0.12 Tc (k) Tj 3.12 1.44 TD /F1 10.08 Tf -0.0594 Tc 0.1314 Tw (] is given by equation \(4\).) Tj -69.36 -18 TD 0.06 Tc 0 Tw (3.) Tj 7.68 0 TD /F4 10.08 Tf 0 Tc 0.0778 Tw ( ) Tj 10.32 0 TD /F1 10.08 Tf -0.056 Tc 1.5132 Tw (The norm of the differences between amplitudes in) Tj 0 -12 TD -0.0409 Tc 1.5529 Tw (the approximation function at the ) Tj 1.68 Tc 0 Tw (3) Tj 148.32 4.56 TD /F1 6.48 Tf -0.1789 Tc (rd) Tj 5.28 -4.56 TD /F1 10.08 Tf -0.0459 Tc 1.3659 Tw ( level,) Tj 0 Tc 0.12 Tw ( ) Tj 29.76 0 TD 0.0422 Tc 0 Tw (da) Tj 9.6 4.56 TD /F1 6.48 Tf 0.12 Tc (x) Tj 3.12 -4.56 TD /F1 10.08 Tf -0.2083 Tc 1.7683 Tw (, for) Tj -196.08 -12 TD -0.0518 Tc 0.0518 Tw (x\(t\) and da) Tj 43.44 4.56 TD /F1 6.48 Tf 0.12 Tc 0 Tw (y) Tj 3.12 -4.56 TD /F1 10.08 Tf -0.0421 Tc 0.1621 Tw (, for y\(t\), calculated from:) Tj ET 134.4 565.44 m 134.4 547.44 l S 132.96 565.44 m 132.96 547.44 l S 223.2 565.44 m 223.2 547.44 l S 221.52 565.44 m 221.52 547.44 l S BT 201.84 558.72 TD /F1 6.72 Tf 0 Tc 0 Tw (2) Tj -2.16 0 TD (,) Tj -4.08 0 TD (x) Tj -0.24 -7.92 TD -0.1427 Tc (CAM) Tj -42 7.92 TD 0 Tc (1) Tj -1.44 0 TD (,) Tj -3.84 0 TD (x) Tj -0.24 -7.92 TD -0.1427 Tc (CAM) Tj -32.64 7.92 TD 0 Tc (x) Tj 101.04 -9.6 TD /F1 4.8 Tf (2) Tj -1.92 0 TD (,) Tj -3.12 0 TD (k) Tj -43.2 0 TD (1) Tj -1.2 0 TD (,) Tj -3.12 0 TD (k) Tj 19.68 4.56 TD /F1 11.52 Tf -0.2774 Tc (va) Tj -47.76 0 TD (va) Tj -32.88 0 TD -0.0374 Tc (da) Tj 71.76 0 TD /F3 11.52 Tf -0.0845 Tc (-) Tj -51.36 0 TD (=) Tj 154.8 0.48 TD /F1 10.08 Tf 0.0017 Tc (\(10\)) Tj ET 134.4 531.12 m 134.4 513.12 l S 132.72 531.12 m 132.72 513.12 l S 223.2 531.12 m 223.2 513.12 l S 221.52 531.12 m 221.52 513.12 l S BT 201.6 524.4 TD /F1 6.72 Tf 0 Tc (2) Tj -2.16 0 TD (,) Tj -3.84 0 TD (y) Tj -0.24 -7.92 TD -0.1427 Tc (CAM) Tj -42.24 7.92 TD 0 Tc (1) Tj -1.44 0 TD (,) Tj -3.84 0 TD (y) Tj -0.24 -7.92 TD -0.1427 Tc (CAM) Tj -32.4 7.92 TD 0 Tc (y) Tj 100.8 -9.6 TD /F1 4.8 Tf (2) Tj -1.68 0 TD (,) Tj -3.12 0 TD (k) Tj -43.2 0 TD (1) Tj -1.44 0 TD (,) Tj -3.12 0 TD (k) Tj 19.68 4.56 TD /F1 11.52 Tf -0.2774 Tc (va) Tj -47.52 0 TD (va) Tj -32.88 0 TD -0.0374 Tc (da) Tj 71.76 0 TD /F3 11.52 Tf -0.0845 Tc (-) Tj -51.36 0 TD (=) Tj 154.8 0.48 TD /F1 10.08 Tf 0.0017 Tc (\(11\)) Tj -197.04 -30.24 TD -0.0237 Tc 0.1437 Tw (where [) Tj 30.48 0 TD -0.1978 Tc 0 Tw (va) Tj 9.36 -1.44 TD /F1 6.48 Tf 0.12 Tc (k) Tj 3.12 1.44 TD /F1 10.08 Tf -0.0703 Tc 0.1903 Tw (] is given by equation \(5\).) Tj -61.2 -18 TD 0.06 Tc 0 Tw (4.) Tj 7.68 0 TD /F4 10.08 Tf 0 Tc 0.0778 Tw ( ) Tj 10.32 0 TD /F1 10.08 Tf -0.0411 Tc 3.6925 Tw (The area of the difference between the warping) Tj 0 -12 TD -0.0329 Tc 0.9929 Tw (function and the corresponding diagonal \(see Figure) Tj T* -0.0165 Tc 1.3065 Tw (3\). We assume that this last parameter recovers the) Tj T* -0.0321 Tc 0.7221 Tw (information related to the velocity that is lost during) Tj T* -0.0259 Tc -0.0941 Tw (the ) Tj 17.28 0 TD -0.046 Tc 2.886 Tw (resampling process to an uniform mesh. This) Tj -17.28 -12 TD -0.055 Tc 1.735 Tw (assumption is based on the simple idea that bigger) Tj 0 -12 TD -0.0595 Tc 3.5795 Tw (differences in speed during signing between two) Tj T* -0.0322 Tc 6.2962 Tw (signatures demand bigger deviations from the) Tj T* -0.0312 Tc 0.0312 Tw (diagonal in the warping function.) Tj ET 0.24 w 1 1 1 rg 76.08 245.76 201.84 107.28 re b 100.32 325.2 m 100.32 268.32 l S 97.92 268.32 m 100.32 268.32 l S 97.92 277.68 m 100.32 277.68 l S 97.92 287.28 m 100.32 287.28 l S 97.92 296.64 m 100.32 296.64 l S 97.92 306.24 m 100.32 306.24 l S 97.92 315.6 m 100.32 315.6 l S 97.92 325.2 m 100.32 325.2 l S 100.32 268.32 m 272.64 268.32 l S 100.32 265.92 m 100.32 268.32 l S 106.8 265.92 m 106.8 268.32 l S 113.04 265.92 m 113.04 268.32 l S 119.52 265.92 m 119.52 268.32 l S 126 265.92 m 126 268.32 l S 132.24 265.92 m 132.24 268.32 l S 138.72 265.92 m 138.72 268.32 l S 144.96 265.92 m 144.96 268.32 l S 151.44 265.92 m 151.44 268.32 l S 157.92 265.92 m 157.92 268.32 l S 164.16 265.92 m 164.16 268.32 l S 170.64 265.92 m 170.64 268.32 l S 177.12 265.92 m 177.12 268.32 l S 183.36 265.92 m 183.36 268.32 l S 189.6 265.92 m 189.6 268.32 l S 196.08 265.92 m 196.08 268.32 l S 202.56 265.92 m 202.56 268.32 l S 209.04 265.92 m 209.04 268.32 l S 215.28 265.92 m 215.28 268.32 l S 221.76 265.92 m 221.76 268.32 l S 228 265.92 m 228 268.32 l S 234.48 265.92 m 234.48 268.32 l S 240.72 265.92 m 240.72 268.32 l S 247.2 265.92 m 247.2 268.32 l S 253.68 265.92 m 253.68 268.32 l S 259.92 265.92 m 259.92 268.32 l S 266.4 265.92 m 266.4 268.32 l S 272.64 265.92 m 272.64 268.32 l S 0.72 w 0 0 0.502 RG 103.44 269.76 m 109.92 271.2 l 116.4 272.4 l 122.88 273.6 l 129.12 276.48 l 135.6 278.16 l 141.84 279.84 l 148.32 283.68 l 154.56 285.6 l 161.04 288.48 l 167.52 290.16 l 173.76 291.6 l 180.24 294 l 186.48 295.2 l 192.96 296.88 l 199.2 298.32 l 205.68 299.52 l 212.16 300.72 l 218.4 301.92 l 224.88 303.36 l 231.12 305.28 l 237.6 306.48 l 244.08 307.92 l 250.32 309.36 l 256.8 310.56 l 263.28 312.48 l 269.52 313.92 l S 0 0.2 0 rg 102.96 269.04 m 107.52 269.76 l 107.52 269.28 l 103.2 268.32 l 102.96 269.04 l f* 110.16 270.24 m 110.16 269.76 l 110.16 270.24 l f* 109.44 270.24 m 113.76 270.96 l 114 270.24 l 109.68 269.76 l 109.44 270.24 l f* 116.64 271.44 m 116.64 270.72 l 116.64 271.44 l f* 115.92 271.44 m 120.24 272.16 l 120.48 271.44 l 116.16 270.72 l 115.92 271.44 l f* 122.88 271.92 0.24 0.72 re f 122.4 272.64 m 126.72 273.36 l 126.96 272.64 l 122.4 271.92 l 122.4 272.64 l f* 128.64 273.84 m 132.96 274.8 l 133.2 274.08 l 128.64 273.12 l 128.64 273.84 l f* 135.6 274.56 0.24 0.72 re f 135.12 275.28 m 139.44 276 l 139.44 275.28 l 135.12 274.56 l 135.12 275.28 l f* 142.08 275.76 0.24 0.72 re f 141.36 276.48 m 145.92 277.2 l 145.92 276.72 l 141.6 275.76 l 141.36 276.48 l f* 148.56 277.68 m 148.56 277.2 l 148.56 277.68 l f* 147.84 277.68 m 152.16 279.12 l 152.16 278.4 l 148.08 277.2 l 147.84 277.68 l f* 154.32 279.84 m 154.8 279.84 l 154.8 279.36 l 154.56 279.12 l 154.32 279.84 l f* 154.08 279.84 m 158.4 280.8 l 158.64 280.08 l 154.32 279.36 l 154.08 279.84 l f* 161.28 281.28 m 161.28 280.56 l 161.28 281.28 l f* 160.56 281.28 m 164.88 282 l 165.12 281.52 l 160.8 280.56 l 160.56 281.28 l f* 167.52 282 0.24 0.48 re f 167.04 282.48 m 171.12 283.92 l 171.36 283.2 l 167.04 282 l 167.04 282.48 l f* 173.76 284.4 m 174 284.64 l 174.24 283.92 l 173.76 283.92 l 173.76 284.4 l f* 173.28 284.64 m 177.84 285.6 l 177.84 284.88 l 173.52 283.92 l 173.28 284.64 l f* 179.76 286.08 m 184.08 287.04 l 184.32 286.32 l 179.76 285.36 l 179.76 286.08 l f* 186.72 286.8 0.24 0.72 re f 186 287.52 m 190.56 288 l 190.56 287.52 l 186.24 286.8 l 186 287.52 l f* 193.2 288.48 m 193.2 288 l 193.2 288.48 l f* 192.48 288.48 m 196.8 289.2 l 197.04 288.48 l 192.72 288 l 192.48 288.48 l f* 198.72 289.68 m 203.04 290.64 l 203.28 289.92 l 198.96 288.96 l 198.72 289.68 l f* 205.68 290.64 0.24 0.48 re f 205.2 291.12 m 209.52 292.56 l 209.52 292.08 l 205.44 290.64 l 205.2 291.12 l f* 211.68 293.52 m 212.16 293.52 l 212.4 293.04 l 211.92 292.8 l 211.68 293.52 l f* 211.68 293.52 m 215.76 294.72 l 216 294.24 l 211.68 293.04 l 211.68 293.52 l f* 218.16 295.68 m 218.64 295.68 l 218.88 295.2 l 218.4 294.96 l 218.16 295.68 l f* 218.16 295.68 m 222.48 296.64 l 222.48 296.16 l 218.16 295.2 l 218.16 295.68 l f* 224.4 297.12 m 228.72 297.6 l 228.96 297.12 l 224.4 296.64 l 224.4 297.12 l f* 231.36 297.36 0.24 0.48 re f 230.64 297.84 m 235.2 298.8 l 235.2 298.32 l 230.88 297.36 l 230.64 297.84 l f* 237.84 299.28 m 237.84 298.8 l 237.84 299.28 l f* 237.12 299.28 m 241.44 300.24 l 241.44 299.76 l 237.36 298.8 l 237.12 299.28 l f* 244.08 300.24 0.24 0.72 re f 243.6 300.96 m 247.92 302.16 l 247.92 301.44 l 243.84 300.24 l 243.6 300.96 l f* 250.56 302.88 m 250.56 302.4 l 250.56 302.88 l f* 249.84 302.88 m 253.68 305.04 l 253.92 304.32 l 250.08 302.16 l 249.84 302.88 l f* 256.08 306 m 256.8 306.48 l 257.04 305.76 l 256.32 305.28 l 256.08 306 l f* BT 131.04 342.24 TD 0 0 0 rg /F4 7.2 Tf 0.0172 Tc 0.0212 Tw (original zero-crossing curves) Tj -40.56 -76.32 TD /F4 7.44 Tf -0.0566 Tc 0 Tw (0) Tj -4.08 9.36 TD (20) Tj 0 9.6 TD (40) Tj 0 9.36 TD (60) Tj 0 9.6 TD (80) Tj -4.08 9.36 TD (100) Tj 0 9.6 TD (120) Tj 19.2 -67.92 TD (1) Tj 12.72 0 TD (3) Tj 12.72 0 TD (5) Tj 12.96 0 TD (7) Tj 12.72 0 TD (9) Tj 10.8 0 TD (11) Tj 12.72 0 TD (13) Tj 12.72 0 TD (15) Tj 12.72 0 TD (17) Tj 12.96 0 TD (19) Tj 12.48 0 TD (21) Tj 12.96 0 TD (23) Tj 12.72 0 TD (25) Tj 12.72 0 TD (27) Tj ET 0.24 w 0 0 0 RG 76.08 245.76 201.84 107.28 re S 1 1 1 rg 77.04 122.16 200.16 107.04 re b 101.04 201.6 m 101.04 144 l S 98.88 144 m 101.04 144 l S 98.88 153.6 m 101.04 153.6 l S 98.88 163.2 m 101.04 163.2 l S 98.88 172.8 m 101.04 172.8 l S 98.88 182.4 m 101.04 182.4 l S 98.88 192 m 101.04 192 l S 98.88 201.6 m 101.04 201.6 l S 101.04 144 m 271.92 144 l S 101.04 141.84 m 101.04 144 l S 107.28 141.84 m 107.28 144 l S 113.76 141.84 m 113.76 144 l S 120 141.84 m 120 144 l S 126.24 141.84 m 126.24 144 l S 132.72 141.84 m 132.72 144 l S 138.96 141.84 m 138.96 144 l S 145.2 141.84 m 145.2 144 l S 151.68 141.84 m 151.68 144 l S 157.92 141.84 m 157.92 144 l S 164.4 141.84 m 164.4 144 l S 170.64 141.84 m 170.64 144 l S 177.12 141.84 m 177.12 144 l S 183.36 141.84 m 183.36 144 l S 189.6 141.84 m 189.6 144 l S 196.08 141.84 m 196.08 144 l S 202.32 141.84 m 202.32 144 l S 208.56 141.84 m 208.56 144 l S 215.04 141.84 m 215.04 144 l S 221.28 141.84 m 221.28 144 l S 227.76 141.84 m 227.76 144 l S 234 141.84 m 234 144 l S 240.48 141.84 m 240.48 144 l S 246.72 141.84 m 246.72 144 l S 253.2 141.84 m 253.2 144 l S 259.44 141.84 m 259.44 144 l S 265.68 141.84 m 265.68 144 l S 271.92 141.84 m 271.92 144 l S 0.72 w 0 0 0.502 RG 104.16 145.44 m 110.64 146.88 l 116.88 148.32 l 123.12 149.52 l 129.36 152.4 l 135.84 154.08 l 142.08 155.76 l 148.56 159.6 l 154.8 161.28 l 161.28 164.4 l 167.52 166.32 l 174 167.52 l 180.24 169.92 l 186.48 171.12 l 192.96 172.8 l 199.2 174.24 l 205.44 175.68 l 211.68 176.88 l 218.16 179.52 l 224.4 182.64 l 230.88 184.08 l 237.12 185.28 l 243.6 188.64 l 249.84 190.32 l 256.32 191.76 l S 0 0.2 0 rg 103.68 144.72 m 107.76 146.16 l 108 145.68 l 103.92 144 l 103.68 144.72 l f* 110.16 147.12 m 110.64 147.36 l 110.88 146.64 l 110.16 146.64 l 110.16 147.12 l f* 110.16 147.36 m 114.48 148.08 l 114.72 147.36 l 110.16 146.64 l 110.16 147.36 l f* 116.4 148.32 m 120.48 149.76 l 120.48 149.28 l 116.4 147.6 l 116.4 148.32 l f* 122.64 150.72 m 123.36 150.96 l 123.6 150.24 l 122.88 150.24 l 122.64 150.72 l f* 122.64 150.96 m 127.2 151.92 l 127.2 151.2 l 122.88 150.24 l 122.64 150.96 l f* 129.12 152.4 m 133.44 153.12 l 133.44 152.4 l 129.12 151.68 l 129.12 152.4 l f* 136.08 152.88 0.24 0.72 re f 135.36 153.6 m 139.44 155.52 l 139.44 154.8 l 135.6 152.88 l 135.36 153.6 l f* 141.6 156.72 m 142.32 156.96 l 142.56 156.48 l 141.84 156 l 141.6 156.72 l f* 141.6 156.96 m 145.68 159.12 l 145.68 158.16 l 141.84 156.24 l 141.6 156.96 l f* 147.84 160.08 m 148.8 160.56 l 148.8 159.84 l 148.08 159.36 l 147.84 160.08 l f* 148.08 160.56 m 152.4 161.52 l 152.64 160.8 l 148.32 160.08 l 148.08 160.56 l f* 154.32 162 m 158.64 163.68 l 158.64 162.96 l 154.56 161.28 l 154.32 162 l f* 161.04 164.4 m 161.28 164.4 l 161.52 163.92 l 161.04 163.68 l 161.04 164.4 l f* 160.8 164.4 m 165.12 165.12 l 165.36 164.4 l 161.04 163.92 l 160.8 164.4 l f* 167.04 165.6 m 171.36 166.56 l 171.36 165.84 l 167.28 164.88 l 167.04 165.6 l f* 174 166.56 0.24 0.48 re f 173.52 167.04 m 177.6 168.72 l 177.84 168 l 173.52 166.56 l 173.52 167.04 l f* 180 169.44 m 180.24 169.68 l 180.48 168.96 l 180.24 168.96 l 180 169.44 l f* 179.76 169.68 m 183.84 170.88 l 184.08 170.16 l 179.76 168.96 l 179.76 169.68 l f* 186.24 171.6 m 186.72 171.84 l 186.96 171.12 l 186.48 171.12 l 186.24 171.6 l f* 186 171.84 m 190.56 172.8 l 190.56 172.08 l 186.24 171.12 l 186 171.84 l f* 192.48 173.28 m 196.8 173.76 l 196.8 173.04 l 192.48 172.56 l 192.48 173.28 l f* 198.72 174 m 203.04 174.96 l 203.28 174.24 l 198.72 173.28 l 198.72 174 l f* 205.68 174.72 0.24 0.72 re f 204.96 175.44 m 209.28 176.4 l 209.52 175.68 l 205.2 174.72 l 204.96 175.44 l f* 211.92 176.4 0.24 0.48 re f 211.2 176.88 m 215.52 178.32 l 215.76 177.6 l 211.44 176.4 l 211.2 176.88 l f* 217.92 179.04 m 218.4 179.04 l 218.4 178.56 l 217.92 178.32 l 217.92 179.04 l f* 217.68 179.04 m 221.52 181.2 l 221.76 180.48 l 217.92 178.32 l 217.68 179.04 l f* 223.92 182.16 0.96 0.24 re f 223.92 182.64 m 228.24 183.6 l 228.48 183.12 l 224.16 182.16 l 223.92 182.64 l f* 230.88 183.6 0.24 0.72 re f 230.4 184.32 m 234.72 185.28 l 234.96 184.56 l 230.64 183.6 l 230.4 184.32 l f* 236.64 185.76 m 240.96 187.2 l 240.96 186.72 l 236.88 185.04 l 236.64 185.76 l f* 243.12 187.68 0.72 0.24 re f 243.12 188.16 m 247.2 189.36 l 247.44 188.64 l 243.12 187.68 l 243.12 188.16 l f* 249.84 189.36 0.24 0.72 re f 249.36 190.08 m 253.68 191.04 l 253.92 190.32 l 249.6 189.36 l 249.36 190.08 l f* 256.32 190.8 0.24 0.72 re f BT 126.24 218.4 TD 0 0 0 rg /F4 7.2 Tf 0.0203 Tc -0.1019 Tw (zero-crossing curves after DTW) Tj -34.8 -76.8 TD 0.0768 Tc 0 Tw (0) Tj -4.08 9.36 TD (20) Tj 0 9.84 TD (40) Tj 0 9.36 TD (60) Tj 0 9.84 TD (80) Tj -4.08 9.36 TD (100) Tj 0 9.84 TD (120) Tj 18.72 -68.16 TD (1) Tj 12.72 0 TD (3) Tj 12.72 0 TD (5) Tj 12.72 0 TD (7) Tj 12.72 0 TD (9) Tj 10.56 0 TD (11) Tj 12.72 0 TD (13) Tj 12.72 0 TD (15) Tj 12.48 0 TD (17) Tj 12.72 0 TD (19) Tj 12.72 0 TD (21) Tj 12.72 0 TD (23) Tj 12.72 0 TD (25) Tj 12.48 0 TD (27) Tj ET 0.24 w 0 0 0 RG 77.04 122.16 200.16 107.04 re S BT 67.68 99.36 TD /F0 10.08 Tf 0 Tc 0.1195 Tw (Figure 5) Tj 36 0 TD /F1 10.08 Tf -0.0593 Tc 0.1393 Tw ( Effect of DTW over zero-crossings extracted) Tj -41.76 -11.52 TD -0.049 Tc 0.139 Tw (from original samples of signatures from the same writer.) Tj 255.6 622.8 TD /F0 10.08 Tf -0.0523 Tc 0.0923 Tw (3.4 Function-based feature extraction) Tj 0 -15.36 TD /F1 10.08 Tf -0.0354 Tc 0.8411 Tw (Basically, the method that includes the wavelet transform) Tj 0 -12 TD -0.0611 Tc 1.6211 Tw (consists of the computation of distances between sets of) Tj T* -0.0631 Tc 1.3831 Tw (features aligned with DTW. In this second approach, we) Tj T* -0.046 Tc 2.0174 Tw (extract the features directly from the normalized curves) Tj T* -0.0349 Tc 3.5149 Tw (x\(t\) and y\(t\) that describe the signature, without any) Tj T* -0.0535 Tc 1.3735 Tw (transformation. In this case, there are only two distances) Tj T* -0.0261 Tc 1.7994 Tw (that can be defined: the minimum that returns from the) Tj T* -0.0487 Tc 0.4087 Tw (DTW between the non-transformed curves and the area of) Tj T* -0.035 Tc 3.8921 Tw (the difference between the warping function and the) Tj T* -0.0283 Tc 0.4363 Tw (corresponding diagonal. This drastically simplifies feature) Tj T* -0.0586 Tc 2.1706 Tw (extraction, but the DTW has now to be applied over ) Tj 2.2445 Tc 0 Tw (a) Tj T* -0.0406 Tc 0.9872 Tw (much bigger number of points than when the only points) Tj T* -0.0685 Tc 2.3143 Tw (to be considered were the zero-crossings from function) Tj T* -0.0669 Tc 2.7309 Tw (WD4. To deal with this great amount of points in an) Tj T* -0.0537 Tc 0.448 Tw (efficient manner, we developed a non-recursive version of) Tj T* -0.0419 Tc 0.2819 Tw (the DTW algorithm.) Tj 81.84 0 TD 1 0 0 rg 0 Tc 0.12 Tw ( ) Tj 2.88 0 TD 0 0 0 rg -0.0455 Tc 0.4055 Tw (Accordingly, in this case the warping) Tj -84.72 -12 TD -0.0481 Tc 1.1014 Tw (function presents shapes like the one showed in Figure ) Tj 1.44 Tc 0 Tw (6) Tj 0 -12 TD -0.061 Tc 1.221 Tw (\(in comparison to Figure 4\). We are again assuming that) Tj T* -0.043 Tc 5.763 Tw (two signatures produced with too different writing) Tj T* -0.0475 Tc 0.5875 Tw (velocity profiles tend to present a much more pronounced) Tj T* -0.0467 Tc 0.1667 Tw (warping effect.) Tj ET 353.76 299.28 m 353.76 434.88 l S 353.76 299.28 m 526.08 299.28 l S 353.76 299.28 m 353.76 434.88 l S 369.36 299.28 m 369.36 300.96 l S q 364.8 290.16 9.12 7.44 re W n BT 364.8 291.12 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (20) Tj ET Q 386.16 299.28 m 386.16 300.96 l S q 381.84 290.16 8.64 7.44 re W n BT 381.84 291.12 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (40) Tj ET Q 402.48 299.28 m 402.48 300.96 l S q 397.92 290.16 8.88 7.44 re W n BT 397.92 291.12 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (60) Tj ET Q 419.04 299.28 m 419.04 300.96 l S q 414.72 290.16 8.88 7.44 re W n BT 414.72 291.12 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (80) Tj ET Q 435.36 299.28 m 435.36 300.96 l S q 429.84 290.16 12 7.44 re W n BT 429.84 291.12 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (100) Tj ET Q 452.16 299.28 m 452.16 300.96 l S q 446.64 290.16 11.76 7.44 re W n BT 446.64 291.12 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (120) Tj ET Q 468.48 299.28 m 468.48 300.96 l S q 462.96 290.16 11.76 7.44 re W n BT 462.96 291.12 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (140) Tj ET Q 484.8 299.28 m 484.8 300.96 l S q 479.28 290.16 11.76 7.44 re W n BT 479.28 291.12 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (160) Tj ET Q 501.36 299.28 m 501.36 300.96 l S q 495.84 290.16 12 7.44 re W n BT 495.84 291.12 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (180) Tj ET Q 517.68 299.28 m 517.68 300.96 l S q 512.16 290.16 12 7.44 re W n BT 512.16 291.12 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (200) Tj ET Q 353.76 312 m 355.44 312 l S q 344.64 307.68 8.88 7.44 re W n BT 344.64 308.64 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (20) Tj ET Q 353.76 325.2 m 355.44 325.2 l S q 345.12 320.88 8.88 7.44 re W n BT 345.12 321.84 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (40) Tj ET Q 353.76 338.64 m 355.44 338.64 l S q 344.64 334.32 8.88 7.44 re W n BT 344.64 335.28 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (60) Tj ET Q 353.76 351.84 m 355.44 351.84 l S q 344.64 347.28 8.88 7.68 re W n BT 344.64 348.48 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (80) Tj ET Q 353.76 364.8 m 355.44 364.8 l S q 341.28 360.48 12 7.68 re W n BT 341.28 361.68 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (100) Tj ET Q 353.76 378.24 m 355.44 378.24 l S q 340.8 374.16 12 7.44 re W n BT 340.8 375.12 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (120) Tj ET Q 353.76 391.44 m 355.44 391.44 l S q 340.8 387.12 12 7.44 re W n BT 340.8 388.08 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (140) Tj ET Q 353.76 405.12 m 355.44 404.88 l S q 340.8 400.8 12 7.44 re W n BT 340.8 401.76 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (160) Tj ET Q 353.76 418.08 m 355.44 418.08 l S q 340.8 413.76 12 7.44 re W n BT 340.8 414.96 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (180) Tj ET Q 353.76 431.76 m 355.44 431.76 l S q 340.8 427.2 12 7.68 re W n BT 340.8 428.4 TD /F4 6.96 Tf -0.0298 Tc 0 Tw (200) Tj ET Q 353.76 299.28 m 353.76 434.88 l S 353.76 299.28 m 354.72 300 l 355.44 300.48 l 357.12 302.16 l 357.84 302.4 l 358.8 303.36 l 359.76 303.84 l 360.48 304.56 l 361.44 305.28 l 362.16 305.52 l 363.84 307.2 l 364.56 307.68 l 365.52 308.4 l 366 308.88 l 366.96 309.6 l 367.68 310.56 l 368.64 310.8 l 369.36 311.76 l 370.08 312.24 l 371.28 312.96 l 372.24 313.44 l 372.96 314.4 l 373.68 314.88 l 374.4 315.6 l 375.36 316.08 l 376.8 317.52 l 377.76 318 l 378.48 318.72 l 379.2 319.68 l 380.16 319.92 l 380.88 320.88 l 381.84 321.12 l 382.8 321.84 l 383.52 322.8 l 384.48 323.04 l 385.2 324 l 386.16 324.72 l 386.88 325.2 l 388.56 326.88 l 389.04 327.12 l 390 328.08 l 390.72 328.32 l 391.68 329.28 l 393.12 330.24 l 394.32 330.96 l 395.28 331.92 l 396 332.4 l 396.72 333.12 l 397.44 333.6 l 399.36 335.04 l 399.84 335.52 l 400.8 336.24 l 401.52 337.2 l 402.48 337.44 l 403.2 338.16 l 403.92 339.12 l 404.88 339.36 l 406.08 340.32 l 406.8 340.56 l 407.52 341.52 l 408.24 342.24 l 409.2 342.72 l 410.64 344.16 l 411.6 344.64 l 412.08 345.36 l 413.04 345.84 l 414 346.56 l 414.72 347.28 l 415.44 347.76 l 416.16 348.48 l 417.36 349.44 l 418.32 349.68 l 419.04 350.64 l 419.76 351.36 l 420.72 351.84 l 421.44 352.56 l 422.4 352.8 l 422.88 353.76 l 423.84 354.48 l 424.56 354.96 l 425.52 355.68 l 426.24 356.64 l 426.96 356.88 l 427.92 357.84 l 429.12 358.08 l 429.84 359.04 l 430.56 359.52 l 431.28 360.24 l 432.24 360.96 l 432.96 361.68 l 433.68 362.16 l 434.64 362.88 l 435.36 363.6 l 436.08 364.08 l 437.04 364.8 l 437.76 365.28 l 438.72 366 l 439.2 366.96 l 440.4 367.2 l 442.08 368.88 l 443.04 369.12 l 443.76 370.08 l 444.48 370.32 l 446.16 372 l 446.88 372.48 l 447.6 373.2 l 448.56 373.92 l 449.28 374.4 l 450 375.36 l 450.96 375.84 l 452.16 376.56 l 453.6 377.52 l 455.28 379.2 l 456 379.68 l 456.72 380.4 l 457.68 381.12 l 458.4 381.6 l 459.12 382.32 l 460.08 382.8 l 461.76 384.48 l 462.24 384.72 l 463.44 385.44 l 464.4 386.4 l 465.12 386.64 l 466.8 388.32 l 467.52 388.8 l 468.48 389.52 l 469.2 390 l 470.64 391.44 l 471.6 391.92 l 473.04 393.36 l 474 393.84 l 475.2 394.56 l 475.92 395.04 l 477.6 396.72 l 478.32 397.2 l 479.28 397.92 l 479.76 398.64 l 480.72 399.12 l 482.4 400.8 l 483.12 401.04 l 483.84 401.76 l 484.8 402.24 l 485.28 402.96 l 486.72 403.92 l 487.44 404.16 l 488.16 405.12 l 489.12 405.84 l 490.56 406.8 l 491.52 407.52 l 492.96 408.96 l 493.92 409.44 l 495.36 410.88 l 496.08 411.36 l 497.04 412.08 l 498.24 413.04 l 498.96 413.28 l 499.68 414.24 l 500.64 414.48 l 501.36 415.44 l 502.32 416.16 l 502.8 416.4 l 504.48 418.08 l 505.44 418.56 l 506.16 419.28 l 506.88 419.76 l 507.84 420.48 l 508.56 421.2 l 509.76 421.68 l 510.48 422.64 l 511.2 423.12 l 512.16 423.84 l 512.88 424.32 l 513.6 425.28 l 514.56 425.76 l 515.28 426.48 l 516 426.96 l 516.96 427.68 l 517.68 428.4 l 518.64 428.88 l 519.12 429.6 l 520.08 430.56 l 521.28 430.8 l 522 431.76 l 522.96 432 l 523.68 432.72 l 524.4 433.68 l 525.36 433.92 l 526.08 434.88 l S 526.08 434.88 m 524.4 433.92 l 522.96 433.68 l 521.28 432.72 l 519.12 432 l 517.68 431.76 l 516 430.8 l 514.56 430.08 l 512.88 429.6 l 512.16 428.16 l 511.2 426.96 l 510.48 425.76 l 509.76 424.08 l 508.56 423.84 l 506.88 422.88 l 505.44 422.16 l 503.76 421.68 l 502.32 420.96 l 500.64 420 l 498.96 419.76 l 497.04 418.8 l 495.36 418.08 l 494.64 417.6 l 493.92 416.16 l 492.96 415.92 l 491.52 414.96 l 489.84 414.24 l 489.12 413.04 l 488.16 411.36 l 487.44 410.16 l 483.84 408.96 l 483.12 408.24 l 482.4 406.8 l 481.44 405.36 l 480.72 405.12 l 479.28 404.16 l 477.6 403.44 l 476.64 402.24 l 475.92 401.04 l 475.2 399.6 l 474 398.4 l 473.04 397.2 l 472.32 395.52 l 471.6 394.32 l 470.64 393.12 l 469.92 391.44 l 468.48 389.04 l 467.52 387.6 l 466.8 387.12 l 466.08 385.44 l 465.12 384.48 l 464.4 383.28 l 463.44 381.6 l 461.76 381.12 l 458.4 379.68 l 456.72 379.2 l 455.28 378.24 l 453.6 377.52 l 452.16 377.04 l 450.96 375.6 l 450 374.4 l 449.28 373.2 l 448.56 372.48 l 447.6 371.28 l 446.88 370.32 l 446.16 369.12 l 445.44 367.68 l 443.76 366.96 l 442.08 366.48 l 440.4 365.76 l 439.2 364.8 l 437.76 364.56 l 437.04 362.88 l 436.08 361.68 l 435.36 360.48 l 434.64 359.04 l 433.68 357.84 l 432.96 356.64 l 432.24 355.68 l 431.28 354.48 l 430.56 352.8 l 429.84 352.56 l 427.92 351.84 l 426.24 351.12 l 424.56 350.64 l 423.84 349.68 l 422.88 348.48 l 422.4 347.04 l 421.44 345.84 l 420.72 344.88 l 419.04 344.64 l 418.32 342.96 l 417.36 341.76 l 416.16 340.56 l 415.44 339.12 l 414 338.64 l 412.08 337.92 l 410.64 337.2 l 409.2 336.72 l 407.52 336 l 406.8 335.04 l 406.08 333.84 l 403.92 333.12 l 403.2 332.64 l 402.48 331.92 l 400.8 330.96 l 399.84 329.76 l 399.36 328.56 l 398.4 327.12 l 397.44 326.88 l 396 325.92 l 394.32 325.2 l 393.12 324.72 l 392.4 323.04 l 391.68 322.8 l 390 321.84 l 388.56 321.12 l 386.88 320.4 l 385.2 319.92 l 384.48 318.48 l 383.52 317.28 l 381.84 316.32 l 380.16 316.08 l 378.48 315.12 l 376.8 314.4 l 375.36 313.92 l 373.68 313.2 l 372.24 312.24 l 371.28 312 l 369.36 311.28 l 367.68 310.56 l 366.96 309.36 l 366 308.16 l 364.56 307.2 l 363.84 306.48 l 363.12 306.24 l 361.44 305.28 l 359.76 304.56 l 357.84 304.08 l 356.16 303.36 l 355.44 302.16 l 354.72 300.48 l 353.76 299.28 l S 525.84 300 m 525.84 435.36 l S 353.76 435.12 m 526.08 435.12 l S 0.48 w 489.84 404.4 m 494.64 389.52 l S BT 480.72 381.36 TD /F1 8.4 Tf -0.0329 Tc 0 Tw (without) Tj 0 -9.84 TD -0.0267 Tc (alignment) Tj -94.8 37.44 TD -0.0138 Tc -0.1662 Tw (with ) Tj 17.04 0 TD -0.0267 Tc 0 Tw (alignment) Tj ET 439.92 409.44 m 474.72 404.4 l S BT 332.88 266.4 TD /F0 10.08 Tf 0 Tc 0.1195 Tw (Figure 6) Tj 36 0 TD /F1 10.08 Tf -0.0505 Tc 0.1305 Tw ( Typical optimal path obtained with DTW) Tj -46.56 -11.52 TD -0.0424 Tc 0.1024 Tw (directly applied to the coordinate functions x\(t\) and y\(t\).) Tj -4.8 -24 TD /F0 10.08 Tf -0.037 Tc 0.157 Tw (3.5 Reference signatures) Tj 0 -15.36 TD /F1 10.08 Tf -0.0624 Tc 2.7538 Tw (During an enrolment stage, 10 sample signatures from) Tj 0 -12 TD -0.0503 Tc 3.4274 Tw (each writer to be enrolled are collected and) Tj 0 Tc 0.12 Tw ( ) Tj 201.36 0 TD -0.0389 Tc 0 Tw (pairwise) Tj -201.36 -12 TD -0.0562 Tc 2.8162 Tw (distances between them are computed. Based on these) Tj 0 -12 TD -0.0355 Tc 0.7155 Tw (distances, a reference signature is selected as the one that) Tj T* -0.0575 Tc 1.1718 Tw (presents minimal overall distance to the others. Actually,) Tj T* -0.0554 Tc 3.002 Tw (to each of the 10 signatures, we create a ) Tj 2.88 Tc 0 Tw (9) Tj 193.2 0 TD /F3 10.08 Tf -0.0139 Tc (\264) Tj 5.52 0 TD /F1 10.08 Tf -0.057 Tc 3.057 Tw (8 matrix) Tj -198.72 -12 TD -0.0564 Tc 1.9524 Tw (containing the 8 distances defined \(4 for x\(t\) and 4 for) Tj 0 -12 TD -0.0418 Tc 1.1698 Tw (y\(t\)\) to each of the other signatures. The reference is the) Tj T* -0.0499 Tc 3.5699 Tw (signature whose distance matrix presents the minimal) Tj T* -0.0558 Tc 0 Tw (norm.) Tj ET endstream endobj 35 0 obj 28664 endobj 33 0 obj << /Type /Page /Parent 5 0 R /Resources << /Font << /F0 6 0 R /F1 8 0 R /F3 18 0 R /F4 22 0 R >> /ProcSet 2 0 R >> /Contents 34 0 R >> endobj 38 0 obj << /Length 39 0 R >> stream BT 79.44 710.4 TD 0 0 0 rg /F1 10.08 Tf -0.0383 Tc 0.8783 Tw (The distances calculated in this step are also used to) Tj -19.92 -12 TD -0.0394 Tc 5.8594 Tw (produce the 8 thresholds to be tested during the) Tj 0 -12 TD -0.0317 Tc 2.0032 Tw (verification stage. Each threshold is computed from the) Tj T* -0.0275 Tc 1.8275 Tw (averages ) Tj 1.6834 Tc 0 Tw (\() Tj ET q 102 671.28 9.12 12 re W n BT 103.68 673.92 TD /F1 10.8 Tf 0.12 Tc (d) Tj ET Q BT 111.12 674.4 TD -0.0541 Tc 1.8541 Tw (\) and standard deviations \(s\) of all possible) Tj -51.6 -12 TD -0.0393 Tc 6.7993 Tw (pairwise distances associated with the 10 sample) Tj 0 -12 TD -0.0393 Tc 0.0393 Tw (signatures, according to:) Tj ET 0.48 w 1 J 1 j 0 0 0 RG 152.88 632.88 m 158.4 632.88 l S BT 196.8 623.28 TD /F1 10.8 Tf 0.1188 Tc 0 Tw (s) Tj -20.16 0 TD 0.12 Tc (96) Tj -2.64 0 TD -0.06 Tc (.) Tj -5.52 0 TD 0.12 Tc (1) Tj -15.6 0 TD (d) Tj -17.52 0 TD -0.1188 Tc (L) Tj 53.76 0 TD /F3 10.8 Tf 0.0708 Tc (\264) Tj -28.08 0 TD (+) Tj -16.8 0 TD (=) Tj 60.24 0.48 TD /F1 10.08 Tf 0 Tc -0.02 Tw ( ) Tj 70.8 0 TD 0.0017 Tc 0.1183 Tw ( \(12\)) Tj -215.76 -24 TD -0.0462 Tc 1.7396 Tw (where the value 1.96 is chosen to assure that, assuming) Tj 0 -12 TD -0.0396 Tc 1.6681 Tw (normal distribution for the distances originated from the) Tj T* -0.0506 Tc 3.4963 Tw (same writer, 97.5% of the distances between original) Tj T* -0.0354 Tc 0.0754 Tw (signatures and references lie under this threshold.) Tj 0 -29.76 TD /F0 10.08 Tf -0.0659 Tc 0.1859 Tw (3.6 Verification) Tj 0 -15.36 TD /F1 10.08 Tf -0.0511 Tc 1.3026 Tw (A test signature, after passing through preprocessing and) Tj 0 -12 TD -0.0429 Tc 6.2029 Tw (feature extraction, is compared with the reference) Tj T* -0.0581 Tc 4.5324 Tw (signature to that writer. The verification consists of) Tj T* -0.0648 Tc 0.7182 Tw (checking if all defined 8 distances thus obtained lie under) Tj T* -0.0468 Tc 0.1668 Tw (the thresholds given by equation \(12\).) Tj 0 -29.52 TD /F0 10.08 Tf -0.0397 Tc 0.0397 Tw (4. Experimental results) Tj 0 -15.36 TD /F1 10.08 Tf -0.0517 Tc 1.9889 Tw (The proposed methodology was tested with the original) Tj 0 -12 TD -0.0414 Tc 0.47 Tw (signatures and the forgeries previously acquired. The tests) Tj T* -0.0384 Tc 0.1927 Tw (consisted in determining false acceptation rates \(FAR\) and) Tj T* -0.0473 Tc 4.0339 Tw (false rejection rates \(FRR\) to each of the 4 writers) Tj T* -0.0438 Tc 0.3696 Tw (enrolled during data acquisition. Tests were executed with) Tj T* -0.0603 Tc 1.6203 Tw (the mother wavelets) Tj 0 Tc -0.12 Tw ( ) Tj 87.36 0 TD -0.0421 Tc 1.6021 Tw (Daubechies 1 ) Tj 1.4434 Tc 0 Tw (\() Tj 63.12 0 TD -0.0837 Tc -0.0363 Tw (Haar\), ) Tj 29.04 0 TD -0.0463 Tc 1.8463 Tw (Daubechies ) Tj 1.92 Tc 0 Tw (6) Tj -179.52 -12 TD -0.0189 Tc 0.1389 Tw (\(db6\), ) Tj 27.84 0 TD -0.0634 Tc 1.1434 Tw (Daubechies 10 \(db10\) and) Tj 0 Tc -0.12 Tw ( ) Tj 111.6 0 TD -0.0508 Tc 1.2508 Tw (Biorthogonal 5.5 ) Tj 1.2034 Tc 0 Tw (\() Tj 75.84 0 TD -0.0564 Tc (Bior.) Tj -215.28 -12 TD -0.0512 Tc 2.4752 Tw (5.5\), at different levels of resolution \(3, 4 and 5\). We) Tj 0 -12 TD -0.0351 Tc 0.7036 Tw (included also a test in which the ) Tj 0.96 Tc 0 Tw (4) Tj 140.4 4.56 TD /F1 6.48 Tf 0.1193 Tc (th) Tj 5.04 -4.56 TD /F1 10.08 Tf -0.0238 Tc 0.8638 Tw ( dissimilarity measure) Tj -145.44 -12 TD -0.052 Tc 2.6406 Tw (\(area between warping function and diagonal\) was not) Tj 0 -12 TD -0.0097 Tc 0 Tw (considered.) Tj 19.92 -18 TD -0.0472 Tc 1.3329 Tw (According to preliminary tests, we chose a standard) Tj -19.92 -12 TD -0.0144 Tc 1.3344 Tw (configuration as:) Tj 0 Tc 0.12 Tw ( ) Tj 72.96 0 TD -0.0485 Tc 1.6428 Tw (db 6 and level of resolution 4. Results) Tj -72.96 -12 TD -0.0523 Tc 1.2223 Tw (for this configuration are presented in Table 1. Although) Tj 0 -12 TD -0.0575 Tc 1.3508 Tw (the FRR may be significant, there was no acceptation of) Tj T* -0.0392 Tc 3.2259 Tw (forgeries at all. It should be noted that, according to) Tj T* -0.0549 Tc 1.3406 Tw (practical considerations, it would be possible to decrease) Tj T* -0.0565 Tc 1.0405 Tw (FRR by relaxing the thresholds, but in this case the FAR) Tj T* -0.052 Tc 0.5148 Tw (would increase. The standard configuration was chosen in) Tj T* -0.0656 Tc 4.5656 Tw (order to provide maximum security) Tj 0 Tc -0.36 Tw ( ) Tj 166.08 0 TD -0.0316 Tc 4.7116 Tw (aginst forgeries,) Tj -166.08 -12 TD -0.058 Tc 1.298 Tw (without taking into account any troubles to the writer by) Tj 0 -12 TD -0.0416 Tc 0.0816 Tw (having original signatures rejected.) Tj 35.28 -28.8 TD -0.0389 Tc 0.1589 Tw (Table 1. ) Tj 35.52 0 TD -0.0437 Tc 0.0837 Tw (db 6, level 4, including distance 4.) Tj -12 -12.24 TD 0.013 Tc 0.107 Tw (Writer 1) Tj 41.76 0 TD (Writer 2) Tj 41.52 0 TD (Writer 3) Tj 42 0 TD (Writer 4) Tj ET 114.24 135.84 0.48 0.48 re f 114.24 135.84 0.48 0.48 re f 114.72 135.84 41.28 0.48 re f 156 135.84 0.48 0.48 re f 156.48 135.84 41.04 0.48 re f 197.52 135.84 0.48 0.48 re f 198 135.84 41.28 0.48 re f 239.28 135.84 0.48 0.48 re f 239.76 135.84 41.28 0.48 re f 281.04 135.84 0.48 0.48 re f 281.04 135.84 0.48 0.48 re f 114.24 124.32 0.48 11.52 re f 156 124.32 0.48 11.52 re f 197.52 124.32 0.48 11.52 re f 239.28 124.32 0.48 11.52 re f 281.04 124.32 0.48 11.52 re f BT 84 114.72 TD -0.0552 Tc 0 Tw (FAR) Tj 44.64 0 TD 0.0017 Tc (0%) Tj 41.76 0 TD (0%) Tj 41.52 0 TD (0%) Tj 41.76 0 TD (0%) Tj ET 72.48 123.84 0.24 0.48 re f 72.72 123.84 0.48 0.48 re f 73.2 123.84 41.04 0.48 re f 114.24 123.84 0.48 0.48 re f 114.72 123.84 41.28 0.48 re f 156 123.84 0.48 0.48 re f 156.48 123.84 41.04 0.48 re f 197.52 123.84 0.48 0.48 re f 198 123.84 41.28 0.48 re f 239.28 123.84 0.48 0.48 re f 239.76 123.84 41.28 0.48 re f 281.04 123.84 0.48 0.48 re f 72.72 112.32 0.48 11.52 re f 114.24 112.32 0.48 11.52 re f 156 112.32 0.48 11.52 re f 197.52 112.32 0.48 11.52 re f 239.28 112.32 0.48 11.52 re f 281.04 112.32 0.48 11.52 re f BT 84.24 102.72 TD -0.0304 Tc (FRR) Tj 41.76 0 TD 0.0011 Tc (37%) Tj 41.76 0 TD (23%) Tj 41.52 0 TD (30%) Tj 42 0 TD (40%) Tj ET 72.72 111.84 0.48 0.48 re f 73.2 111.84 41.04 0.48 re f 114.24 111.84 0.48 0.48 re f 114.72 111.84 41.28 0.48 re f 156 111.84 0.48 0.48 re f 156.48 111.84 41.04 0.48 re f 197.52 111.84 0.48 0.48 re f 198 111.84 41.28 0.48 re f 239.28 111.84 0.48 0.48 re f 239.76 111.84 41.28 0.48 re f 281.04 111.84 0.48 0.48 re f 72.72 100.32 0.48 11.52 re f 72.72 99.84 0.48 0.48 re f 72.72 99.84 0.48 0.48 re f 73.2 99.84 41.04 0.48 re f 114.24 100.32 0.48 11.52 re f 114.24 99.84 0.48 0.48 re f 114.72 99.84 41.28 0.48 re f 156 100.32 0.48 11.52 re f 156 99.84 0.48 0.48 re f 156.48 99.84 41.04 0.48 re f 197.52 100.32 0.48 11.52 re f 197.52 99.84 0.48 0.48 re f 198 99.84 41.28 0.48 re f 239.28 100.32 0.48 11.52 re f 239.28 99.84 0.48 0.48 re f 239.76 99.84 41.28 0.48 re f 281.04 100.32 0.48 11.52 re f 281.04 99.84 0.48 0.48 re f 281.04 99.84 0.48 0.48 re f BT 337.44 698.88 TD -0.0644 Tc 1.5444 Tw (The tests showed in Table 2 justify the adoption of) Tj -19.92 -12 TD -0.0266 Tc 3.5666 Tw (level 4 as the reference. Although presenting a light) Tj 0 -12 TD -0.0495 Tc 2.1375 Tw (decreasing in FRR on the average, the data in Table ) Tj 2.4 Tc 0 Tw (2) Tj T* -0.0348 Tc 2.2548 Tw (show unacceptable values to the FAR, meaning that at) Tj T* 0 Tc 0.1193 Tw (levels other than the 4) Tj 88.8 4.56 TD /F1 6.48 Tf 0.1193 Tc 0 Tw (th) Tj 5.04 -4.56 TD /F1 10.08 Tf -0.0731 Tc 0.4331 Tw ( , this verification system would be) Tj -93.84 -12 TD -0.042 Tc 0.162 Tw (unsafe for the cases studied.) Tj 0 -24.24 TD -0.0465 Tc 1.9531 Tw (Table 2. Mother wavelet db6, levels 3 and 5, including) Tj 0 -11.28 TD -0.0512 Tc 0.1712 Tw (distance 4.) Tj 7.92 -23.76 TD -0.0727 Tc 0 Tw (Resolution) Tj 12 -11.52 TD -0.1271 Tc (level) Tj 43.92 11.52 TD -0.0778 Tc (Error) Tj 0.24 -11.52 TD -0.0149 Tc (taxes) Tj 32.88 11.52 TD -0.0648 Tc (Writer) Tj 10.56 -11.52 TD 0 Tc (1) Tj 24.72 11.52 TD -0.0648 Tc (Writer) Tj 10.56 -11.52 TD 0 Tc (2) Tj 24.72 11.52 TD -0.0648 Tc (Writer) Tj 10.56 -11.52 TD 0 Tc (3) Tj 24 11.52 TD -0.0648 Tc (Writer) Tj 10.56 -11.52 TD 0 Tc (4) Tj ET 320.16 588.72 0.48 0.48 re f 320.16 588.72 0.48 0.48 re f 320.64 588.72 53.28 0.48 re f 373.92 588.72 0.48 0.48 re f 374.4 588.72 35.04 0.48 re f 409.44 588.72 0.48 0.48 re f 409.92 588.72 35.04 0.48 re f 444.96 588.72 0.48 0.48 re f 445.44 588.72 34.8 0.48 re f 480.24 588.72 0.48 0.48 re f 480.72 588.72 35.04 0.48 re f 515.76 588.72 0.48 0.48 re f 516.24 588.72 33.36 0.48 re f 549.6 588.72 0.48 0.48 re f 549.6 588.72 0.48 0.48 re f 320.16 565.68 0.48 23.04 re f 373.92 565.68 0.48 23.04 re f 409.44 565.68 0.48 23.04 re f 444.96 565.68 0.48 23.04 re f 480.24 565.68 0.48 23.04 re f 515.76 565.68 0.48 23.04 re f 549.6 565.68 0.48 23.04 re f BT 382.32 556.08 TD -0.0552 Tc (FAR) Tj 38.4 0 TD 0.0017 Tc (0%) Tj 32.88 0 TD 0.0011 Tc (23%) Tj 37.92 0 TD 0.0017 Tc (3%) Tj 31.92 0 TD 0.0011 Tc (23%) Tj ET 320.16 565.2 0.48 0.48 re f 320.64 565.2 53.28 0.48 re f 373.92 565.2 0.48 0.48 re f 374.4 565.2 35.04 0.48 re f 409.44 565.2 0.48 0.48 re f 409.92 565.2 35.04 0.48 re f 444.96 565.2 0.48 0.48 re f 445.44 565.2 34.8 0.48 re f 480.24 565.2 0.48 0.48 re f 480.72 565.2 35.04 0.48 re f 515.76 565.2 0.48 0.48 re f 516.24 565.2 33.36 0.48 re f 549.6 565.2 0.48 0.48 re f 320.16 553.68 0.48 11.52 re f 373.92 553.68 0.48 11.52 re f 409.44 553.68 0.48 11.52 re f 444.96 553.68 0.48 11.52 re f 480.24 553.68 0.48 11.52 re f 515.76 553.68 0.48 11.52 re f 549.6 553.68 0.48 11.52 re f BT 341.76 556.08 TD 0 Tc (3) Tj 5.04 4.56 TD /F1 6.48 Tf 0.0611 Tc (rd) Tj 35.76 -16.56 TD /F1 10.08 Tf -0.0304 Tc (FRR) Tj 35.76 0 TD 0.0011 Tc (23%) Tj 35.28 0 TD (13%) Tj 35.28 0 TD (40%) Tj 34.56 0 TD (37%) Tj ET 320.16 553.2 0.48 0.48 re f 373.92 553.2 0.48 0.48 re f 374.4 553.2 35.04 0.48 re f 409.44 553.2 0.48 0.48 re f 409.92 553.2 35.04 0.48 re f 444.96 553.2 0.48 0.48 re f 445.44 553.2 34.8 0.48 re f 480.24 553.2 0.48 0.48 re f 480.72 553.2 35.04 0.48 re f 515.76 553.2 0.48 0.48 re f 516.24 553.2 33.36 0.48 re f 549.6 553.2 0.48 0.48 re f 320.16 541.68 0.48 11.52 re f 373.92 541.68 0.48 11.52 re f 409.44 541.68 0.48 11.52 re f 444.96 541.68 0.48 11.52 re f 480.24 541.68 0.48 11.52 re f 515.76 541.68 0.48 11.52 re f 549.6 541.68 0.48 11.52 re f BT 382.32 532.08 TD -0.0552 Tc (FAR) Tj 38.4 0 TD 0.0017 Tc (0%) Tj 32.88 0 TD 0.0011 Tc (53%) Tj 37.92 0 TD 0.0017 Tc (0%) Tj 34.56 0 TD (7%) Tj ET 320.16 541.2 0.48 0.48 re f 320.64 541.2 53.28 0.48 re f 373.92 541.2 0.48 0.48 re f 374.4 541.2 35.04 0.48 re f 409.44 541.2 0.48 0.48 re f 409.92 541.2 35.04 0.48 re f 444.96 541.2 0.48 0.48 re f 445.44 541.2 34.8 0.48 re f 480.24 541.2 0.48 0.48 re f 480.72 541.2 35.04 0.48 re f 515.76 541.2 0.48 0.48 re f 516.24 541.2 33.36 0.48 re f 549.6 541.2 0.48 0.48 re f 320.16 529.68 0.48 11.52 re f 373.92 529.68 0.48 11.52 re f 409.44 529.68 0.48 11.52 re f 444.96 529.68 0.48 11.52 re f 480.24 529.68 0.48 11.52 re f 515.76 529.68 0.48 11.52 re f 549.6 529.68 0.48 11.52 re f BT 342 532.08 TD 0 Tc (5) Tj 5.04 4.56 TD /F1 6.48 Tf 0.1193 Tc (th) Tj 35.52 -16.56 TD /F1 10.08 Tf -0.0304 Tc (FRR) Tj 35.76 0 TD 0.0011 Tc (30%) Tj 35.28 0 TD (33%) Tj 35.28 0 TD (33%) Tj 34.56 0 TD (27%) Tj ET 320.16 529.2 0.48 0.48 re f 373.92 529.2 0.48 0.48 re f 374.4 529.2 35.04 0.48 re f 409.44 529.2 0.48 0.48 re f 409.92 529.2 35.04 0.48 re f 444.96 529.2 0.48 0.48 re f 445.44 529.2 34.8 0.48 re f 480.24 529.2 0.48 0.48 re f 480.72 529.2 35.04 0.48 re f 515.76 529.2 0.48 0.48 re f 516.24 529.2 33.36 0.48 re f 549.6 529.2 0.48 0.48 re f 320.16 517.68 0.48 11.52 re f 320.16 517.2 0.48 0.48 re f 320.16 517.2 0.48 0.48 re f 320.64 517.2 53.28 0.48 re f 373.92 517.68 0.48 11.52 re f 373.92 517.2 0.48 0.48 re f 374.4 517.2 35.04 0.48 re f 409.44 517.68 0.48 11.52 re f 409.44 517.2 0.48 0.48 re f 409.92 517.2 35.04 0.48 re f 444.96 517.68 0.48 11.52 re f 444.96 517.2 0.48 0.48 re f 445.44 517.2 34.8 0.48 re f 480.24 517.68 0.48 11.52 re f 480.24 517.2 0.48 0.48 re f 480.72 517.2 35.04 0.48 re f 515.76 517.68 0.48 11.52 re f 515.76 517.2 0.48 0.48 re f 516.24 517.2 33.36 0.48 re f 549.6 517.68 0.48 11.52 re f 549.6 517.2 0.48 0.48 re f 549.6 517.2 0.48 0.48 re f BT 337.44 496.08 TD -0.0544 Tc 2.7544 Tw (We also performed an investigation to check if ) Tj 2.7245 Tc 0 Tw (a) Tj -19.92 -12 TD -0.0558 Tc 1.5558 Tw (substitution of the mother wavelet) Tj 0 Tc 0.12 Tw ( ) Tj 146.16 0 TD -0.0344 Tc 1.5944 Tw (Daubechies by others) Tj -146.16 -12 TD -0.0394 Tc 1.3061 Tw (would produce better results. To this end, the same tests) Tj 0 -12 TD -0.0476 Tc 2.2247 Tw (from the standard case were re-executed, just replacing) Tj T* -0.0609 Tc 1.3329 Tw (db6 successively by db1, db10 and) Tj 0 Tc -0.12 Tw ( ) Tj 149.04 0 TD -0.0522 Tc 1.2922 Tw (bior 5.5. Our results,) Tj -149.04 -12 TD -0.0461 Tc 0.1901 Tw (showed in Table 3, indicate that, even though it is possible) Tj 0 -12 TD -0.0568 Tc 1.2968 Tw (to find some improvement in FRR, there are again some) Tj T* -0.0446 Tc 0.4646 Tw (important security failures due to high FAR, meaning that) Tj T* -0.0547 Tc 0.1447 Tw (db6 was effectively the most indicated in this case.) Tj 0 -28.8 TD -0.0592 Tc 0.5906 Tw (Table 3. Mother wavelets db1, db10 and ) Tj 167.76 0 TD -0.061 Tc 0.901 Tw (bior 5.5, level 4,) Tj -167.76 -11.52 TD -0.0355 Tc 0.1555 Tw (including distance 4.) Tj 4.8 -12.24 TD -0.0659 Tc 0 Tw (Mother) Tj -0.72 -11.52 TD -0.0898 Tc (wavelet) Tj 49.2 11.52 TD -0.0778 Tc (Error) Tj 0.24 -11.52 TD -0.0149 Tc (taxes) Tj 37.68 11.52 TD -0.0648 Tc (Writer) Tj 10.56 -11.52 TD 0 Tc (1) Tj 27.84 11.52 TD -0.0648 Tc (Writer) Tj 10.56 -11.52 TD 0 Tc (2) Tj 27.84 11.52 TD -0.0648 Tc (Writer) Tj 10.56 -11.52 TD 0 Tc (3) Tj 27.6 11.52 TD -0.0648 Tc (Writer) Tj 10.56 -11.52 TD 0 Tc (4) Tj ET 313.92 356.64 0.48 0.48 re f 313.92 356.64 0.48 0.48 re f 314.4 356.64 45.36 0.48 re f 359.76 356.64 0.48 0.48 re f 360.24 356.64 42 0.48 re f 402.24 356.64 0.48 0.48 re f 402.72 356.64 37.92 0.48 re f 440.64 356.64 0.48 0.48 re f 441.12 356.64 37.92 0.48 re f 479.04 356.64 0.48 0.48 re f 479.52 356.64 37.92 0.48 re f 517.44 356.64 0.48 0.48 re f 517.92 356.64 37.92 0.48 re f 555.84 356.64 0.48 0.48 re f 555.84 356.64 0.48 0.48 re f 313.92 333.6 0.48 23.04 re f 359.76 333.6 0.48 23.04 re f 402.24 333.6 0.48 23.04 re f 440.64 333.6 0.48 23.04 re f 479.04 333.6 0.48 23.04 re f 517.44 333.6 0.48 23.04 re f 555.84 333.6 0.48 23.04 re f BT 371.76 324 TD -0.0552 Tc (FAR) Tj 43.2 0 TD 0.0017 Tc (0%) Tj 36 0 TD 0.0011 Tc (50%) Tj 40.8 0 TD 0.0017 Tc (0%) Tj 35.76 0 TD 0.0011 Tc (13%) Tj ET 313.92 333.12 0.48 0.48 re f 314.4 333.12 45.36 0.48 re f 359.76 333.12 0.48 0.48 re f 360.24 333.12 42 0.48 re f 402.24 333.12 0.48 0.48 re f 402.72 333.12 37.92 0.48 re f 440.64 333.12 0.48 0.48 re f 441.12 333.12 37.92 0.48 re f 479.04 333.12 0.48 0.48 re f 479.52 333.12 37.92 0.48 re f 517.44 333.12 0.48 0.48 re f 517.92 333.12 37.92 0.48 re f 555.84 333.12 0.48 0.48 re f 313.92 321.6 0.48 11.52 re f 359.76 321.6 0.48 11.52 re f 402.24 321.6 0.48 11.52 re f 440.64 321.6 0.48 11.52 re f 479.04 321.6 0.48 11.52 re f 517.44 321.6 0.48 11.52 re f 555.84 321.6 0.48 11.52 re f BT 328.56 324 TD -0.1859 Tc (Db1) Tj -4.56 -11.52 TD 0.0034 Tc (\() Tj 3.36 0 TD 0.0676 Tc (Haar\)) Tj 44.64 -0.48 TD -0.0304 Tc (FRR) Tj 40.56 0 TD 0.0011 Tc (20%) Tj 40.8 0 TD 0.0017 Tc (7%) Tj 36 0 TD 0.0011 Tc (30%) Tj 38.16 0 TD (20%) Tj ET 313.92 321.12 0.48 0.48 re f 359.76 321.12 0.48 0.48 re f 360.24 321.12 42 0.48 re f 402.24 321.12 0.48 0.48 re f 402.72 321.12 37.92 0.48 re f 440.64 321.12 0.48 0.48 re f 441.12 321.12 37.92 0.48 re f 479.04 321.12 0.48 0.48 re f 479.52 321.12 37.92 0.48 re f 517.44 321.12 0.48 0.48 re f 517.92 321.12 37.92 0.48 re f 555.84 321.12 0.48 0.48 re f 313.92 309.6 0.48 11.52 re f 359.76 309.6 0.48 11.52 re f 402.24 309.6 0.48 11.52 re f 440.64 309.6 0.48 11.52 re f 479.04 309.6 0.48 11.52 re f 517.44 309.6 0.48 11.52 re f 555.84 309.6 0.48 11.52 re f BT 371.76 300 TD -0.0552 Tc (FAR) Tj 43.2 0 TD 0.0017 Tc (0%) Tj 36 0 TD 0.0011 Tc (27%) Tj 40.8 0 TD 0.0017 Tc (0%) Tj 35.76 0 TD 0.0011 Tc (23%) Tj ET 313.92 309.12 0.48 0.48 re f 314.4 309.12 45.36 0.48 re f 359.76 309.12 0.48 0.48 re f 360.24 309.12 42 0.48 re f 402.24 309.12 0.48 0.48 re f 402.72 309.12 37.92 0.48 re f 440.64 309.12 0.48 0.48 re f 441.12 309.12 37.92 0.48 re f 479.04 309.12 0.48 0.48 re f 479.52 309.12 37.92 0.48 re f 517.44 309.12 0.48 0.48 re f 517.92 309.12 37.92 0.48 re f 555.84 309.12 0.48 0.48 re f 313.92 297.6 0.48 11.52 re f 359.76 297.6 0.48 11.52 re f 402.24 297.6 0.48 11.52 re f 440.64 297.6 0.48 11.52 re f 479.04 297.6 0.48 11.52 re f 517.44 297.6 0.48 11.52 re f 555.84 297.6 0.48 11.52 re f BT 326.16 300 TD -0.0794 Tc (Db10) Tj 45.84 -12 TD -0.0304 Tc (FRR) Tj 42.96 0 TD 0.0017 Tc (7%) Tj 36 0 TD 0.0011 Tc (23%) Tj 38.4 0 TD (30%) Tj 38.16 0 TD (37%) Tj ET 313.92 297.12 0.48 0.48 re f 359.76 297.12 0.48 0.48 re f 360.24 297.12 42 0.48 re f 402.24 297.12 0.48 0.48 re f 402.72 297.12 37.92 0.48 re f 440.64 297.12 0.48 0.48 re f 441.12 297.12 37.92 0.48 re f 479.04 297.12 0.48 0.48 re f 479.52 297.12 37.92 0.48 re f 517.44 297.12 0.48 0.48 re f 517.92 297.12 37.92 0.48 re f 555.84 297.12 0.48 0.48 re f 313.92 285.6 0.48 11.52 re f 359.76 285.6 0.48 11.52 re f 402.24 285.6 0.48 11.52 re f 440.64 285.6 0.48 11.52 re f 479.04 285.6 0.48 11.52 re f 517.44 285.6 0.48 11.52 re f 555.84 285.6 0.48 11.52 re f BT 371.76 276 TD -0.0552 Tc (FAR) Tj 43.2 0 TD 0.0017 Tc (0%) Tj 36 0 TD 0.0011 Tc (20%) Tj 40.8 0 TD 0.0017 Tc (0%) Tj 38.16 0 TD (0%) Tj ET 313.92 285.12 0.48 0.48 re f 314.4 285.12 45.36 0.48 re f 359.76 285.12 0.48 0.48 re f 360.24 285.12 42 0.48 re f 402.24 285.12 0.48 0.48 re f 402.72 285.12 37.92 0.48 re f 440.64 285.12 0.48 0.48 re f 441.12 285.12 37.92 0.48 re f 479.04 285.12 0.48 0.48 re f 479.52 285.12 37.92 0.48 re f 517.44 285.12 0.48 0.48 re f 517.92 285.12 37.92 0.48 re f 555.84 285.12 0.48 0.48 re f 313.92 273.6 0.48 11.52 re f 359.76 273.6 0.48 11.52 re f 402.24 273.6 0.48 11.52 re f 440.64 273.6 0.48 11.52 re f 479.04 273.6 0.48 11.52 re f 517.44 273.6 0.48 11.52 re f 555.84 273.6 0.48 11.52 re f BT 320.64 276 TD 0.0283 Tc 0.0917 Tw (Bior 5.5) Tj 51.36 -12 TD -0.0304 Tc 0 Tw (FRR) Tj 40.56 0 TD 0.0011 Tc (40%) Tj 38.4 0 TD (27%) Tj 38.4 0 TD (30%) Tj 38.16 0 TD (20%) Tj ET 313.92 273.12 0.48 0.48 re f 359.76 273.12 0.48 0.48 re f 360.24 273.12 42 0.48 re f 402.24 273.12 0.48 0.48 re f 402.72 273.12 37.92 0.48 re f 440.64 273.12 0.48 0.48 re f 441.12 273.12 37.92 0.48 re f 479.04 273.12 0.48 0.48 re f 479.52 273.12 37.92 0.48 re f 517.44 273.12 0.48 0.48 re f 517.92 273.12 37.92 0.48 re f 555.84 273.12 0.48 0.48 re f 313.92 261.6 0.48 11.52 re f 313.92 261.12 0.48 0.48 re f 313.92 261.12 0.48 0.48 re f 314.4 261.12 45.36 0.48 re f 359.76 261.6 0.48 11.52 re f 359.76 261.12 0.48 0.48 re f 360.24 261.12 42 0.48 re f 402.24 261.6 0.48 11.52 re f 402.24 261.12 0.48 0.48 re f 402.72 261.12 37.92 0.48 re f 440.64 261.6 0.48 11.52 re f 440.64 261.12 0.48 0.48 re f 441.12 261.12 37.92 0.48 re f 479.04 261.6 0.48 11.52 re f 479.04 261.12 0.48 0.48 re f 479.52 261.12 37.92 0.48 re f 517.44 261.6 0.48 11.52 re f 517.44 261.12 0.48 0.48 re f 517.92 261.12 37.92 0.48 re f 555.84 261.6 0.48 11.52 re f 555.84 261.12 0.48 0.48 re f 555.84 261.12 0.48 0.48 re f BT 337.44 240 TD -0.0412 Tc 1.5669 Tw (To check if the information associated with writing) Tj -19.92 -12 TD -0.0532 Tc 5.4532 Tw (motion is really relevant in the methodology with) Tj 0 -12 TD -0.0414 Tc 0.6114 Tw (wavelets, a test was devised, in which the 4) Tj 177.6 4.56 TD /F1 6.48 Tf -0.1207 Tc 0 Tw (th) Tj 5.04 -4.56 TD /F1 10.08 Tf -0.0377 Tc 0.6377 Tw ( dissimilarity) Tj -182.64 -12 TD -0.0412 Tc 5.6012 Tw (measure \(area between warping and diagonal\) was) Tj 0 -12 TD -0.0539 Tc 0.6299 Tw (ignored. The results to this case, shown in Table 4, reveal) Tj T* 0.0203 Tc -0.0203 Tw (that the 4) Tj 37.44 4.56 TD /F1 6.48 Tf -0.1207 Tc 0 Tw (th) Tj 5.04 -4.56 TD /F1 10.08 Tf -0.0378 Tc 0.0678 Tw ( measure of distance is an essential parameter to) Tj -42.48 -12 TD -0.0494 Tc 0.1094 Tw (prevent forgeries to be accepted.) Tj 0 -28.8 TD -0.0627 Tc 0.1827 Tw (Table 4. Mother wavelet db6, level 4, without distance 4.) Tj 48 -12.24 TD 0.013 Tc 0.107 Tw (Writer 1) Tj 49.92 0 TD (Writer 2) Tj 49.68 0 TD (Writer 3) Tj 48.72 0 TD (Writer 4) Tj ET 357.12 136.08 0.48 0.48 re f 357.12 136.08 0.48 0.48 re f 357.6 136.08 49.68 0.48 re f 407.28 136.08 0.48 0.48 re f 407.76 136.08 49.2 0.48 re f 456.96 136.08 0.48 0.48 re f 457.44 136.08 49.2 0.48 re f 506.64 136.08 0.48 0.48 re f 507.12 136.08 47.76 0.48 re f 554.88 136.08 0.48 0.48 re f 554.88 136.08 0.48 0.48 re f 357.12 124.56 0.48 11.52 re f 407.28 124.56 0.48 11.52 re f 456.96 124.56 0.48 11.52 re f 506.64 124.56 0.48 11.52 re f 554.88 124.56 0.48 11.52 re f BT 326.64 114.96 TD -0.0552 Tc 0 Tw (FAR) Tj 49.2 0 TD 0.0017 Tc (0%) Tj 49.92 0 TD (3%) Tj 49.68 0 TD (0%) Tj 48.72 0 TD (3%) Tj ET 314.4 124.08 0.24 0.48 re f 314.64 124.08 0.48 0.48 re f 315.12 124.08 42 0.48 re f 357.12 124.08 0.48 0.48 re f 357.6 124.08 49.68 0.48 re f 407.28 124.08 0.48 0.48 re f 407.76 124.08 49.2 0.48 re f 456.96 124.08 0.48 0.48 re f 457.44 124.08 49.2 0.48 re f 506.64 124.08 0.48 0.48 re f 507.12 124.08 47.76 0.48 re f 554.88 124.08 0.48 0.48 re f 314.64 112.56 0.48 11.52 re f 357.12 112.56 0.48 11.52 re f 407.28 112.56 0.48 11.52 re f 456.96 112.56 0.48 11.52 re f 506.64 112.56 0.48 11.52 re f 554.88 112.56 0.48 11.52 re f BT 326.88 102.96 TD -0.0304 Tc (FRR) Tj 46.32 0 TD 0.0011 Tc (37%) Tj 49.92 0 TD (17%) Tj 49.68 0 TD (23%) Tj 48.72 0 TD (27%) Tj ET 314.64 112.08 0.48 0.48 re f 315.12 112.08 42 0.48 re f 357.12 112.08 0.48 0.48 re f 357.6 112.08 49.68 0.48 re f 407.28 112.08 0.48 0.48 re f 407.76 112.08 49.2 0.48 re f 456.96 112.08 0.48 0.48 re f 457.44 112.08 49.2 0.48 re f 506.64 112.08 0.48 0.48 re f 507.12 112.08 47.76 0.48 re f 554.88 112.08 0.48 0.48 re f 314.64 100.56 0.48 11.52 re f 314.64 100.08 0.48 0.48 re f 314.64 100.08 0.48 0.48 re f 315.12 100.08 42 0.48 re f 357.12 100.56 0.48 11.52 re f 357.12 100.08 0.48 0.48 re f 357.6 100.08 49.68 0.48 re f 407.28 100.56 0.48 11.52 re f 407.28 100.08 0.48 0.48 re f 407.76 100.08 49.2 0.48 re f 456.96 100.56 0.48 11.52 re f 456.96 100.08 0.48 0.48 re f 457.44 100.08 49.2 0.48 re f 506.64 100.56 0.48 11.52 re f 506.64 100.08 0.48 0.48 re f 507.12 100.08 47.76 0.48 re f 554.88 100.56 0.48 11.52 re f 554.88 100.08 0.48 0.48 re f 554.88 100.08 0.48 0.48 re f endstream endobj 39 0 obj 22959 endobj 36 0 obj << /Type /Page /Parent 37 0 R /Resources << /Font << /F0 6 0 R /F1 8 0 R /F3 18 0 R >> /ProcSet 2 0 R >> /Contents 38 0 R >> endobj 41 0 obj << /Length 42 0 R >> stream BT 79.44 710.4 TD 0 0 0 rg /F1 10.08 Tf -0.0391 Tc 1.1877 Tw (Finally, the wavelet transform was removed and the) Tj -19.92 -12 TD -0.0459 Tc 4.3659 Tw (distances were obtained directly from the coordinate) Tj 0 -12 TD -0.0325 Tc 1.2805 Tw (functions x\(t\) and y\(t\). In this case, the difference in the) Tj T* -0.0402 Tc 4.7502 Tw (number of points between a test signature and the) Tj T* -0.0572 Tc 1.2332 Tw (reference can become very large, so we had to include ) Tj 1.0445 Tc 0 Tw (a) Tj T* -0.057 Tc 2.6113 Tw ("filter", based on two global parameters: total duration) Tj T* -0.0346 Tc 1.6186 Tw (time of the signature and its total length. Even with the) Tj T* -0.0453 Tc 0.7653 Tw (inclusion of this filter the FAR obtained in this case were) Tj T* -0.0533 Tc 3.3733 Tw (not satisfactory at all and showed that, for the cases) Tj T* -0.0666 Tc 0.1866 Tw (studied, the wavelet step is essential to ensure security.) Tj 19.92 -24.24 TD -0.0468 Tc 0.1668 Tw (Table 5. Function-based, with filter.) Tj 23.28 -12.24 TD 0.013 Tc 0.107 Tw (Writer 1) Tj 50.4 0 TD (Writer 2) Tj 50.16 0 TD (Writer 3) Tj 49.92 0 TD (Writer 4) Tj ET 94.08 575.04 0.48 0.48 re f 94.08 575.04 0.48 0.48 re f 94.56 575.04 49.92 0.48 re f 144.48 575.04 0.48 0.48 re f 144.96 575.04 50.4 0.48 re f 195.36 575.04 0.48 0.48 re f 195.84 575.04 48.96 0.48 re f 244.8 575.04 0.48 0.48 re f 245.28 575.04 49.92 0.48 re f 295.2 575.04 0.48 0.48 re f 295.2 575.04 0.48 0.48 re f 94.08 563.52 0.48 11.52 re f 144.48 563.52 0.48 11.52 re f 195.36 563.52 0.48 11.52 re f 244.8 563.52 0.48 11.52 re f 295.2 563.52 0.48 11.52 re f BT 66.96 553.92 TD -0.0552 Tc 0 Tw (FAR) Tj 45.84 0 TD 0.0017 Tc (3%) Tj 48 0 TD 0.0011 Tc (70%) Tj 52.8 0 TD 0.0017 Tc (0%) Tj 49.92 0 TD (3%) Tj ET 58.32 563.04 0.24 0.48 re f 58.56 563.04 0.48 0.48 re f 59.04 563.04 35.04 0.48 re f 94.08 563.04 0.48 0.48 re f 94.56 563.04 49.92 0.48 re f 144.48 563.04 0.48 0.48 re f 144.96 563.04 50.4 0.48 re f 195.36 563.04 0.48 0.48 re f 195.84 563.04 48.96 0.48 re f 244.8 563.04 0.48 0.48 re f 245.28 563.04 49.92 0.48 re f 295.2 563.04 0.48 0.48 re f 58.56 551.52 0.48 11.52 re f 94.08 551.52 0.48 11.52 re f 144.48 551.52 0.48 11.52 re f 195.36 551.52 0.48 11.52 re f 244.8 551.52 0.48 11.52 re f 295.2 551.52 0.48 11.52 re f BT 67.2 541.92 TD -0.0304 Tc (FRR) Tj 43.2 0 TD 0.0011 Tc (13%) Tj 50.4 0 TD (13%) Tj 50.16 0 TD (23%) Tj 49.92 0 TD (17%) Tj ET 58.56 551.04 0.48 0.48 re f 59.04 551.04 35.04 0.48 re f 94.08 551.04 0.48 0.48 re f 94.56 551.04 49.92 0.48 re f 144.48 551.04 0.48 0.48 re f 144.96 551.04 50.4 0.48 re f 195.36 551.04 0.48 0.48 re f 195.84 551.04 48.96 0.48 re f 244.8 551.04 0.48 0.48 re f 245.28 551.04 49.92 0.48 re f 295.2 551.04 0.48 0.48 re f 58.56 539.52 0.48 11.52 re f 58.56 539.04 0.48 0.48 re f 58.56 539.04 0.48 0.48 re f 59.04 539.04 35.04 0.48 re f 94.08 539.52 0.48 11.52 re f 94.08 539.04 0.48 0.48 re f 94.56 539.04 49.92 0.48 re f 144.48 539.52 0.48 11.52 re f 144.48 539.04 0.48 0.48 re f 144.96 539.04 50.4 0.48 re f 195.36 539.52 0.48 11.52 re f 195.36 539.04 0.48 0.48 re f 195.84 539.04 48.96 0.48 re f 244.8 539.52 0.48 11.52 re f 244.8 539.04 0.48 0.48 re f 245.28 539.04 49.92 0.48 re f 295.2 539.52 0.48 11.52 re f 295.2 539.04 0.48 0.48 re f 295.2 539.04 0.48 0.48 re f BT 59.52 517.92 TD /F0 10.08 Tf -0.0656 Tc 0.1856 Tw (5. Conclusions) Tj 0 -15.36 TD /F1 10.08 Tf -0.0442 Tc 4.0942 Tw (We concluded that the error taxes obtained were at) Tj 0 -12 TD -0.0684 Tc 2.2284 Tw (acceptable levels for this kind of biometry. This shows) Tj T* -0.0333 Tc 1.6961 Tw (that the chosen methodology, consisting basically in the) Tj T* -0.0581 Tc 1.7209 Tw (application of the Dynamic Time Warping algorithm on) Tj T* -0.0552 Tc 6.4952 Tw (features extracted with the application of wavelet) Tj T* -0.0441 Tc 2.8041 Tw (transforms, is suitable to on-line signature verification.) Tj T* -0.0534 Tc 3.56 Tw (The need of a wavelet transform step was tested by) Tj T* -0.0491 Tc 1.3391 Tw (comparison with a simplified system based solely on the) Tj T* -0.04 Tc 0.6933 Tw (coordinate functions x\(t\) and y\(t\). We concluded that it is) Tj T* -0.053 Tc 2.333 Tw (worth to include the wavelet transform in the analysis.) Tj T* -0.0431 Tc 0.6731 Tw (The main tool to comparison of signatures is undoubtedly) Tj T* -0.0522 Tc 0.9722 Tw (the DTW, but the inclusion of the wavelet transform was) Tj T* -0.0675 Tc 5.0475 Tw (an essential step for the achievement of low false) Tj T* -0.0257 Tc 2.1724 Tw (acceptation rates. It was only with the inclusion of the) Tj T* -0.0464 Tc 0.5664 Tw (wavelet transform, in the right level of resolution, that we) Tj T* -0.0528 Tc 2.8471 Tw (managed to completely prevent trained forgeries to be) Tj T* -0.0487 Tc 1.262 Tw (accepted \(0% FAR\) in the cases studied. This result was) Tj T* -0.0463 Tc 0.7492 Tw (expected, since, through wavelet transforms, it is possible) Tj T* -0.0331 Tc 0.4411 Tw (to analyze the problem in a resolution level suitable to the) Tj T* -0.0505 Tc 0.1705 Tw (problem of comparison of signatures.) Tj 0 -29.76 TD /F0 10.08 Tf -0.0418 Tc 0.1618 Tw (6. Acknowledgements) Tj 0 -15.36 TD /F1 10.08 Tf -0.0655 Tc 2.7989 Tw (During this work, the first author was supported by ) Tj 2.7245 Tc 0 Tw (a) Tj 0 -12 TD -0.0556 Tc 1.0327 Tw (scholarship from CAPES \(the Brazilian Agency for Post-) Tj T* -0.0297 Tc 0.1497 Tw (Graduate Studies\).) Tj 0 -29.52 TD /F0 10.08 Tf 0.06 Tc 0.06 Tw (7. ) Tj 10.32 0 TD -0.0213 Tc 0 Tw (References) Tj -10.32 -15.36 TD /F1 10.08 Tf -0.0064 Tc 8.2864 Tw ([1] E.) Tj 0 Tc -0.12 Tw ( ) Tj 42.24 0 TD -0.0727 Tc 8.5927 Tw (Newham, ) Tj 8.6074 Tc 0 Tw (") Tj 53.52 0 TD -0.0913 Tc 0.2113 Tw (Survey: ) Tj 41.76 0 TD 0 Tc -0.1204 Tw (Signature ) Tj 49.68 0 TD -0.0789 Tc 0 Tw (Verification) Tj -169.44 -11.76 TD -0.0331 Tc 0.1531 Tw (Technologies", ) Tj 63.12 0 TD /F5 10.08 Tf -0.0011 Tc 0 Tw (Bit) Tj 11.52 0 TD /F1 10.08 Tf -0.0359 Tc 0.1559 Tw ( \(2000\), 8--10.) Tj -92.4 -15.36 TD -0.0544 Tc 4.9744 Tw ([2] L.) Tj 0 Tc -0.12 Tw ( ) Tj 35.04 0 TD -0.0477 Tc 5.2077 Tw (Rabiner, B.) Tj 0 Tc 0.12 Tw ( ) Tj 58.56 0 TD -0.0594 Tc 0.1794 Tw (Juang, ) Tj 33.36 0 TD /F5 10.08 Tf -0.0665 Tc -0.2935 Tw (Fundamentals ) Tj 64.56 0 TD -0.0811 Tc -0.0389 Tw (of ) Tj 15.36 0 TD -0.0378 Tc 0 Tw (Speech) Tj -189.12 -11.52 TD -0.0215 Tc (Recognition) Tj 48.48 0 TD /F1 10.08 Tf -0.12 Tc (, ) Tj 5.04 0 TD -0.0372 Tc 0.1572 Tw (Prentice-Hall, 1993.) Tj -71.28 -15.36 TD -0.0382 Tc 2.0782 Tw ([3] Y.) Tj 0 Tc 0.12 Tw ( ) Tj 30.48 0 TD -0.0686 Tc 2.1086 Tw (Sato, K.) Tj 0 Tc 0.12 Tw ( ) Tj 38.88 0 TD -0.0625 Tc 2.3425 Tw (Kogure, "On-line) Tj 0 Tc -0.12 Tw ( ) Tj 76.32 0 TD -0.0526 Tc -0.3074 Tw (signature ) Tj 41.28 0 TD -0.0589 Tc 0 Tw (Verification) Tj -169.2 -12 TD -0.0791 Tc 0.1991 Tw (Based ) Tj 30.72 0 TD 0 Tc 0.36 Tw (on ) Tj 16.56 0 TD -0.0459 Tc -0.0741 Tw (Shape, ) Tj 33.36 0 TD -0.0681 Tc 4.0281 Tw (Motion, and) Tj 0 Tc -0.12 Tw ( ) Tj 59.04 0 TD -0.057 Tc -0.063 Tw (Writing ) Tj 37.44 0 TD -0.0464 Tc 0 Tw (Pressure",) Tj 80.88 615.84 TD /F5 10.08 Tf -0.0071 Tc 2.0471 Tw (Proc. ) Tj 2.16 Tc 0 Tw (6) Tj 31.44 4.56 TD /F5 6.48 Tf 0.1193 Tc (th) Tj 5.04 -4.56 TD /F5 10.08 Tf -0.0627 Tc 2.3427 Tw ( Int. Conf.) Tj 0 Tc -0.12 Tw ( ) Tj 49.68 0 TD -0.12 Tc 0 Tw (on ) Tj 14.64 0 TD -0.0343 Tc 0.1543 Tw (Pattern ) Tj 34.56 0 TD -0.0433 Tc -0.0767 Tw (Recognition ) Tj 53.04 0 TD /F1 10.08 Tf -0.0162 Tc 0 Tw (\(1982\),) Tj -188.4 -11.76 TD -0.0393 Tc (823--826.) Tj -17.76 -15.36 TD -0.0233 Tc 1.3433 Tw ([4] B.) Tj 0 Tc 0.12 Tw ( ) Tj 28.56 0 TD -0.0854 Tc 1.4054 Tw (Wirtz, ) Tj 1.4074 Tc 0 Tw (") Tj 32.88 0 TD -0.0442 Tc 1.3642 Tw (Stroke-based Time) Tj 0 Tc -0.12 Tw ( ) Tj 81.12 0 TD -0.0703 Tc 1.6303 Tw (Warping for) Tj 0 Tc 0.36 Tw ( ) Tj 54.48 0 TD 0 Tc 0 Tw (Signature) Tj -179.28 -11.52 TD -0.0271 Tc -0.0929 Tw (Verification", ) Tj 57.6 0 TD /F5 10.08 Tf -0.0832 Tc 0.2032 Tw (Proc. IEEE) Tj 46.08 0 TD /F1 10.08 Tf -0.0292 Tc 0.0292 Tw ( \(1995\), 179--182.) 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