A Heuristic for Short Homology Basis of Digital Objects.

Finding the minimum homology basis of a simplicial complex is a hard problem unless one only considers the first homology group. In this paper, we introduce a general heuristic for finding a short homology basis of any dimension for digital objects (that is, for their associated cubical complexes) with complexity O ( m 3 + β q · n 3 ) , where m is the size of the bounding box of the object, n is the size of the object and β q is the rank of its q th homology group. Our heuristic makes use of the thickness-breadth balls, a tool for visualizing and locating holes in digital objects. We evaluate our algorithm with a data set of 3D digital objects and compare it with an adaptation of the best current algorithm for computing the minimum radius homology basis by Dey, Li and Wang [ 10 ].