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Pixelations of planar
semialgebraic sets and shape recognition
Liviu I Nicolaescu and Brandon Rowekamp |
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Algebraic & Geometric Topology 14 (2014) 3345–3394
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Abstract |
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We describe an algorithm that associates to each positive real number and each finite collection of planar pixels of size a planar piecewise linear set with the following property: If is the collection of pixels of size that touch a given compact semialgebraic set , then the normal cycle of converges in the sense of currents to the normal cycle of . In particular, in the limit we can recover the homotopy type of and its geometric invariants such as area, perimeter and curvature measures. At its core, this algorithm is a discretization of stratified Morse theory. |
Keywords
semialgebraic sets, pixelations, normal cycle, total
curvature, Morse theory
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Mathematical Subject Classification 2010
Primary: 53A04
Secondary: 53C65, 58A35
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References |
Publication
Received: 5 August 2013
Revised: 22 April 2014
Accepted: 24 April 2014
Published: 15 January 2015
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Authors |
| Liviu I Nicolaescu | |
| Department of Mathematics University of Notre Dame 255 Hurley Notre Dame, IN 46556-4618 USA |
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| http://www.nd.edu/~lnicolae/ | |
| Brandon Rowekamp | |
| Department of Mathematics &
Statistics Minnesota State University, Mankato 273 Wissink Hall Mankato, MN 56001 USA |
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