8 February 2005 Iterative relaxation algorithm for noisy jacquard image segmentation
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Abstract
The Mumford-Shah model has been well acknowledged as an important method for image segmentation. This paper discussed the problem of simultaneous image segmentation and smoothing by approaching the Mumford-Shah paradigm from a numerical approximation perspective. In particular, a novel iterative relaxation algorithm for the numerical solving of the Mumford-Shah model was proposed. First, the paper presented mathematically the existence of a solution in the weak formulation of GSBV space. Second, some approximations and numerical methods for computing the weak solution were discussed. Finally, a minimization method based on a quasi-Newton algorithm was put forward. The proposed algorithm found accurately the absolute minimum of the functional at each iteration. Considering the important role of a discrete finite element approximation method in the sense of Γ-convergence, an adjustment scheme for adaptive triangulation was applied to improve the efficiency of iteration. Experimental results on noisy synthetic and jacquard images demonstrate the efficacy of the proposed algorithm.
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Zhilin Feng, Jianwei Yin, Lingwu Wang, Gang Chen, Jinxiang Dong, "Iterative relaxation algorithm for noisy jacquard image segmentation", Proc. SPIE 5637, Electronic Imaging and Multimedia Technology IV, (8 February 2005); doi: 10.1117/12.581249; https://doi.org/10.1117/12.581249
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