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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.28078 |
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| _version_ | 1866910096177496064 |
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| author | Giga, Yoshikazu Kubo, Ayato Kuroda, Hirotoshi Sakakibara, Koya |
| author_facet | Giga, Yoshikazu Kubo, Ayato Kuroda, Hirotoshi Sakakibara, Koya |
| contents | We consider a Kobayashi-Warren-Carter (KWC) type total variation energy with a fidelity term. Since the energy is non-convex, the profiles of minimizers are quite different from those of the original Rudin-Osher-Fatemi energy. In one-dimensional setting, we prove that KWC type energy (and its generalization) with fidelity must have a piecewise constant minimizer if the data in fidelity is bounded not necessarily in $BV$. Moreover, we give quantitative estimates of the energy for a monotone data in fidelity. This estimate shows that any minimizer must be piecewise constant with an improved estimate of the number of jumps for a monotone data. We also show the non-uniqueness of minimizers. Since this energy is useful from the point of segmentation or clustering, we compare with results of segmentation by the original Rudin-Osher-Fatemi energy and Mumford-Shah energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28078 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Segmentation of monotone data by Kobayashi-Warren-Carter type total variation energies Giga, Yoshikazu Kubo, Ayato Kuroda, Hirotoshi Sakakibara, Koya Analysis of PDEs 49AQ20, 74A50, 74N05 We consider a Kobayashi-Warren-Carter (KWC) type total variation energy with a fidelity term. Since the energy is non-convex, the profiles of minimizers are quite different from those of the original Rudin-Osher-Fatemi energy. In one-dimensional setting, we prove that KWC type energy (and its generalization) with fidelity must have a piecewise constant minimizer if the data in fidelity is bounded not necessarily in $BV$. Moreover, we give quantitative estimates of the energy for a monotone data in fidelity. This estimate shows that any minimizer must be piecewise constant with an improved estimate of the number of jumps for a monotone data. We also show the non-uniqueness of minimizers. Since this energy is useful from the point of segmentation or clustering, we compare with results of segmentation by the original Rudin-Osher-Fatemi energy and Mumford-Shah energy. |
| title | Segmentation of monotone data by Kobayashi-Warren-Carter type total variation energies |
| topic | Analysis of PDEs 49AQ20, 74A50, 74N05 |
| url | https://arxiv.org/abs/2603.28078 |