Abstract
Given a 3D binary digital image I, we define and compute an edge-weighted tree, called Homological Region Tree (or Hom-Tree, for short). It coincides, as unweighted graph, with the classical Region Adjacency Tree of black 6-connected components (CCs) and white 26-connected components of I. In addition, we define the weight of an edge (R, S) as the number of tunnels that the CCs R and S “share”. The Hom-Tree structure is still an isotopic invariant of I. Thus, it provides information about how the different homology groups interact between them, while preserving the duality of black and white CCs.
An experimentation with a set of synthetic images showing different shapes and different complexity of connected component nesting is performed for numerically validating the method.
Work supported by the Spanish research projects TOP4COG:MTM2016-81030-P (AEI/FEDER, UE), COFNET (AEI/FEDER, UE) and the VPPI of University of Seville.
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Real, P., Molina-Abril, H., Díaz-del-Río, F., Blanco-Trejo, S. (2019). Homological Region Adjacency Tree for a 3D Binary Digital Image via HSF Model. In: Vento, M., Percannella, G. (eds) Computer Analysis of Images and Patterns. CAIP 2019. Lecture Notes in Computer Science(), vol 11678. Springer, Cham. https://doi.org/10.1007/978-3-030-29888-3_30
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