@InProceedings{LewinerCrai:2008:PrEsPo,
               author = "Lewiner, Thomas and Craizer, Marcos",
          affiliation = "Department of Mathematics, PUC–Rio de Janeiro, Brazil and 
                         Department of Mathematics, PUC–Rio de Janeiro, Brazil",
                title = "Projective estimators for point/tangent representations of planar 
                         curves",
            booktitle = "Proceedings...",
                 year = "2008",
               editor = "Jung, Cl{\'a}udio Rosito and Walter, Marcelo",
         organization = "Brazilian Symposium on Computer Graphics and Image Processing, 21. 
                         (SIBGRAPI)",
            publisher = "IEEE Computer Society",
              address = "Los Alamitos",
             keywords = "Projective Differential Geometry, Projective Curvature, Projective 
                         Lenght, Discrete estimators.",
             abstract = "Recognizing shapes in multiview imaging is still a challenging 
                         task, which usually relies on geometrical invariants estimations. 
                         However, very few geometric estimators that are projective 
                         invariant have been devised. This paper proposes projective length 
                         and projective curvature estimators for plane curves, when the 
                         curves are represented by points together with their tangent 
                         directions. In this context, the estimations can be performed with 
                         only the four point-tangent samples for the projective length and 
                         five for the projective curvature. The proposed length estimator 
                         is based on affine estimators and is proved to be convergent. The 
                         curvature estimator relies on the length to fit logarithmic 
                         spirals to the point-tangent samples. It is projective invariant 
                         and experiments indicate its convergence. Preliminary results 
                         using both estimators together are promising, although the 
                         estimators lack of robustness would require additional work for 
                         noisy cases.",
  conference-location = "Campo Grande, MS, Brazil",
      conference-year = "12-15 Oct. 2008",
                  doi = "10.1109/SIBGRAPI.2008.6",
                  url = "http://dx.doi.org/10.1109/SIBGRAPI.2008.6",
             language = "en",
                  ibi = "6qtX3pFwXQZG2LgkFdY/UMQz4",
                  url = "http://urlib.net/ibi/6qtX3pFwXQZG2LgkFdY/UMQz4",
           targetfile = "lewiner-projective.pdf",
        urlaccessdate = "2024, May 02"
}