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Coupled Geodesic Active Regions for Image Segmentation: A Level Set Approach

  • Nikos Paragios
  • Rachid Deriche
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1843)

Abstract

This paper presents a novel variational method for im age segmentation that unifies boundary and region-based information sources under the Geodesic Active Region framework. A statistical analysis based on the Minimum Description Length criterion and the Maximum Likelihood Principle for the observed density function (image histogram) using a mixture of Gaussian elements, indicates the number of the different regions and their intensity properties. Then, the boundary information is determined using a probabilistic edge detector, while the region information is estimated using the Gaussian components of the mixture model. The defined objective function is mini mized using a gradientdescent method where a level set approach is used to implement the resulting PDE system. According to the motion equations, the set of initial curves is propagated toward the segmentation result under the influence of boundary and region-based segmentation forces, and being constrained by a regularity force. The changes of topology are naturally handled thanks to the level set implementation, while a coupled multi-phase propagation is adopted that increases the robustness and the convergence rate by imposing the idea of mutually exclusive propagating curves. Finally, to reduce the required computational cost and the risk of convergence to local minima, a multi-scale approach is also considered. The performance of our method is demonstrated on a variety of real images.

Keywords

Image Segmentation Minimum Description Length Active Contour Model Intensity Property Boundary Information 
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.

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References

  1. 1.
    D. Adalsteinsson and J. Sethian. A Fast Level Set. Method for Propagating Interfaces. Journal of Computational Physics, 118:269–277, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    R. Adams and L. Bischof. Seeded Region Growing. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16:641 647, 1994.CrossRefGoogle Scholar
  3. 3.
    V. Caselles, R. Kimmel, and G. Sapiro. Geodesic active contours. In IEEE ICCV, Boston, USA, 1995.Google Scholar
  4. 4.
    A. Chakraborty, H. Staib, and J. Duncan. Deformable Boundary Finding in Medical Images by Integrating Gradient and Region Information. IEEE Transactions on Medical Imaging, 15(6):859–870, 1996.CrossRefGoogle Scholar
  5. 5.
    T. Chan and L. Vese. An Active Contour Model without Edges. In International Conference on Scale-Space Theories in Computer Vision, pages 141–151, 1999.Google Scholar
  6. 6.
    D. Cohen. On active contour models and balloons. CVGIPr Image Understanding, 53:211–218, 1991.zbMATHCrossRefGoogle Scholar
  7. 7.
    D. Comaniciu and P. Meer. Mean Shift Analysis and Applications. In IEEE ICCV, pages 1197–1203, Corfu, Greece, 1999.Google Scholar
  8. 8.
    R. Duda and P. Hart. Pattern Classification and Scene Analysis. John Wiley & Sons, Inc., 1973.Google Scholar
  9. 9.
    D. Geiger and A. Yuille. A common framework for image segmentation. International Journal of Computer Vision, 6:227–243, 1991.CrossRefGoogle Scholar
  10. 10.
    S. Geman and D. Geman. Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6:721–741, 1984.zbMATHCrossRefGoogle Scholar
  11. 11.
    F. Heitz, P. Perez, and P. Bouthemy. Multiscale minimization of global energy functions in some visual recovery problems. CVGIPr Image Understanding, 59:125–134, 1994.Google Scholar
  12. 12.
    M. Kass, A. Witkin, and D. Terzopoulos. Snakes: Active contour models. International Journal of Computer Vision, 1:321–332, 1988.CrossRefGoogle Scholar
  13. 13.
    S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, and A. Yezzi. Gradient flows and geometric active contour models. In IEEE ICCV, pages 810–815, Boston, USA, 1995.Google Scholar
  14. 14.
    S. Osher and J. Sethian. Fronts propagating with curvature-dependent speed: algorithms based on the hamilton-jacobi formulation. Journal of Computational Physics, 79:12–49, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    N. Paragios. Geodesic Active Regions and Level Set Methods: Contributions and Applications in Artificial Vision. PhD thesis, University of Nice/ Sophia Antipolis, Jan. 2000.Google Scholar
  16. 16.
    N. Paragios and R. Deriche. Geodesic Active Regions for Texture Segmentation. Research Report 3440, INRIA, France, 1998. http://www.inria.fr/RRRT/RR-3440.html.Google Scholar
  17. 17.
    N. Paragios and R. Deriche. Coupled Geodesic Active Regions for image segmentation. Research Report 3783, INRIA, France, Oct. 1999. http://www.inria.fr/RRRT/RR-3783.html.Google Scholar
  18. 18.
    N. Paragios and R. Deriche. Geodesic Active Contours for Supervised Texture Segmentation. In IEEE CVPR, Colorado, USA, 1999.Google Scholar
  19. 19.
    N. Paragios and R. Deriche. Geodesic Active regions for Motion Estimation and Tracking. In IEEE ICCV, pages 688–674, Corfu, Greece, 1999.Google Scholar
  20. 20.
    N. Paragios and R. Deriche. Geodesic Active regions for Supervised Texture Segmentation. In IEEE ICCV, pages 926–932, Corfu, Greece, 1999.Google Scholar
  21. 21.
    T. Pavlidis and Y. Liow. Integrating region growing and edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12:225–233, 1990.CrossRefGoogle Scholar
  22. 22.
    J. Rissanen. Modeling by the Shortest Data Description. Automatica, 14:465–471, 1978.zbMATHCrossRefGoogle Scholar
  23. 23.
    C. Samson, L. Blanc-Feraud, G. Aubert, and J. Zerubia. A Level Set Model for image classification. In International Conference on Scale-Space Theories in Computer Vision, pages 306–317, 1999. http://www.inria.fr/RRRT/RR-3662.html.
  24. 24.
    A. Yezzi, A. Tsai, and A. Willsky. A Statistical Approach to Snakes for Bimodal and Trimodal Imagery. In IEEE ICCV, pages 898–903, Corfu, Greece, 1999.Google Scholar
  25. 25.
    H.-K. Zhao, T. Chan, and S. Osher. A variational level set approach to multiphase motion. Journal of Computational Physics, 127:179–195, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    S. Zhu and A. Yuille. Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18:884–900, 1996.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Nikos Paragios
    • 1
  • Rachid Deriche
    • 2
  1. 1.Imaging and Visualization DepartmentSiemens Corporate ResearchPrincetonUSA
  2. 2.I.N.R.I.ASophia Antipolis CedexFrance

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