Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds

Zhang, Kewei and 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

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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.

Item Type: Article
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.worldscientific.com/doi/abs/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.
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1142/S0218202515500207
Depositing User: Eprints, Support
Date Deposited: 28 Feb 2017 11:51
Last Modified: 01 Mar 2017 11:20
URI: http://eprints.nottingham.ac.uk/id/eprint/40900

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