Abstract
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 \(\mathcal {O}(m^3 + \beta _q \cdot n^3)\), where m is the size of the bounding box of the object, n is the size of the object and \(\beta _q\) is the rank of its qth 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].
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Gonzalez-Lorenzo, A., Bac, A., Mari, JL. (2022). A Heuristic for Short Homology Basis of Digital Objects. In: Baudrier, É., Naegel, B., Krähenbühl, A., Tajine, M. (eds) Discrete Geometry and Mathematical Morphology. DGMM 2022. Lecture Notes in Computer Science, vol 13493. Springer, Cham. https://doi.org/10.1007/978-3-031-19897-7_6
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