Spatiotemporal Barcodes for Image Sequence Analysis

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 $$v\in K$$, 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.