author = "Dornelles, Marta Magda and Hirata, Nina Sumiko Tomita",
          affiliation = "Department of Exact and Technological Sciences, Universidade 
                         Estadual de Santa Cruz and Institute of Mathematics and 
                         Statistics, University of S{\~a}o Paulo",
                title = "Selection of windows for W-operator combination from entropy based 
            booktitle = "Proceedings...",
                 year = "2015",
               editor = "Papa, Jo{\~a}o Paulo and Sander, Pedro Vieira and Marroquim, 
                         Ricardo Guerra and Farrell, Ryan",
         organization = "Conference on Graphics, Patterns and Images, 28. (SIBGRAPI)",
            publisher = "IEEE Computer Society",
              address = "Los Alamitos",
             keywords = "binary image, morphological operator design, W-operator 
                         combination, conditional entropy, sequential forward selection.",
             abstract = "When training morphological operators that are locally defined 
                         with respect to a neighborhood window, one must deal with the 
                         tradeoff between window size and statistical precision of the 
                         learned operator. More precisely, too small windows result in 
                         large restriction errors due to the constrained operator space 
                         and, on the other hand, too large windows result in large variance 
                         error due to often insufficient number of samples. A two-level 
                         training method that combines a number of operators designed on 
                         distinct windows of moderate size is an effective way to mitigate 
                         this issue. However, in order to train combined operators, one 
                         must specify not only how many operators will be combined, but 
                         also the windows for each of them. To date, a genetic algorithm 
                         that searches for window combinations has produced the best 
                         results for this problem. In this work we propose an alternative 
                         approach that is computationally much more efficient. The proposed 
                         method consists in efficiently reducing the search space by 
                         ranking windows of a collection according to an entropy based 
                         measure estimated from input- output joint probabilities. 
                         Computational efficiency comes from the fact that only few 
                         operators need to be trained. Experimental results show that this 
                         method produces results that outperform the best results obtained 
                         with manually selected combinations and are competitive with 
                         results obtained with the genetic algorithm based solution. The 
                         proposed approach is, thus, a promising step towards fully 
                         automating the process of binary morphological operator design.",
  conference-location = "Salvador",
      conference-year = "Aug. 26-29, 2015",
             language = "en",
           targetfile = "PID3771543.pdf",
        urlaccessdate = "2021, Dec. 04"