THE EULER NUMBER FROM THE DISTANCE FUNCTION

Ximo Gual-Arnau

Abstract

We present a new method to obtain the Euler number of a domain based on the tangent counts of concentric spheres in ℝ³ (or circles in ℝ², with respect to the center O, that sweeps the domain. This method is derived from the Poincaré-Hopf Theorem, when the index of critical points of the square of the distance function with respect to the origin O are considered.

Keywords
critical points; distance function; Euler number; stereology; tangent counts

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DOI: 10.5566/ias.v32.p175-181

Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)