Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: applications to contour lines, sparse data and inpainting
This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [55]. We apply our methods to (i) surface reconstruction starting from the knowledge of finitely many level sets (or ‘contour lines’); (ii) scattered data ap...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2018
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| Online Access: | https://eprints.nottingham.ac.uk/55065/ |
| _version_ | 1848799110932463616 |
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| author | Zhang, Kewei Crooks, Elaine Orlando, Antonio |
| author_facet | Zhang, Kewei Crooks, Elaine Orlando, Antonio |
| author_sort | Zhang, Kewei |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [55]. We apply our methods to (i) surface reconstruction starting from the knowledge of finitely many level sets (or ‘contour lines’); (ii) scattered data approximation; (iii) image inpainting. For (i) and (ii) our methods give interpolations. For the case of finite sets (scattered data), in particular, our approximations provide a natural triangulation and piecewise affine interpolation. Prototype examples of explicitly calculated approximations and inpainting results are presented for both finite and compact sets. We also show numerical experiments for applications of our methods to high density salt & pepper noise reduction in image processing, for image inpainting and for approximation and interpolations of continuous functions sampled on finitely many level sets and on scattered points. |
| first_indexed | 2025-11-14T20:30:28Z |
| format | Article |
| id | nottingham-55065 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:30:28Z |
| publishDate | 2018 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-550652018-10-24T04:30:30Z https://eprints.nottingham.ac.uk/55065/ Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: applications to contour lines, sparse data and inpainting Zhang, Kewei Crooks, Elaine Orlando, Antonio This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [55]. We apply our methods to (i) surface reconstruction starting from the knowledge of finitely many level sets (or ‘contour lines’); (ii) scattered data approximation; (iii) image inpainting. For (i) and (ii) our methods give interpolations. For the case of finite sets (scattered data), in particular, our approximations provide a natural triangulation and piecewise affine interpolation. Prototype examples of explicitly calculated approximations and inpainting results are presented for both finite and compact sets. We also show numerical experiments for applications of our methods to high density salt & pepper noise reduction in image processing, for image inpainting and for approximation and interpolations of continuous functions sampled on finitely many level sets and on scattered points. Society for Industrial and Applied Mathematics 2018-08-23 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/55065/1/SIIMS-M116152RR-accepted.pdf Zhang, Kewei, Crooks, Elaine and Orlando, Antonio (2018) Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: applications to contour lines, sparse data and inpainting. SIAM Journal on Imaging Sciences . ISSN 1936-4954 (In Press) |
| spellingShingle | Zhang, Kewei Crooks, Elaine Orlando, Antonio Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: applications to contour lines, sparse data and inpainting |
| title | Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: applications to contour lines, sparse data and inpainting |
| title_full | Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: applications to contour lines, sparse data and inpainting |
| title_fullStr | Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: applications to contour lines, sparse data and inpainting |
| title_full_unstemmed | Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: applications to contour lines, sparse data and inpainting |
| title_short | Compensated convexity methods for approximations and interpolations of sampled functions in Euclidean spaces: applications to contour lines, sparse data and inpainting |
| title_sort | compensated convexity methods for approximations and interpolations of sampled functions in euclidean spaces: applications to contour lines, sparse data and inpainting |
| url | https://eprints.nottingham.ac.uk/55065/ |