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Linkage between piecewise constant Mumford-Shah model and Rudin-Osher-Fatemi model and its virtue in image segmentation

Linkage between piecewise constant Mumford-Shah model and Rudin-Osher-Fatemi model and its virtue in image segmentation
Linkage between piecewise constant Mumford-Shah model and Rudin-Osher-Fatemi model and its virtue in image segmentation
The piecewise constant Mumford-Shah (PCMS) model and the Rudin-Osher-Fatemi (ROF) model are two important variational models in image segmentation and image restoration, respectively. In this paper, we explore a linkage between these models. We prove that for the twophase segmentation problem a partial minimizer of the PCMS model can be obtained by thresholding the minimizer of the ROF model. A similar linkage is still valid for multiphase segmentation under specific assumptions. Thus it opens a new segmentation paradigm: image segmentation can be done via image restoration plus thresholding. This new paradigm, which circumvents the innate nonconvex property of the PCMS model, therefore, improves the segmentation performance in both efficiency (much faster than state-of-the-art methods based on the PCMS model, particularly when the phase number is high)the and effectiveness (producing segmentation results with better quality) due to the flexibility of the ROF model in tackling degraded images, such as noisy images, blurry images, or images with information loss. As a by-product of the new paradigm, we derive a novel segmentation method, called thresholded-ROF (T-ROF) method, to illustrate the virtue of managing image segmentation through image restoration techniques. The convergence of the T-ROF method is proved, and elaborate experimental results and comparisons are presented.
Chan-Vese model, Image restoration, Image segmentation, Mumford{Shah model, Thresholding, Total variation ROF model
1064-8275
B1310-B1340
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Chan, Raymond
9185af9b-f073-4e3d-8f22-1dac8d28db58
Schönlieb, Carola Bibiane
655fcff7-df67-4700-ac57-c318656c4722
Steidl, Gabriele
c61576e3-9691-455d-bf74-7014841fb0de
Zeng, Tieyong
8bae04dd-2c0d-49f2-898b-30cdc0f5e286
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Chan, Raymond
9185af9b-f073-4e3d-8f22-1dac8d28db58
Schönlieb, Carola Bibiane
655fcff7-df67-4700-ac57-c318656c4722
Steidl, Gabriele
c61576e3-9691-455d-bf74-7014841fb0de
Zeng, Tieyong
8bae04dd-2c0d-49f2-898b-30cdc0f5e286

Cai, Xiaohao, Chan, Raymond, Schönlieb, Carola Bibiane, Steidl, Gabriele and Zeng, Tieyong (2019) Linkage between piecewise constant Mumford-Shah model and Rudin-Osher-Fatemi model and its virtue in image segmentation. SIAM Journal on Scientific Computing, 41 (6), B1310-B1340. (doi:10.1137/18M1202980).

Record type: Article

Abstract

The piecewise constant Mumford-Shah (PCMS) model and the Rudin-Osher-Fatemi (ROF) model are two important variational models in image segmentation and image restoration, respectively. In this paper, we explore a linkage between these models. We prove that for the twophase segmentation problem a partial minimizer of the PCMS model can be obtained by thresholding the minimizer of the ROF model. A similar linkage is still valid for multiphase segmentation under specific assumptions. Thus it opens a new segmentation paradigm: image segmentation can be done via image restoration plus thresholding. This new paradigm, which circumvents the innate nonconvex property of the PCMS model, therefore, improves the segmentation performance in both efficiency (much faster than state-of-the-art methods based on the PCMS model, particularly when the phase number is high)the and effectiveness (producing segmentation results with better quality) due to the flexibility of the ROF model in tackling degraded images, such as noisy images, blurry images, or images with information loss. As a by-product of the new paradigm, we derive a novel segmentation method, called thresholded-ROF (T-ROF) method, to illustrate the virtue of managing image segmentation through image restoration techniques. The convergence of the T-ROF method is proved, and elaborate experimental results and comparisons are presented.

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More information

Accepted/In Press date: 16 October 2019
e-pub ahead of print date: 5 December 2019
Published date: 2019
Keywords: Chan-Vese model, Image restoration, Image segmentation, Mumford{Shah model, Thresholding, Total variation ROF model

Identifiers

Local EPrints ID: 438778
URI: http://eprints.soton.ac.uk/id/eprint/438778
ISSN: 1064-8275
PURE UUID: 3cc6054a-937b-4ed7-98f4-0c4c4d50975d

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Date deposited: 24 Mar 2020 17:30
Last modified: 14 Sep 2021 17:43

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Contributors

Author: Xiaohao Cai
Author: Raymond Chan
Author: Carola Bibiane Schönlieb
Author: Gabriele Steidl
Author: Tieyong Zeng

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