Abstract
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.
Citation
Liviu Nicolaescu. Brandon Rowekamp. "Pixelations of planar semialgebraic sets and shape recognition." Algebr. Geom. Topol. 14 (6) 3345 - 3394, 2014. https://doi.org/10.2140/agt.2014.14.3345
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