Advertisement

Bregman Divergence Applied to Hierarchical Segmentation Problems

  • Daniela Portes L. Ferreira
  • André R. Backes
  • Celia A. Zorzo Barcelos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9423)

Abstract

Image segmentation is one of the first steps in any process concerning digital image analysis and its accuracy will go on to determine the quality of this analysis. A classic model used in image segmentation is the Mumford-Shah functional, which includes both the information to pertaining the region and the length of its borders. In this work, by using the concept of loss in Bregman Information a functional is defined which is a generalization of the Mumford-Shah functional, once it is obtained from the proposed function by means of the Squared Euclidean distance as a measure of similarity. The algorithm is constructed by using a fusion criterion, which minimizes the loss in Bregman Information. It is shown that the proposed hierarchical segmentation method generalizes the algorithm which minimizes the piecewise constant Mumford-Shah functional. The results obtained through use of the Generalized I-Divergence, Itakura-Saito and Squared Euclidean distance, show that the algorithm attained a good performance.

Keywords

Hierarchical segmentation Mumford-Shah functional Fusion region 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Burrus, N., Thierry, M.B., Jolion, J.M.: Image segmentation by a contrario simulation. Pattern Recognition 42(7), 1520–1532 (2009)CrossRefzbMATHGoogle Scholar
  2. 2.
    Banerjee, A., Merugu, S., Dhillon, I.S., Ghosh, J.: Clustering with Bregman divergences. Journal of Machine Learning Research 6, 1705–1749 (2005)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Bregman, L.M.: The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR, Computational Mathematics and Mathematical Physics 200–217 (1967)Google Scholar
  4. 4.
    Cardelino, J., Bertalmio, M., Caselles, V., Randall G.: A contrario hierarchical segmentation. In: 16th IEEE International Conference Image Processing (ICIP), pp. 4041–4044 (2009)Google Scholar
  5. 5.
    Koepfler, G., Lopez, C., Morel, J.M.: A multi scale algorithm for image segmentation by variational method. SIAM Journal on Numerical Analysis 31(1), 282–299 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Pure Appl. Math. (1989)Google Scholar
  7. 7.
    Petitot, J.: An introduction to the Mumford-Shah segmentation model. Journal of Physiology, Paris 97(2–3), 335–342 (2003)CrossRefGoogle Scholar
  8. 8.
    Telgarsky, M. and Dasgupta, S.: Agglomerative Bregman clustering. In: Proc. ICML (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Daniela Portes L. Ferreira
    • 1
  • André R. Backes
    • 1
  • Celia A. Zorzo Barcelos
    • 2
  1. 1.Faculdade de ComputaçãoUniversidade Federal de UberlândiaUberlândiaBrazil
  2. 2.Faculdade de MatemáticaUniversidade Federal de UberlândiaUberlândiaBrazil

Personalised recommendations