Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 6 (2014), 3345-3394.
Pixelations of planar semialgebraic sets and shape recognition
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.
Algebr. Geom. Topol., Volume 14, Number 6 (2014), 3345-3394.
Received: 5 August 2013
Revised: 22 April 2014
Accepted: 24 April 2014
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53A04: Curves in Euclidean space
Secondary: 53C65: Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx] 58A35: Stratified sets [See also 32S60]
Nicolaescu, Liviu; Rowekamp, Brandon. Pixelations of planar semialgebraic sets and shape recognition. Algebr. Geom. Topol. 14 (2014), no. 6, 3345--3394. doi:10.2140/agt.2014.14.3345. https://projecteuclid.org/euclid.agt/1513716043