Lecture on Imaging
- April 9th (Thursday)
- Room 1212 (Lecture room 1), National Institute of Informatics
- Professor Raymond H. Chan
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong.
A Two-stage Image Segmentation Method using a Convex Variant of the Mumford-Shah Model and Thresholding
- 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 $K$ ($K\ge 2$) 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.
*Please replace [at] with @.