Generalizing Mumford-Shah Model for Multiphase Piecewise Smooth Image Segmentation

This paper concerns multiphase piecewise smooth image segmentation with intensity inhomogeneities. Traditional methods based on the Mumford-Shah (MS) model require solving complicated diffusion equations evolving in irregular subdomains, leading to significant difficulties in efficient and accurate...

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Main Authors: Xiong, Wei, Gu, Ying, Wang, Li-Lian, Cheng, Jierong
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2017
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Online Access:https://hdl.handle.net/10356/85311
http://hdl.handle.net/10220/43681
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-853112020-03-07T12:31:30Z Generalizing Mumford-Shah Model for Multiphase Piecewise Smooth Image Segmentation Xiong, Wei Gu, Ying Wang, Li-Lian Cheng, Jierong School of Physical and Mathematical Sciences Mathematical Model Image Segmentation This paper concerns multiphase piecewise smooth image segmentation with intensity inhomogeneities. Traditional methods based on the Mumford-Shah (MS) model require solving complicated diffusion equations evolving in irregular subdomains, leading to significant difficulties in efficient and accurate segmentation, especially in multiphase scenarios. In this paper, we propose a general framework to modify the MS model by using smoothing operators that can avoid the complicated implementation and inaccurate segmentation of traditional approaches. A detailed analysis connecting the smoothing operators and the diffusion equations is given to justify the modification. In addition, we present an efficient algorithm based on the direct augmented Lagrangian method, which requires fewer parameters than the commonly used augmented Lagrangian method. Typically, the smoothing operator in the general model is chosen to be Gaussian kernel, the bilateral kernel, and the directional diffusion kernel, respectively. Ample numerical results are provided to demonstrate the efficiency and accuracy of the modified model and the proposed minimization algorithm through various comparisons with existing approaches. MOE (Min. of Education, S’pore) 2017-09-04T08:12:46Z 2019-12-06T16:01:18Z 2017-09-04T08:12:46Z 2019-12-06T16:01:18Z 2017 Journal Article Gu, Y., Xiong, W., Wang, L.-L., & Cheng, J. (2017). Generalizing Mumford-Shah Model for Multiphase Piecewise Smooth Image Segmentation. IEEE Transactions on Image Processing, 26(2), 942-952. 1057-7149 https://hdl.handle.net/10356/85311 http://hdl.handle.net/10220/43681 10.1109/TIP.2016.2636450 en IEEE Transactions on Image Processing © 2016 IEEE.
institution Nanyang Technological University
building NTU Library
country Singapore
collection DR-NTU
language English
topic Mathematical Model
Image Segmentation
spellingShingle Mathematical Model
Image Segmentation
Xiong, Wei
Gu, Ying
Wang, Li-Lian
Cheng, Jierong
Generalizing Mumford-Shah Model for Multiphase Piecewise Smooth Image Segmentation
description This paper concerns multiphase piecewise smooth image segmentation with intensity inhomogeneities. Traditional methods based on the Mumford-Shah (MS) model require solving complicated diffusion equations evolving in irregular subdomains, leading to significant difficulties in efficient and accurate segmentation, especially in multiphase scenarios. In this paper, we propose a general framework to modify the MS model by using smoothing operators that can avoid the complicated implementation and inaccurate segmentation of traditional approaches. A detailed analysis connecting the smoothing operators and the diffusion equations is given to justify the modification. In addition, we present an efficient algorithm based on the direct augmented Lagrangian method, which requires fewer parameters than the commonly used augmented Lagrangian method. Typically, the smoothing operator in the general model is chosen to be Gaussian kernel, the bilateral kernel, and the directional diffusion kernel, respectively. Ample numerical results are provided to demonstrate the efficiency and accuracy of the modified model and the proposed minimization algorithm through various comparisons with existing approaches.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Xiong, Wei
Gu, Ying
Wang, Li-Lian
Cheng, Jierong
format Article
author Xiong, Wei
Gu, Ying
Wang, Li-Lian
Cheng, Jierong
author_sort Xiong, Wei
title Generalizing Mumford-Shah Model for Multiphase Piecewise Smooth Image Segmentation
title_short Generalizing Mumford-Shah Model for Multiphase Piecewise Smooth Image Segmentation
title_full Generalizing Mumford-Shah Model for Multiphase Piecewise Smooth Image Segmentation
title_fullStr Generalizing Mumford-Shah Model for Multiphase Piecewise Smooth Image Segmentation
title_full_unstemmed Generalizing Mumford-Shah Model for Multiphase Piecewise Smooth Image Segmentation
title_sort generalizing mumford-shah model for multiphase piecewise smooth image segmentation
publishDate 2017
url https://hdl.handle.net/10356/85311
http://hdl.handle.net/10220/43681
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