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arXiv · 1109.2573

Pixelations of planar semialgebraic sets and shape recognition

Liviu I. Nicolaescu·Brandon Rowekamp
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Abstract

We describe an algorithm that associates to each positive real number $r$ and each finite collection $C_r$ of planar pixels of size $r$ a planar piecewise linear set $S_r$ with the following additional property: if $C_r$ is the collection of pixels of size $r$ that touch a given compact semialgebraic set $S$, then the normal cycle of $S_r$ converges to the normal cycle of $S$ in the sense of currents. In particular, in the limit we can recover the homotopy type of $S$ and its geometric invariants such as area, perimeter and curvature measures. At its core, this algorithm is a discretization of stratified Morse theory.

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Liviu I. Nicolaescu, Brandon Rowekamp. 2011-09-12. Pixelations of planar semialgebraic sets and shape recognition. https://doi.org/10.2140/agt.2014.14.3345

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