Vertex Codification Applied to 3-D Binary Image Euler Number Computation

Abstract

A three dimensional (3-D) digital image emerges as a straightforward extension of a two dimensional (2-D) digital image. A 3-D digital image can be obtained by digitizing the 3-D space in which one or more objects of interest can be contained. From each object in the digital image, several features describing their geometry and topology can be computed. One of these features is the Euler number. An alternative method to compute the Euler number of a 3-D digital object (image) in terms of a codification of the vertices of the object voxels is described. The set of formal propositions baseline of the proposal operation are provided, demonstrated and numerically validated with simple objects. Examples with images of different complexity show the applicability of the proposal. The proposed method emerges as an extension of the proposal introduced for the 2-D case in [21] and as alternative of the formulation well described in [22].