Parallel computation of the Euler number via Connectivity Graph

Abstract This paper regards the computation of the Euler number (EN) of a binary image by means of the Connectivity Graph (CG), which is derived from the Cylindrical Algebraic Decomposition of the Euclidean plane. The corresponding decomposition of the discrete plane has shown how the CG reflects the topological structure of a binary image, and how it is a powerful data structure for the computation of shape indicators as the Euler number. Here some properties related to the CG and the EN are introduced; moreover two methods to compute the EN of a binary image are shown; a parallel algorithm is described in detail.