Diffusion Snakes: Statistical Shape Knowledge in

Mumford-Shah Based Segmentation

Daniel Cremers, Christoph Schnörr and Joachim Weickert



Related Publications

S u m m a r y

We propose to extend the Mumford-Shah functional for image segmentation
by a statistical shape energy which favors the formation of ``familiar'' contours.
We recently extended this method to incorporate a nonlinear statistical shape prior.

We present a modification of the Mumford-Shah functional and its cartoon limit which facilitates the incorporation of 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. The statistical prior is automatically generated on the basis of a set of binary training images. We propose a closed-form, parameter-free solution for incorporating invariance with respect to similarity transformations into the variational framework. As a consequence the evolving contour is restricted to a subspace of familiar shapes while being entirely free to translate, rotate and scale. We show segmentation results on artificial and real-world images with and without prior shape information. In the case 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.

The main contributions of our approach are:
  • The diffusion snake: A modification of the Mumford-Shah functional for spline contours.

  • A variational framework for segmentation which combines region-based low-level cues with a higher-level statistical shape prior.

  • A closed-form, parameter-free solution for the incorporation of similarity invariance into the shape energy.

  • Numerous demonstrations of the capacity of the shape prior to compensate for missing or misleading information due to noise, clutter or occlusion.

D e m o n s t r a t i o n s

Here you can find demonstrations of our method.

The examples on the left show segmentation results for the diffusion snake without any statistical shape prior. In contrast, the examples on the right show the corresponding segmentation process with a statistical shape prior, generated automatically from a set of binary training images.

Click on the images to watch the evolution of the segmenting contour.

Segmentation without
Statistical Shape Prior
Explanation Segmentation with a
Statistical Shape Prior
The basic principle:
The statistical shape prior restricts the evolving contour to a subspace of familiar shapes.
The resulting knowledge-driven segmentation process becomes robust against noise, clutter and occlusion.
Cluttered Background:
Due to the statistical shape prior, the background clutter is ignored.
Noisy Input Image:
Segmentation on an image with 75% random noise.
The statistical shape prior compensates for missing information due to the noise.
Partially Occluded Input Image:
Due to the statistical shape prior, the silhouette of the object of interest is reconstructed in parts where it is occluded.
In contrast, the corresponding segmentation process without shape prior is not able to produce the desired segmentation (even if optimally initialized - see movie on the left).
R e l a t e d   P u b l i c a t i o n s
Articles in Journals
  • "Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional"
    [D. Cremers, F. Tischhäuser, J. Weickert & C. Schnörr]
    International Journal of Computer Vision, to appear, 2002.

Conference Articles

Daniel Cremers
Last update: July 23, 2002