@article{Gual-Arnau_2013, title={THE EULER NUMBER FROM THE DISTANCE FUNCTION}, volume={32}, url={https://www.ias-iss.org/ojs/IAS/article/view/1006}, DOI={10.5566/ias.v32.p175-181}, abstractNote={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 <em>O</em>, 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 <em>O</em> are considered.}, number={3}, journal={Image Analysis and Stereology}, author={Gual-Arnau, Ximo}, year={2013}, month={Nov.}, pages={175–181} }