Open AccessTHE EULER NUMBER FROM THE DISTANCE FUNCTION
Author(s) -
Ximo GualArnau
Publication year - 2013
Publication title -
image analysis and stereology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.237
H-Index - 27
eISSN - 1854-5165
pISSN - 1580-3139
DOI - 10.5566/ias.v32.p175-181
Subject(s) - mathematics , tangent , euler's formula , domain (mathematical analysis) , square (algebra) , concentric , mathematical analysis , function (biology) , euler characteristic , geometry , evolutionary biology , biology
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