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A two-stage image segmentation method using a convex variant of the Mumford-Shah model and thresholding

A two-stage image segmentation method using a convex variant of the Mumford-Shah model and thresholding
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 paper, 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 that 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 multiphase segmentation methods for very general images, including antimass, tubular, MRI, noisy, and blurry images. © 2013 Society for Industrial and Applied Mathematics.
Image segmentation, Mumford-Shah model, Split-Bregman, Total variation
368-390
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Chan, Raymond
9185af9b-f073-4e3d-8f22-1dac8d28db58
Zeng, Tieyong
8bae04dd-2c0d-49f2-898b-30cdc0f5e286
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Chan, Raymond
9185af9b-f073-4e3d-8f22-1dac8d28db58
Zeng, Tieyong
8bae04dd-2c0d-49f2-898b-30cdc0f5e286

Cai, Xiaohao, Chan, Raymond and Zeng, Tieyong (2013) A two-stage image segmentation method using a convex variant of the Mumford-Shah model and thresholding. SIAM Journal on Imaging Sciences, 6 (1), 368-390. (doi:10.1137/120867068).

Record type: Article

Abstract

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 paper, 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 that 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 multiphase segmentation methods for very general images, including antimass, tubular, MRI, noisy, and blurry images. © 2013 Society for Industrial and Applied Mathematics.

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More information

Published date: 19 February 2013
Keywords: Image segmentation, Mumford-Shah model, Split-Bregman, Total variation

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Local EPrints ID: 438602
URI: http://eprints.soton.ac.uk/id/eprint/438602
PURE UUID: 7494664f-046e-4c75-b5c3-6b989dc4ef15

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Date deposited: 18 Mar 2020 17:30
Last modified: 19 May 2020 17:02

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