This article introduces a new image segmentation method that makes use of non-local comparisons between pairs of patches of features. A non-local energy is defined by summing the interactions between pairs of patches inside and outside the segmented domain. A maximum radius of interaction can be adapted to fit the amount of variation of the features inside and outside the region to be segmented. This non-local energy is minimized using a level set approach. The corresponding curve evolution defines a non-local active contour that converges to a local minimum of our energy. In contrast to previous segmentation methods, this approach only requires a local homogeneity of the features inside and outside the region to be segmented. This does not impose a global homogeneity as required by region-based segmentation methods. This comparison principle is also less sensitive to initialization than edge-based approaches. We instantiate this novel framework using patches of intensity or color values as well as Gabor features. This allows us to segment regions with smoothly varying intensity or colors as well as complicated textures with a spatially varying local orientation.


Active Contour Texture Image Object Boundary Edge Function Active Contour Model 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. International Journal of Computer Vision 1, 321–331 (1988)CrossRefzbMATHGoogle Scholar
  2. 2.
    Osher, S., Sethian, J.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 79, 12–49 (1988)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Cohen, L.: On active contour models and balloons. CVGIP: Image Underst. 53, 211–218 (1991)CrossRefzbMATHGoogle Scholar
  4. 4.
    Caselles, V., Catté, F., Coll, T., Dibos, F.: A geometric model for active contours in image processing. Numerische Mathematik 66, 1–31 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Malladi, R., Sethian, J.A., Vemuri, B.C.: Shape modeling with front propagation: A level set approach. IEEE Trans. Patt. Anal. and Mach. Intell. 17, 158–175 (1995)CrossRefGoogle Scholar
  6. 6.
    Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. International Journal of Computer Vision 22, 61–79 (1997)CrossRefzbMATHGoogle Scholar
  7. 7.
    Cohen, L.D.: Avoiding local minima for deformable curves in image analysis. In: Le Méhauté, A., Rabut, C., Schumaker, L.L. (eds.) Curves and Surfaces with Applications in CAGD. Vanderbilt University Press, Nashville (1997)Google Scholar
  8. 8.
    Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics XLII (1989)Google Scholar
  9. 9.
    Chan, T., Vese, L.: Active contours without edges. IEEE Trans. Image Proc. 10, 266–277 (2001)CrossRefzbMATHGoogle Scholar
  10. 10.
    Chan, T., Sandberg, B., Vese, L.: Active contours without edges for vector-valued images. J. Vis. Comm. Image Repr. 11, 130–141 (2000)CrossRefGoogle Scholar
  11. 11.
    Sandberg, B., Chan, T., Vese, L.: A level-set and Gabor based active contour algorithm for segmenting textured images. UCLA CAM Report 02-39 (2002)Google Scholar
  12. 12.
    Kimmel, R.: Fast edge integration. In: Osher, S., Paragios, N. (eds.) Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer, New York (2003)Google Scholar
  13. 13.
    Sagiv, C., Sochen, N.A., Zeevi, Y.Y.: Integrated active contours for texture segmentation. IEEE Trans. Image Proc. 15, 1633–1646 (2006)CrossRefGoogle Scholar
  14. 14.
    Tsai, A., Yezzi, A., Willsky, A.S.: Curve evolution implementation of the mumford-shah functional for image segmentation, denoising, interpolation, and magnification. IEEE Trans. Image Proc. 10, 1169–1186 (2001)CrossRefzbMATHGoogle Scholar
  15. 15.
    Li, C., Kao, C., Gore, J., Ding, Z.: Implicit active contours driven by local binary fitting energy. In: Proceedings of the CVPR 2007, pp. 1–7 (2007)Google Scholar
  16. 16.
    Wang, X., Huang, D., Xu, H.: An efficient local chan–vese model for image segmentation. Pattern Recognition 43, 603–618 (2010)CrossRefzbMATHGoogle Scholar
  17. 17.
    Lee, T.S., Mumford, D., Yuille, A.: Texture segmentation by minimizing vector-valued energy functionals: The coupled-membrane model. In: Sandini, G. (ed.) ECCV 1992. LNCS, vol. 588, pp. 165–173. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  18. 18.
    Efros, A., Leung, T.: Texture synthesis by non-parametric sampling. In: IEEE International Conference on Computer Vision, vol. 2, pp. 10–33 (1999)Google Scholar
  19. 19.
    Efros, A., Freeman, W.T.: Image quilting for texture synthesis and transfer. In: Proceedings of SIGGRAPH, pp. 341–346 (2001)Google Scholar
  20. 20.
    Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. SIAM Mul. Model. and Simul. 4, 490–530 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Kindermann, S., Osher, S., Jones, P.W.: Deblurring and denoising of images by nonlocal functionals. SIAM Mult. Model. and Simul. 4, 1091–1115 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. SIAM Multiscale Modeling and Simulation 7, 1005–1028 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Peyré, G., Bougleux, S., Cohen, L.: Non-local regularization of inverse problems. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 57–68. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  24. 24.
    Gilboa, G., Osher, S.: Nonlocal linear image regularization and supervised segmentation. SIAM Mul. Model. and Simul. 6, 595–630 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    Elmoataz, A., Lezoray, O., Bougleux, S.: Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing. IEEE Trans. Image Process 17, 1047–1060 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Houhou, N., Bresson, X., Szlam, A., Chan, T., Thiran, J.: Semi-supervised segmentation based on non-local continuous min-cut. In: Tai, X.-C., Mørken, K., Lysaker, M., Lie, K.-A. (eds.) SSVM 2009. LNCS, vol. 5567, pp. 112–123. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  27. 27.
    Bresson, X., Chan, T.: Non-local unsupervised variational image segmentation models. UCLA CAM Report 08-67 (2008)Google Scholar
  28. 28.
    Caldairou, B., Rousseau, F., Passat, N., Habas, P., Studholme, C., Heinrich, C.: A non-local fuzzy segmentation method: Application to brain mri. In: Jiang, X., Petkov, N. (eds.) CAIP 2009. LNCS, vol. 5702, pp. 606–613. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  29. 29.
    Shi, J., Malik, J.: Normlaized cuts and image segmentation. IEEE Trans. Patt. Anal. and Mach. Intell. 22, 888–905 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Miyoun Jung
    • 1
  • Gabriel Peyré
    • 1
  • Laurent D. Cohen
    • 1
  1. 1.Ceremade, UMR 7534 CNRS Université Paris-DauphineParisFrance

Personalised recommendations