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Active Contours for Multi-region Image Segmentation with a Single Level Set Function

  • Conference paper
Scale Space and Variational Methods in Computer Vision (SSVM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7893))

Abstract

Segmenting the image into an arbitrary number of parts is at the core of image understanding. Many formulations of the task have been suggested over the years. Among these are axiomatic functionals, which are hard to implement and analyze, while graph-based alternatives impose a non-geometric metric on the problem.

We propose a novel approach to tackle the problem of multiple-region segmentation for an arbitrary number of regions. The proposed framework allows generic region appearance models while avoiding metrication errors. Updating the segmentation in this framework is done by level set evolution. Yet, unlike most existing methods, evolution is executed using a single non-negative level set function, through the Voronoi Implicit Interface Method for a multi-phase interface evolution. We apply the proposed framework to synthetic and real images, with various number of regions, and compare it to state-of-the-art image segmentation algorithms.

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References

  1. Adam, A., Kimmel, R., Rivlin, E.: On scene segmentation and histograms-based curve evolution. IEEE-TPAMI 31(9), 1708–1714 (2009)

    Article  Google Scholar 

  2. Amiaz, T., Lubetzky, E., Kiryati, N.: Coarse to over-fine optical flow estimation. Pattern Recognition 40(9), 2496–2503 (2007)

    Article  MATH  Google Scholar 

  3. Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts. IEEE-TPAMI 23(11), 1222–1239 (2001)

    Article  Google Scholar 

  4. Brox, T., Weickert, J.: Level set segmentation with multiple regions. IEEE-TIP 15(10), 3213–3218 (2006)

    Google Scholar 

  5. Caselles, V., Catté, F., Coll, T., Dibos, F.: A geometric model for active contours in image processing. Numerische Mathematik 66(1), 1–31 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  6. Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. IJCV 22(1), 61–79 (1997)

    Article  MATH  Google Scholar 

  7. Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. JMIV 40(1), 120–145 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chan, T., Vese, L.: Active contours without edges. IEEE-TIP 10(2), 266–277 (2001)

    MATH  Google Scholar 

  9. Chopp, D.L.: Some improvements of the fast marching method. SIAM Journal on Scientific Computing 23(1), 230–244 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Comaniciu, D., Meer, P.: Mean shift: A robust approach toward feature space analysis. IEEE-TPAMI 24(5), 603–619 (2002)

    Article  Google Scholar 

  11. Cremers, D., Kohlberger, T., Schnörr, C.: Shape statistics in kernel space for variational image segmentation. Pattern Recognition 36(9), 1929–1943 (2003)

    Article  MATH  Google Scholar 

  12. Delong, A., Osokin, A., Isack, H.N., Boykov, Y.: Fast approximate energy minimization with label costs. IJCV 96(1), 1–27 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Freedman, D., Zhang, T.: Active contours for tracking distributions. IEEE-TIP 13(4), 518–526 (2004)

    Google Scholar 

  14. Greenspan, H., Ruf, A., Goldberger, J.: Constrained Gaussian mixture model framework for automatic segmentation of MR brain images. IEEE Transactions on Medical Imaging 25(9), 1233–1245 (2006)

    Article  Google Scholar 

  15. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. IJCV 1(4), 321–331 (1988)

    Article  Google Scholar 

  16. Leventon, M.E., Grimson, W.E.L., Faugeras, O.D.: Statistical shape influence in geodesic active contours. In: CVPR, pp. 1316–1323 (2000)

    Google Scholar 

  17. Lucas, B.C., Kazhdan, M., Taylor, R.H.: Multi-object spring level sets (MUSCLE). In: Ayache, N., Delingette, H., Golland, P., Mori, K. (eds.) MICCAI 2012, Part I. LNCS, vol. 7510, pp. 495–503. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  18. Malladi, R., Sethian, J., Vemuri, B.: Shape modeling with front propagation: A level set approach. IEEE-TPAMI 17(2), 158–175 (1995)

    Article  Google Scholar 

  19. McLachlan, G., Peel, D.: Finite mixture models. Wiley-Interscience (2000)

    Google Scholar 

  20. Michailovich, O., Rathi, Y., Tannenbaum, A.: Image segmentation using active contours driven by the Bhattacharyya gradient flow. IEEE-TIP 16(11), 2787–2801 (2007)

    MathSciNet  Google Scholar 

  21. Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics 42(5), 577–685 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  22. Ni, K., Bresson, X., Chan, T., Esedoglu, S.: Local histogram based segmentation using the Wasserstein distance. IJCV 84(1), 97–111 (2009)

    Article  Google Scholar 

  23. Osher, S., Sethian, J.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 79(1), 12–49 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  24. Paragios, N., Deriche, R.: Geodesic active regions: A new framework to deal with frame partition problems in computer vision. Journal of Visual Communication and Image Representation 13(1-2), 249–268 (2002)

    Article  Google Scholar 

  25. Pock, T., Schoenemann, T., Graber, G., Bischof, H., Cremers, D.: A convex formulation of continuous multi-label problems. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 792–805. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  26. Riklin-Raviv, T., Kiryati, N., Sochen, N.: Prior-based segmentation by projective registration and level sets. In: ICCV, vol. 1, pp. 204–211. IEEE (2005)

    Google Scholar 

  27. Rother, C., Kolmogorov, V., Blake, A.: “grabcut”: interactive foreground extraction using iterated graph cuts. ACM Trans. Graph. 23(3), 309–314 (2004)

    Article  Google Scholar 

  28. Sagiv, C., Sochen, N., Zeevi, Y.: Integrated active contours for texture segmentation. IEEE-TIP 15(6), 1633–1646 (2006)

    Google Scholar 

  29. Samson, C., Blanc-Féraud, L., Aubert, G., Zerubia, J.: A level set model for image classification. IJCV 40(3), 187–197 (2000)

    Article  MATH  Google Scholar 

  30. Saye, R., Sethian, J.: The Voronoi Implicit Interface Method for computing multiphase physics. Proceedings of the National Academy of Science 108(49), 19498–19503 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  31. Sethian, J.: A fast marching level set method for monotonically advancing fronts. Proceedings of the National Academy of Sciences 93(4), 1591 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  32. Stauffer, C., Grimson, W.: Adaptive background mixture models for real-time tracking. In: CVPR, vol. 2. IEEE (1999)

    Google Scholar 

  33. Tsai, A., Yezzi Jr., A., Willsky, A.: Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification. IEEE-TIP 10(8), 1169–1186 (2001)

    MATH  Google Scholar 

  34. Vese, L., Chan, T.: A multiphase level set framework for image segmentation using the Mumford and Shah model. IJCV 50(3), 271–293 (2002)

    Article  MATH  Google Scholar 

  35. Yezzi Jr, A., Tsai, A., Willsky, A.: A statistical approach to snakes for bimodal and trimodal imagery. In: ICCV, vol. 2, pp. 898–903. IEEE (1999)

    Google Scholar 

  36. Zhao, H., Chan, T., Merriman, B., Osher, S.: A variational level set approach to multiphase motion. J. of Computational Physics 127(1), 179–195 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  37. Zhu, S., Yuille, A.: Region competition: Unifying snakes, region growing, and bayes/mdl for multiband image segmentation. IEEE-TPAMI 18(9), 884–900 (1996)

    Article  Google Scholar 

  38. Zivkovic, Z.: Improved adaptive Gaussian mixture model for background subtraction. In: ICPR, vol. 2, pp. 28–31. IEEE (2004)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science Department, Technion - IIT, Haifa, Israel

    Anastasia Dubrovina, Guy Rosman & Ron Kimmel

Authors
  1. Anastasia Dubrovina
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  2. Guy Rosman
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  3. Ron Kimmel
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Editor information

Editors and Affiliations

  1. Fraunhofer Gesellschaft, Institut für Graphische Datenverarbeitung, Fraunhoferstraße 5, 64283, Darmstadt, Germany

    Arjan Kuijper

  2. Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010, Graz, Austria

    Kristian Bredies

  3. Institute for Computer Graphics and Vision, Graz University of Technology, Inffeldgasse 16, 8010, Graz, Austria

    Thomas Pock  & Horst Bischof  & 

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Dubrovina, A., Rosman, G., Kimmel, R. (2013). Active Contours for Multi-region Image Segmentation with a Single Level Set Function. In: Kuijper, A., Bredies, K., Pock, T., Bischof, H. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2013. Lecture Notes in Computer Science, vol 7893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38267-3_35

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  • DOI: https://doi.org/10.1007/978-3-642-38267-3_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38266-6

  • Online ISBN: 978-3-642-38267-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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