Spatiotemporal Barcodes for Image Sequence Analysis

Abstract

Taking as input a time-varying sequence of two-dimensional (2D) binary images, we develop an algorithm for computing a spatiotemporal 0–barcode encoding lifetime of connected components on the image sequence over time. This information may not coincide with the one provided by the 0–barcode encoding the 0–persistent homology, since the latter does not respect the principle that it is not possible to move backwards in time. A cell complex K is computed from the given sequence, being the cells of K classified as spatial or temporal depending on whether they connect two consecutive frames or not. A spatiotemporal path is defined as a sequence of edges of K forming a path such that two edges of the path cannot connect the same two consecutive frames. In our algorithm, for each vertex v ∈ K, a spatiotemporal path from v to the “oldest” spatiotemporally-connected vertex is computed and the corresponding spatiotemporal 0–bar is added to the spatiotemporal 0–barcode.