Real Jurado, PedroMolina Abril, HelenaDíaz del Río, FernandoBlanco Trejo, Sergio2020-02-262020-02-262019Real Jurado, P., Molina Abril, H., Díaz del Río, F. y Blanco Trejo, S. (2019). Homological Region Adjacency Tree for a 3D Binary Digital Image via HSF Model. En CAIP 2019: 18th International Conference on Computer Analysis of Images and Patterns (375-387), Salerno, Italy: Springer.978-3-030-29887-60302-9743https://hdl.handle.net/11441/93652Given 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Binary 3D digital imageRegion Adjacency TreeCombinatorial topologyHomological Spanning Forestinfo:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1007/978-3-030-29888-3_30