A ridge and corner preserving model for surface restoration
One challenge in surface restoration is to design surface diffusion preserving ridges and sharp corners. In this paper, we propose a new surface restoration model based on the observation that surfaces' implicit representations are continuous functions whose first order derivatives have discont...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
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| Online Access: | https://hdl.handle.net/10356/97541 http://hdl.handle.net/10220/13175 |
| _version_ | 1811695574642065408 |
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| author | Chan, Tony F. Lai, Rongjie Tai, Xue Cheng |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Chan, Tony F. Lai, Rongjie Tai, Xue Cheng |
| author_sort | Chan, Tony F. |
| collection | NTU |
| description | One challenge in surface restoration is to design surface diffusion preserving ridges and sharp corners. In this paper, we propose a new surface restoration model based on the observation that surfaces' implicit representations are continuous functions whose first order derivatives have discontinuities at ridges and sharp corners. Regularized by vectorial total variation on the derivatives of surfaces' implicit representation functions, the proposed model has ridge and corner preserving properties validated by numerical experiments. To solve the proposed fourth order and convex problem efficiently, we further design a numerical algorithm based on the augmented Lagrangian method. Moreover, the theoretical convergence analysis of the proposed algorithm is also provided. To demonstrate the efficiency and robustness of the proposed method, we show restoration results on several different surfaces and also conduct comparisons with the mean curvature flow method and the nonlocal mean method. |
| first_indexed | 2024-10-01T07:25:38Z |
| format | Journal Article |
| id | ntu-10356/97541 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:25:38Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/975412023-02-28T19:40:44Z A ridge and corner preserving model for surface restoration Chan, Tony F. Lai, Rongjie Tai, Xue Cheng School of Physical and Mathematical Sciences One challenge in surface restoration is to design surface diffusion preserving ridges and sharp corners. In this paper, we propose a new surface restoration model based on the observation that surfaces' implicit representations are continuous functions whose first order derivatives have discontinuities at ridges and sharp corners. Regularized by vectorial total variation on the derivatives of surfaces' implicit representation functions, the proposed model has ridge and corner preserving properties validated by numerical experiments. To solve the proposed fourth order and convex problem efficiently, we further design a numerical algorithm based on the augmented Lagrangian method. Moreover, the theoretical convergence analysis of the proposed algorithm is also provided. To demonstrate the efficiency and robustness of the proposed method, we show restoration results on several different surfaces and also conduct comparisons with the mean curvature flow method and the nonlocal mean method. Published version 2013-08-22T04:08:09Z 2019-12-06T19:43:44Z 2013-08-22T04:08:09Z 2019-12-06T19:43:44Z 2013 2013 Journal Article Lai, R., Tai, X. C.,& Chan, T. F. (2013). A Ridge and Corner Preserving Model for Surface Restoration. SIAM Journal on Scientific Computing, 35(2), A675-A695. https://hdl.handle.net/10356/97541 http://hdl.handle.net/10220/13175 10.1137/110846634 en SIAM journal on scientific computing © 2013 Society for Industrial and Applied Mathematics. This paper was published in SIAM Journal on Scientific Computing and is made available as an electronic reprint (preprint) with permission of Society for Industrial and Applied Mathematics. The paper can be found at the following official DOI: [http://dx.doi.org/10.1137/110846634]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. application/pdf |
| spellingShingle | Chan, Tony F. Lai, Rongjie Tai, Xue Cheng A ridge and corner preserving model for surface restoration |
| title | A ridge and corner preserving model for surface restoration |
| title_full | A ridge and corner preserving model for surface restoration |
| title_fullStr | A ridge and corner preserving model for surface restoration |
| title_full_unstemmed | A ridge and corner preserving model for surface restoration |
| title_short | A ridge and corner preserving model for surface restoration |
| title_sort | ridge and corner preserving model for surface restoration |
| url | https://hdl.handle.net/10356/97541 http://hdl.handle.net/10220/13175 |
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