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...
| Main Authors: | , , , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2017
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/85311 http://hdl.handle.net/10220/43681 |
| _version_ | 1811683267967975424 |
|---|---|
| author | Xiong, Wei Gu, Ying Wang, Li-Lian Cheng, Jierong |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Xiong, Wei Gu, Ying Wang, Li-Lian Cheng, Jierong |
| author_sort | Xiong, Wei |
| collection | NTU |
| 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. |
| first_indexed | 2024-10-01T04:10:02Z |
| format | Journal Article |
| id | ntu-10356/85311 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:10:02Z |
| publishDate | 2017 |
| record_format | dspace |
| spelling | ntu-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. |
| spellingShingle | Mathematical Model Image Segmentation Xiong, Wei Gu, Ying Wang, Li-Lian Cheng, Jierong Generalizing Mumford-Shah Model for Multiphase Piecewise Smooth Image Segmentation |
| title | 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_short | Generalizing Mumford-Shah Model for Multiphase Piecewise Smooth Image Segmentation |
| title_sort | generalizing mumford shah model for multiphase piecewise smooth image segmentation |
| topic | Mathematical Model Image Segmentation |
| url | https://hdl.handle.net/10356/85311 http://hdl.handle.net/10220/43681 |
| work_keys_str_mv | AT xiongwei generalizingmumfordshahmodelformultiphasepiecewisesmoothimagesegmentation AT guying generalizingmumfordshahmodelformultiphasepiecewisesmoothimagesegmentation AT wanglilian generalizingmumfordshahmodelformultiphasepiecewisesmoothimagesegmentation AT chengjierong generalizingmumfordshahmodelformultiphasepiecewisesmoothimagesegmentation |