Advertisement

Shape Distances for Binary Image Segmentation

  • Frank R. SchmidtEmail author
  • Lena Gorelick
  • Ismail Ben Ayed
  • Yuri Boykov
  • Thomas Brox
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

Shape distances are an important measure to guide the task of shape classification. In this chapter we show that the right choice of shape similarity is also important for the task of image segmentation, even at the absence of any shape prior. To this end, we will study three different shape distances and explore how well they can be used in a trust region framework. In particular, we explore which distance can be easily incorporated into trust region optimization and how well these distances work for theoretical and practical examples.

Keywords

Image Segmentation Trust Region Shape Space Trust Region Method Sign Distance Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Trans. PAMI 26 (9), 1124–1137 (2004)CrossRefzbMATHGoogle Scholar
  2. 2.
    Boykov, Y., Kolmogorov, V., Cremers, D., Delong, A.: An integral solution to surface evolution PDEs via Geo-Cuts. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) European Conference on Computer Vision. LNCS, vol. 3953, pp. 409–422. Springer, Graz (2006)Google Scholar
  3. 3.
    Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE Trans. PAMI 23 (11), 1222–1239 (2001)CrossRefGoogle Scholar
  4. 4.
    Brox, T., Rousson, M., Deriche, R., Weickert, J.: Unsupervised segmentation incorporating colour, texture, and motion. In: Petkov, N., Westenberg, M.A. (eds.) Computer Analysis of Images and Patterns. LNCS, vol. 2756, pp. 353–360. Springer, Groningen (2003)CrossRefGoogle Scholar
  5. 5.
    Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40 (1), 120–145 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Chan, T., Esedoḡlu, S., Nikolova, M.: Algorithms for finding global minimizers of image segmentation and denoising models. SIAM J. Appl. Math. 66 (5), 1632–1648 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Cremers, D., Osher, S.J., Soatto, S.: Kernel density estimation and intrinsic alignment for shape priors in level set segmentation. Int. J. Comput. Vis. 69 (3), 335–351 (2006)CrossRefGoogle Scholar
  8. 8.
    Cremers, D., Schmidt, F.R., Barthel, F.: Shape priors in variational image segmentation: convexity, Lipschitz continuity and globally optimal solutions. In: IEEE International Conference on Computer Vision and Pattern Recognition, Anchorage (2008)Google Scholar
  9. 9.
    Cremers, D., Soatto, S.: A pseudo-distance for shape priors in level set segmentation. In: Paragios, N. (ed.) IEEE 2nd International Workshop on Variational, Geometric and Level Set Methods, Nice, pp. 169–176 (2003)Google Scholar
  10. 10.
    Delong, A., Gorelick, L., Schmidt, F.R., Veksler, O., Boykov, Y.: Interactive segmentation with super-labels. In: International Conference on Energy Minimization Methods for Computer Vision and Pattern Recognition. LNCS, vol. 6819, pp. 147–162. Springer, Saint Petersburg (2011)Google Scholar
  11. 11.
    Delong, A., Osokin, A., Isack, H.N., Boykov, Y.: Fast approximate energy minimization with label costs. Int. J. Comput. Vis. 96 (1), 1–27 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Gao, T., Koller, B.P.D.: A segmentation-aware object detection model with occlusion handling. In: IEEE International Conference on Computer Vision and Pattern Recognition, Colorado Springs, pp. 1361–1368 (2011)Google Scholar
  13. 13.
    Gorelick, L., Ayed, I.B., Schmidt, F.R., Boykov, Y.: An experimental comparison of trust region and level sets. arXiv http://arxiv.org/abs/1311.2102 (2013)
  14. 14.
    Gorelick, L., Schmidt, F.R., Boykov, Y.: Fast trust region for segmentation. In: IEEE International Conference on Computer Vision and Pattern Recognition, Portland (2013)CrossRefGoogle Scholar
  15. 15.
    Leventon, M., Grimson, W., Faugeras, O.: Statistical shape influence in geodesic active contours. In: IEEE International Conference on Computer Vision and Pattern Recognition, Hilton Head Island, vol. 1, pp. 316–323 (2000)Google Scholar
  16. 16.
    Li, C., Xu, C., Gui, C., Fox, M.D.: Level set evolution without re-initialization: a new variational formulation. In: IEEE International Conference on Computer Vision and Pattern Recognition, pp. 430–436 (2005)Google Scholar
  17. 17.
    Ling, H., Jacobs, D.W.: Shape classification using the innerdistance. IEEE Trans. PAMI 29 (02), 286–299 (2007)CrossRefGoogle Scholar
  18. 18.
    Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42, 577–685 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Nieuwenhuis, C., Strekalovskiy, E., Cremers, D.: Proportion priors for image sequence segmentation. In: IEEE International Conference on Computer Vision, Sydney, pp. 1769–1776 (2013)Google Scholar
  20. 20.
    Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, Berlin (2006)zbMATHGoogle Scholar
  21. 21.
    Osher, S.J., Sethian, J.A.: Fronts propagation with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79, 12–49 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Rousson, M., Paragios, N.: Shape priors for level set representations. In: Heyden, A., et al. (eds.) European Conference on Computer Vision, Copenhagen. LNCS, vol. 2351, pp. 78–92. Springer (2002)Google Scholar
  23. 23.
    Schmidt, F.R., Boykov, Y.: Hausdorff distance constraint for multi-surface segmentation. In: European Conference on Computer Vision. LNCS, vol. 7572, pp. 598–611. Springer, Florence (2012)Google Scholar
  24. 24.
    Soares, J.V.B., Cesar, J.J.G.L.R.M., Jelinek, H.F., Cree, M.J.: Retinal vessel segmentation using the 2-d gabor wavelet and supervised classification. IEEE Trans. Med. Imaging 25 (9), 1214–1222 (2006)CrossRefGoogle Scholar
  25. 25.
    Tang, M., Gorelick, L., Veksler, O., Boykov, Y.: Grabcut in one cut. In: IEEE International Conference on Computer Vision, Sydney, pp. 1769–1776 (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Frank R. Schmidt
    • 1
    Email author
  • Lena Gorelick
    • 2
  • Ismail Ben Ayed
    • 3
  • Yuri Boykov
    • 2
  • Thomas Brox
    • 1
  1. 1.Computer Science Department and BIOSS Centre for Biological Signalling StudiesUniversity of FreiburgFreiburgGermany
  2. 2.Computer Science DepartmentUniversity of Western OntarioLondonCanada
  3. 3.École de Technologie SupérieureUniversity of QuebecMontrealCanada

Personalised recommendations