International Journal of Computer Vision

, Volume 50, Issue 3, pp 295–313

Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional

Authors

  • Daniel Cremers
    • Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer ScienceUniversity of Mannheim, D-68131
  • Florian Tischhäuser
    • Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer ScienceUniversity of Mannheim, D-68131
  • Joachim Weickert
    • Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer ScienceUniversity of Mannheim, D-68131
  • Christoph Schnörr
    • Computer Vision, Graphics, and Pattern Recognition Group, Department of Mathematics and Computer ScienceUniversity of Mannheim, D-68131
Article

DOI: 10.1023/A:1020826424915

Cite this article as:
Cremers, D., Tischhäuser, F., Weickert, J. et al. International Journal of Computer Vision (2002) 50: 295. doi:10.1023/A:1020826424915

Abstract

We present a modification of the Mumford-Shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour. By minimizing a single energy functional, we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes. We propose a closed-form, parameter-free solution for incorporating invariance with respect to similarity transformations in the variational framework. We show segmentation results on artificial and real-world images with and without prior shape information. In the cases of noise, occlusion or strongly cluttered background the shape prior significantly improves segmentation. Finally we compare our results to those obtained by a level set implementation of geodesic active contours.

image segmentationshape recognitionstatistical learningvariational methodsdiffusion snakegeodesic active contours

Copyright information

© Kluwer Academic Publishers 2002