Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds
We apply compensated convex transforms to define a multiscale Hausdorff stable method to extract intersections between smooth compact manifolds represented by their characteristic functions or as point clouds embedded in Rn. We prove extraction results on intersections of smooth compact manifolds an...
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| Format: | Article |
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World Scientific Publishing
2015
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| Online Access: | https://eprints.nottingham.ac.uk/40900/ |
| _version_ | 1848796158500012032 |
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| author | Zhang, Kewei Orlando, Antonio Crooks, Elaine |
| author_facet | Zhang, Kewei Orlando, Antonio Crooks, Elaine |
| author_sort | Zhang, Kewei |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We apply compensated convex transforms to define a multiscale Hausdorff stable method to extract intersections between smooth compact manifolds represented by their characteristic functions or as point clouds embedded in Rn. We prove extraction results on intersections of smooth compact manifolds and for points of high curvature. As a result of the Hausdorff–Lipschitz continuity of our transforms, we show that our method is stable against dense sampling of smooth manifolds with noise. Examples of explicitly calculated prototype models for some simple cases are presented, which are also used in the proofs of our main results. Numerical experiments in two- and three-dimensional space, and applications to geometric objects are also shown. |
| first_indexed | 2025-11-14T19:43:32Z |
| format | Article |
| id | nottingham-40900 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:32Z |
| publishDate | 2015 |
| publisher | World Scientific Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-409002020-05-04T17:07:47Z https://eprints.nottingham.ac.uk/40900/ Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds Zhang, Kewei Orlando, Antonio Crooks, Elaine We apply compensated convex transforms to define a multiscale Hausdorff stable method to extract intersections between smooth compact manifolds represented by their characteristic functions or as point clouds embedded in Rn. We prove extraction results on intersections of smooth compact manifolds and for points of high curvature. As a result of the Hausdorff–Lipschitz continuity of our transforms, we show that our method is stable against dense sampling of smooth manifolds with noise. Examples of explicitly calculated prototype models for some simple cases are presented, which are also used in the proofs of our main results. Numerical experiments in two- and three-dimensional space, and applications to geometric objects are also shown. World Scientific Publishing 2015-05-31 Article PeerReviewed Zhang, Kewei, Orlando, Antonio and Crooks, Elaine (2015) Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds. Mathematical Models and Methods in Applied Sciences, 25 (05). pp. 839-873. ISSN 1793-6314 Compensated convex transforms; mathematical morphology; non-flat morphological operators; characteristic function; point clouds; Hausdorff–Lipschitz continuity; locality property; surface-to-surface intersection; transversal intersections; random samples. http://www.worldscientific.com/doi/abs/10.1142/S0218202515500207 doi:10.1142/S0218202515500207 doi:10.1142/S0218202515500207 |
| spellingShingle | Compensated convex transforms; mathematical morphology; non-flat morphological operators; characteristic function; point clouds; Hausdorff–Lipschitz continuity; locality property; surface-to-surface intersection; transversal intersections; random samples. Zhang, Kewei Orlando, Antonio Crooks, Elaine Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds |
| title | Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds |
| title_full | Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds |
| title_fullStr | Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds |
| title_full_unstemmed | Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds |
| title_short | Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds |
| title_sort | compensated convexity and hausdorff stable extraction of intersections for smooth manifolds |
| topic | Compensated convex transforms; mathematical morphology; non-flat morphological operators; characteristic function; point clouds; Hausdorff–Lipschitz continuity; locality property; surface-to-surface intersection; transversal intersections; random samples. |
| url | https://eprints.nottingham.ac.uk/40900/ https://eprints.nottingham.ac.uk/40900/ https://eprints.nottingham.ac.uk/40900/ |