A Fast Optimization Method for Level Set Segmentation

  • Thord Andersson
  • Gunnar Läthén
  • Reiner Lenz
  • Magnus Borga
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5575)


Level set methods are a popular way to solve the image segmentation problem in computer image analysis. A contour is implicitly represented by the zero level of a signed distance function, and evolved according to a motion equation in order to minimize a cost function. This function defines the objective of the segmentation problem and also includes regularization constraints. Gradient descent search is the de facto method used to solve this optimization problem. Basic gradient descent methods, however, are sensitive for local optima and often display slow convergence. Traditionally, the cost functions have been modified to avoid these problems. In this work, we instead propose using a modified gradient descent search based on resilient propagation (Rprop), a method commonly used in the machine learning community. Our results show faster convergence and less sensitivity to local optima, compared to traditional gradient descent.


Image segmentation level set method optimization gradient descent Rprop variational problems active contours 


  1. 1.
    Charpiat, G., Keriven, R., Pons, J.P., Faugeras, O.: Designing spatially coherent minimizing flows for variational problems based on active contours. In: Tenth IEEE International Conference on Computer Vision, ICCV 2005, October 2005, vol. 2, pp. 1403–1408 (2005)Google Scholar
  2. 2.
    Sundaramoorthi, G., Yezzi, A., Mennucci, A.: Sobolev active contours. International Journal of Computer Vision 73(3), 345–366 (2007)CrossRefzbMATHGoogle Scholar
  3. 3.
    Riedmiller, M., Braun, H.: A direct adaptive method for faster backpropagation learning: The rprop algorithm. In: Proceedings of the IEEE International Conference on Neural Networks, pp. 586–591 (1993)Google Scholar
  4. 4.
    Riedmiller, M., Braun, H.: Rprop – description and implementation details. Technical report, Universitat Karlsruhe (1994)Google Scholar
  5. 5.
    Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  6. 6.
    Schiffmann, W., Joost, M., Werner, R.: Comparison of optimized backpropagation algorithms. In: Proc. of ESANN 1993, Brussels, pp. 97–104 (1993)Google Scholar
  7. 7.
    Kimmel, R.: Fast edge integration. In: Geometric Level Set Methods in Imaging, Vision and Graphics. Springer, Heidelberg (2003)Google Scholar
  8. 8.
    Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 79, 12–49 (1988)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Osher, S., Fedkiw, R.: Level Set and Dynamic Implicit Surfaces. Springer, New York (2003)CrossRefzbMATHGoogle Scholar
  10. 10.
    Peng, D., Merriman, B., Osher, S., Zhao, H.K., Kang, M.: A pde-based fast local level set method. Journal of Computational Physics 155(2), 410–438 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Sethian, J.: A fast marching level set method for monotonically advancing fronts. Proceedings of the National Academy of Science 93, 1591–1595 (1996)Google Scholar
  12. 12.
    Zhao, H.K.: A fast sweeping method for eikonal equations. Mathematics of Computation (74), 603–627 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Läthén, G., Jonasson, J., Borga, M.: Phase based level set segmentation of blood vessels. In: Proceedings of 19th International Conference on Pattern Recognition, IAPR, Tampa, FL, USA (December 2008)Google Scholar
  14. 14.
    Granlund, G.H., Knutsson, H.: Signal Processing for Computer Vision. Kluwer Academic Publishers, Netherlands (1995)CrossRefGoogle Scholar
  15. 15.
    Staal, J., Abramoff, M., Niemeijer, M., Viergever, M., van Ginneken, B.: Ridge based vessel segmentation in color images of the retina. IEEE Transactions on Medical Imaging 23(4), 501–509 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Thord Andersson
    • 1
    • 3
  • Gunnar Läthén
    • 2
    • 3
  • Reiner Lenz
    • 2
    • 3
  • Magnus Borga
    • 1
    • 3
  1. 1.Department of Biomedical EngineeringLinköping UniversitySweden
  2. 2.Department of Science and TechnologyLinköping UniversitySweden
  3. 3.Center for Medical Image Science and Visualization (CMIV)Linköping UniversitySweden

Personalised recommendations