Bayesian Object Detection through Level Curves Selection

  • Charles Kervrann
Conference paper
Part of the Lecture Notes in Computer Science 2106 book series (LNCS, volume 2106)


Bayesian statistical theory is a convenient way of taking a priori information into consideration when inference is made from images. In Bayesian image detection, the a priori distribution should capture the knowledge about objects. Taking inspiration from [1], we design a prior density that penalizes the area of homogeneous parts in images. The detection problem is further formulated as the estimation of the set of curves that maximizes the posterior distribution. In this paper, we explore a posterior distribution model for which its maximal mode is given by a subset of level curves, that is the boundaries of image level sets. For the completeness of the paper, we present a stepwise greedy algorithm for computing partitions with connected components.


Image Segmentation Level Line Active Contour Model Homogeneous Part Connected Component Label 
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.
    L. Alvarez, Y. Gousseau, and J.M. Morel. Scales in natural images and a consequence on their bounded variation. In Int. Conf. on Scale-Space Theories Comp. Vis., pages 247–258, Kerkyra, Greece, September 1999.Google Scholar
  2. 2.
    A. Blake and A. Zisserman. Visual Reconstruction. MIT Press, Cambridge, Mass, 1987.Google Scholar
  3. 3.
    V. Caselles, B. Coll, and J.M. Morel. Topographic maps and local contrast changes in natural images. Int J. Computer Vision, 33(1):5–27, 1999.MathSciNetCrossRefGoogle Scholar
  4. 4.
    T. Chan and L. Vese. Active contour model without edges. In Int. Conf. on Scale-Space Theories Comp. Vis., pages 141–151, Kerkyra, Greece, September 1999.Google Scholar
  5. 5.
    L.D. Cohen. On active contour models and balloons. CVGIP: Image Understanding, 53(2):211–218, 1991.zbMATHCrossRefGoogle Scholar
  6. 6.
    J. Crespo, R. Schafer, J. Serra, C. Gratin, and F. Meyer. The flat zone approach: a general low-level region merging segmentation method. Signal Processing, 62(1):37–60, 1997.zbMATHCrossRefGoogle Scholar
  7. 7.
    J. Froment. Perceptible level lines and isoperimetric ratio. In Int. Conf. on Image Processing, Vancouver, Canada, 2000.Google Scholar
  8. 8.
    S. Geman and D. Geman. Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Trans. Patt. Anal. and Mach. Int., 6(6):721–741, 1984.zbMATHCrossRefGoogle Scholar
  9. 9.
    U. Grenander and M.I. Miller. Representations of knowledge in complex systems. J. Royal Statistical Society, series B, 56(4):549–603, April 1994.MathSciNetzbMATHGoogle Scholar
  10. 10.
    R. Jones. Connecting filtering and segmentation using component trees. Computer Vision and Image Understanding, 75(3):215–228, 1999.CrossRefGoogle Scholar
  11. 11.
    J.N. Kapur, P.K. Sahoo, and A.K.C. Wong. A new method for gray-level picture thresholding using the entropy of the histogram. Comp. Vis. Graphics and Image Proc., 29:273–285, 1985.CrossRefGoogle Scholar
  12. 12.
    M. Kass, A. Witkin, and D. Terzopoulos. Snakes: active contour models. Int J. Computer Vision, 12(1):321–331, 1987.Google Scholar
  13. 13.
    C. Kervrann, M. Hoebeke, and A. Trubuil. Level lines as global minimizers of energy functionals in image segmentation. In Euro. Conf. on Comp. Vis., pages 241–256, Dublin, Ireland, June 2000.Google Scholar
  14. 14.
    G. Koepfler, C. Lopez, and J.M. Morel. A multiscale algorithm for image segmentation by variational method. SIAM J. Numerical Analysis, 31(1):282–299, 1994.MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    G. Matheron. Random Sets and Integral Geometry. John Wiley, New York, 1975.zbMATHGoogle Scholar
  16. 16.
    J. M∅ller and R.P. Waagepertersen. Markov connected component fields. Adv. in Applied Probability, pages 1–35, 1998.Google Scholar
  17. 17.
    J.M. Morel and S. Solimini. Variational methods in image segmentation. Birkhauser, 1994.Google Scholar
  18. 18.
    D. Mumford and J. Shah. Optimal approximations by piecewise smooth functions and variational problems. Communication on Pure and applied Mathematics, 42(5):577–685, 1989.MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    S. Osher and J. Sethian. Fronts propagating with curvature dependent speed: algorithms based on the hamilton-jacobi formulation. J. Computational Physics, 79:12–49, 1988.MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    N. Paragios and R. Deriche. Coupled geodesic active regions for image segmentation: a level set approach. In Euro. Conf. on Comp. Vis., pages 224–240, Dublin, Ireland, June 2000.Google Scholar
  21. 21.
    P. Salembier and J. Serra. Flat zones filtering, connected operators, and filters by reconstruction. IEEE Trans. Image Processing, 4(8):1153–1160, 1995.CrossRefGoogle Scholar
  22. 22.
    J. Sethian. Level Sets Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Material Science. Cambridges University Press, 1996.Google Scholar
  23. 23.
    L. Vincent and P. Soille. Watershed in digital spaces: an efficient algorithm based on immersion simulations. IEEE Trans. Patt. Anal. and Mach. Int., 13(6):583–598, 1991.CrossRefGoogle Scholar
  24. 24.
    A. Yezzi, A. Tsai, and A. Willsky. A statistical approach to snakes for bimodal and trimodal imagery. In Int. Conf. on Comp. Vis., pages 898–903, Kerkyra, Greece, September 1999.Google Scholar
  25. 25.
    S.C Zhu and A. Yuille. Region competition: unifying snakes, region growing, and bayes/mdl for multiband image segmentation. IEEE Trans. Patt. Anal. and Mach. Int., 18(9):884–900, 1996.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Charles Kervrann
    • 1
  1. 1.INRA - Biométrie, Domaine de VilvertJouy-en-JosasFrance

Personalised recommendations