Adaptive wavelet collocation methods for image segmentation using TV–Allen–Cahn type models
An adaptive wavelet-based method is proposed for solving TV(total variation)–Allen–Cahn type models for multi-phase image segmentation. The adaptive algorithm integrates (i) grid adaptation based on a threshold of the sparse wavelet representation of the locally-structured solution; and (ii) effecti...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/97108 http://hdl.handle.net/10220/17921 |
| _version_ | 1811680982374285312 |
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| author | Tai, Xue Cheng Rong, Zhijian Wang, Li-Lian |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Tai, Xue Cheng Rong, Zhijian Wang, Li-Lian |
| author_sort | Tai, Xue Cheng |
| collection | NTU |
| description | An adaptive wavelet-based method is proposed for solving TV(total variation)–Allen–Cahn type models for multi-phase image segmentation. The adaptive algorithm integrates (i) grid adaptation based on a threshold of the sparse wavelet representation of the locally-structured solution; and (ii) effective finite difference on irregular stencils. The compactly supported interpolating-type wavelets enjoy very fast wavelet transforms, and act as a piecewise constant function filter. These lead to fairly sparse computational grids, and relax the stiffness of the nonlinear PDEs. Equipped with this algorithm, the proposed sharp interface model becomes very effective for multi-phase image segmentation. This method is also applied to image restoration and similar advantages are observed. |
| first_indexed | 2024-10-01T03:33:42Z |
| format | Journal Article |
| id | ntu-10356/97108 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:33:42Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/971082020-03-07T12:34:40Z Adaptive wavelet collocation methods for image segmentation using TV–Allen–Cahn type models Tai, Xue Cheng Rong, Zhijian Wang, Li-Lian School of Physical and Mathematical Sciences DRNTU::Science::Mathematics An adaptive wavelet-based method is proposed for solving TV(total variation)–Allen–Cahn type models for multi-phase image segmentation. The adaptive algorithm integrates (i) grid adaptation based on a threshold of the sparse wavelet representation of the locally-structured solution; and (ii) effective finite difference on irregular stencils. The compactly supported interpolating-type wavelets enjoy very fast wavelet transforms, and act as a piecewise constant function filter. These lead to fairly sparse computational grids, and relax the stiffness of the nonlinear PDEs. Equipped with this algorithm, the proposed sharp interface model becomes very effective for multi-phase image segmentation. This method is also applied to image restoration and similar advantages are observed. 2013-11-29T05:44:25Z 2019-12-06T19:39:02Z 2013-11-29T05:44:25Z 2019-12-06T19:39:02Z 2013 2013 Journal Article Rong, Z., Wang, L.-L., & Tai, X.-C. (2013). Adaptive wavelet collocation methods for image segmentation using TV–Allen–Cahn type models. Advances in computational mathematics, 38(1), 101-131. https://hdl.handle.net/10356/97108 http://hdl.handle.net/10220/17921 10.1007/s10444-011-9227-y en Advances in computational mathematics |
| spellingShingle | DRNTU::Science::Mathematics Tai, Xue Cheng Rong, Zhijian Wang, Li-Lian Adaptive wavelet collocation methods for image segmentation using TV–Allen–Cahn type models |
| title | Adaptive wavelet collocation methods for image segmentation using TV–Allen–Cahn type models |
| title_full | Adaptive wavelet collocation methods for image segmentation using TV–Allen–Cahn type models |
| title_fullStr | Adaptive wavelet collocation methods for image segmentation using TV–Allen–Cahn type models |
| title_full_unstemmed | Adaptive wavelet collocation methods for image segmentation using TV–Allen–Cahn type models |
| title_short | Adaptive wavelet collocation methods for image segmentation using TV–Allen–Cahn type models |
| title_sort | adaptive wavelet collocation methods for image segmentation using tv allen cahn type models |
| topic | DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/97108 http://hdl.handle.net/10220/17921 |
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