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Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds

Zhang, Kewei; Orlando, Antonio; Crooks, Elaine

Authors

KEWEI ZHANG Kewei.Zhang@nottingham.ac.uk
Professor of Mathematical Analysis

Antonio Orlando

Elaine Crooks



Abstract

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.

Journal Article Type Article
Publication Date May 31, 2015
Journal Mathematical Models and Methods in Applied Sciences
Print ISSN 0218-2025
Electronic ISSN 1793-6314
Publisher World Scientific
Peer Reviewed Peer Reviewed
Volume 25
Issue 5
APA6 Citation Zhang, K., Orlando, A., & Crooks, E. (2015). Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds. Mathematical Models and Methods in Applied Sciences, 25(5), https://doi.org/10.1142/S0218202515500207
DOI https://doi.org/10.1142/S0218202515500207
Keywords 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.
Publisher URL http://www.worldscientific.com/doi/abs/10.1142/S0218202515500207
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information Electronic version of an article published as Mathematical Models and Methods in Applied Sciences, v. 25, no. 5, 2015, p. 839-873, doi:10.1142/S0218202515500207, © copyright World Scientific Publishing Company. http://www.worldscienti....1142/S0218202515500207

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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