Algebraic topological analysis of time-sequence of digital images

Abstract

This paper introduces an algebraic framework for a topological analysis of time-varying 2D digital binary–valued images, each of them defined as 2D arrays of pixels. Our answer is based on an algebraic-topological coding, called AT–model, for a nD (n=2,3) digital binary-valued image I consisting simply in taking I together with an algebraic object depending on it. Considering AT–models for all the 2D digital images in a time sequence, it is possible to get an AT–model for the 3D digital image consisting in concatenating the successive 2D digital images in the sequence. If the frames are represented in a quadtree format, a similar positive result can be derived.