2-n-D gloablly minimal surfaces for segmentation
H. Talbot

Abstract:

The main idea behind active contours (snakes) and level sets formulation of the image segmentation problem is to minimise a contour integral by variational methods (or a surface integral in 3D). Most know methods use a gradient descent numerical procedure to evolve implicit or explicit contour towards a global minimum, but often get stuck in local minima.
The computation of globally minimal surfaces by discrete maximal flow methods is a classical graph-based method that has also been recently applied to image segmentation. Unlike gradient descent formulation, they are able to find the global minimum in many cases. This has been often used in stereo reconstruction to find the minimal surface in disparity space. However this discrete solution is typically biased by the digital grid in an obvious manner.
In this talk we propose to study a model of maximal flow using a system of constrained PDEs that yield an isotropic solution, identical to that of globally optimal geodesic active contours in 2D but that extend readily in arbitrary dimension. We discuss a simple and efficient implementation and applications in medical image segmentation and stereo-vision.

[1] Ben Appleton & Hugues Talbot. Globally optimal surfaces by continuous maximal flows. Proc. VIIth Digital Image Computing: Techniques and Applications, Sun C., Talbot H., Ourselin S. and Adriaansen T. (Eds.), 10-12 Dec. 2003, Sydney.

see also this article (pdf-document)

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