Extracting cell complexes from digital images

Abstract

In this paper, we define a method for constructing cell complexes from 4-dimensional binary digital images on a dual grid. First, we revisit a method similar to Kenmochi et al. method [6], [7], [8] for treating with images of dimension 3. Then, we extend this method to 4-dimensional images. The idea consists in considering the black 4-xels of the image as 0-cells of a cell complex. The cells of higher dimension of the complex are constructed by deforming the 4-cubes of the dual grid. Finally, the resulting complex can be simplified, for instance, by merging adjacent 4-cells which share a common 3-cell. More concretely, 0,1,2,3-cells non-incident to 4-cells are stored, together with 3-cells (and their boundary) incident to exactly one 4-cell