A Level Set Framework for Active Contours and Mumford-Shah Segmentation

Monday, October 16, 2000 - 9:30am - 10:25am
Keller 3-180
Tony Chan (University of California, Los Angeles)
In this talk, I will present a common framework for active contours and Mumford-Shah segmentation, based on the level set method of S. Osher and J. Sethian. First I will introduce an active contour model without edges, based on segmentation and level sets. By this model, we can detect objects whose boundaries are not necessarily defined by gradient, as well as interior contours automatically. Then I will show how this level set model can be generalized, in order to minimize the Mumford-Shah energy for segmentation, for piecewise-constant and piecewise-smooth approximations. We represent the set of edges via one or more level set functions, and we propose a new multiphase level set representation, which has some advantages: we use only $n$ level set functions to represent $2^n$ phases, and in addition, we do not have the problems of vacuum and overlap, naturally arising in multiphase problems. Also, we will see that triple junctions can be detected and represented. Finally, I will show numerical results on various images, in order to validate the algorithm.