Getting Topological Information for a 80-Adjacency Doxel-Based 4D Volume through a Polytopal Cell Complex

Abstract

Abstract. Given an 80-adjacency doxel-based digital four-dimensional hypervolume V , we construct here an associated oriented 4-dimensional polytopal cell complex K(V ), having the same integer homological information (that related to n-dimensional holes that object has) than V . This is the first step toward the construction of an algebraic-topological representation (AT-model) for V , which suitably codifies it mainly in terms of its homological information. This AT-model is especially suitable for global and local topological analysis of digital 4D images.

Associating Cell Complexes to Four Dimensional Digital Objects

“…In Figure 2 we can see the digital object, the associated cell complex and the extracted homological information. The shown method, presents some computational improvements respect to similar methods such as the shown in [8]. Here, unnecessary data corresponding to the simplicialization of the convex hull of the unit hypercube are not to saved, and consequently the convex hull of each one of the bricks is obtained directly.…”