CENTER FOR COMPUTATION & TECHNOLOGY

The Mumford-Shah model is one of the most important image segmentation models, and has been studied extensively in the last twenty years. In this talk, we will first survey the past development of the method. Then we introduce our two-stage segmentation method based on the Mumford-Shah model. The first stage of our method is to find a smooth solution g to a convex variant of the Mumford-Shah model. Once g is obtained, then in the second stage, the segmentation is done by thresholding g into different phases. The thresholds can be given by the users or can be obtained automatically using any clustering methods. Because of the convexity of the model, g can be solved efficiently by standard techniques. We prove that our method is convergent and the solution g is always unique. Experimental results show that our two-stage method performs better than many standard two-phase or multi-phase segmentation methods for very general images, including anti-mass, tubular, MRI, noisy, and blurry images; and for very general noise models such as Gaussian, Poisson and multiplicative Gamma noise. We will also mention the generalization to color images.