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A Fast Level Set Approach to Image Segmentation Based on Mumford-Shah Model

LI Jun YANG Xin SHI Peng-Fei(Institute of Image Processing & Pattern Recognition, Shanghai Jiaotong University, Shanghai 200030)  
A new level set PDE based on the simplified Mumford-Shah model for image segmentation was proposed by Chan and Vese, which shows less insensibility of initialization and noise affect, and has the ability of detecting both inner and outer edges of targets with inner hole just by one enclosed active contour. However, the edges far way from the active contours would be seriously suppressed by the dirac function in the proposed PDE. To solve this problem, this paper improved the C-V's PDE by replacing the dirac function δεE(φ) with |(?)φ| , which eliminates the suppression against the edges wide of the active contours, such that the improved PDE gives global optimization of Mumford-Shah model and need less evolution loops than that of the C-V's PDE. Besides, in order to further stabilize and fasten the level set evolution procedures, the paper addresses an improved approach to construction of the signed distance function using Voronoi source scanning method, which extends the Voronoi source of the grids nearest to active contours to the far grids along with characteristic lines, only needs simple comparison and few multiplication operations with computational complication O(N), faster than the traditional approaches. At last, a new sign map labeling method is proposed to distinguish the inside and outside of the 2D closed active contour by fast marching method. These three improvements dramatically give more efficiency and performance than the C-V approach, for example, typically all edges of an 512×512 large image will be picked up only within 10 iterating times by one initial active con-tour. The segmentation tests for synthesized and biomedical images prove the proposed segmenting method is very fast and robust.
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