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Seminario del 2015
2015
27 luglio
Raymond H. Chan, Department of Mathematics, The Chinese University of Hong Kong
nell'ambito della serie: AM^2 SEMINARS
Seminario di analisi numerica
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 propose a 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 techniques like the split-Bregman algorithm or
the Chambolle-Pock method. We prove that our method is convergent and the solution g is always
unique. In our method, there is no need to specify the number of segments K (K>= 2) before
finding g. We can obtain any K-phase segmentations by choosing (K -1) thresholds after g is
found in the first stage; and in the second stage there is no need to recompute g if the thresholds
are changed to reveal different segmentation features in the image. 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.