Abstract
In [4], given a binary 26-adjacency voxel-based digital volume V, the homological information (that related to n-dimensional holes: connected components, ”tunnels” and cavities) is extracted from a linear map (called homology gradient vector field) acting on a polyhedral cell complex P(V) homologically equivalent to V. We develop here an alternative way for constructing P(V) based on homological algebra arguments as well as a new more efficient algorithm for computing a homology gradient vector field based on the contractibility of the maximal cells of P(V).
This work has been partially supported by ”Computational Topology and Applied Mathematics” PAICYT research project FQM-296, ”Andalusian research project PO6-TIC-02268 and Spanish MEC project MTM2006-03722, and the Austrian Science Fund under grant P20134-N13.
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Real, P., Molina-Abril, H. (2009). Cell AT-Models for Digital Volumes . In: Torsello, A., Escolano, F., Brun, L. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2009. Lecture Notes in Computer Science, vol 5534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02124-4_32
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DOI: https://doi.org/10.1007/978-3-642-02124-4_32
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