Image Decomposition with G-norm Weighted by Total Symmetric Variation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916665138085888 |
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| author | He, Roy Y. Huska, Martin Liu, Hao |
| author_facet | He, Roy Y. Huska, Martin Liu, Hao |
| contents | In this paper, we propose a novel variational model for decomposing images into their respective cartoon and texture parts. Our model characterizes certain non-local features of any Bounded Variation (BV) image by its Total Symmetric Variation (TSV). We demonstrate that TSV is effective in identifying regional boundaries. Based on this property, we introduce a weighted Meyer's $G$-norm to identify texture interiors without including contour edges. For BV images with bounded TSV, we show that the proposed model admits a solution. Additionally, we design a fast algorithm based on operator-splitting to tackle the associated non-convex optimization problem. The performance of our method is validated by a series of numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Image Decomposition with G-norm Weighted by Total Symmetric Variation He, Roy Y. Huska, Martin Liu, Hao Computer Vision and Pattern Recognition In this paper, we propose a novel variational model for decomposing images into their respective cartoon and texture parts. Our model characterizes certain non-local features of any Bounded Variation (BV) image by its Total Symmetric Variation (TSV). We demonstrate that TSV is effective in identifying regional boundaries. Based on this property, we introduce a weighted Meyer's $G$-norm to identify texture interiors without including contour edges. For BV images with bounded TSV, we show that the proposed model admits a solution. Additionally, we design a fast algorithm based on operator-splitting to tackle the associated non-convex optimization problem. The performance of our method is validated by a series of numerical experiments. |
| title | Image Decomposition with G-norm Weighted by Total Symmetric Variation |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2503.22560 |