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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.03125 |
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| _version_ | 1866909498501758976 |
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| author | Alkämper, Martin Hilb, Stephan Langer, Andreas |
| author_facet | Alkämper, Martin Hilb, Stephan Langer, Andreas |
| contents | Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general $L^1$-$L^2$-$TV$ functional over the space of functions of bounded variations by adaptivity in a finite element setting. For automatically generating an adaptive grid we introduce indicators based on a-posteriori error estimates. Further we discuss data interpolation methods on unstructured grids in the context of image processing and present a pixel-based interpolation method. The efficiency of our derived adaptive finite element scheme is demonstrated on image inpainting and the task of computing the optical flow in image sequences. In particular, for optical flow estimation we derive an adaptive finite element coarse-to-fine scheme which allows resolving large displacements and speeds-up the computing time significantly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A primal-dual adaptive finite element method for total variation minimization Alkämper, Martin Hilb, Stephan Langer, Andreas Numerical Analysis Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general $L^1$-$L^2$-$TV$ functional over the space of functions of bounded variations by adaptivity in a finite element setting. For automatically generating an adaptive grid we introduce indicators based on a-posteriori error estimates. Further we discuss data interpolation methods on unstructured grids in the context of image processing and present a pixel-based interpolation method. The efficiency of our derived adaptive finite element scheme is demonstrated on image inpainting and the task of computing the optical flow in image sequences. In particular, for optical flow estimation we derive an adaptive finite element coarse-to-fine scheme which allows resolving large displacements and speeds-up the computing time significantly. |
| title | A primal-dual adaptive finite element method for total variation minimization |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.03125 |