Abstract
An appropriate generalization of the classical notion of abstract cell complex, called primal-dual abstract cell complex (pACC for short) is the combinatorial notion used here for modeling and analyzing the topology of nD digital objects and images. Let \(D\subset I\) be a set of n-xels (ROI) and I be a n-dimensional digital image. We design a theoretical parallel algorithm for constructing a topologically meaningful asymmetric pACC HSF(D), called Homological Spanning Forest of D (HSF of D, for short) starting from a canonical symmetric pACC associated to I and based on the application of elementary homotopy operations to activate the pACC processing units. From this HSF-graph representation of D, it is possible to derive complete homology and homotopy information of it. The preprocessing procedure of computing HSF(I) is thoroughly discussed. In this way, a significant advance in understanding how the efficient HSF framework for parallel topological computation of 2D digital images developed in [2] can be generalized to higher dimension is made.
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Acknowledgments
This work has been supported by the Spanish research projects (supported by the Ministerio de EconomÃa y Competitividad and FEDER funds) COFNET (Event-based Cognitive Visual and Auditory Sensory Fusion, TEC2016-77785-P) and TOP4COG (Topological Recognition of 4D Digital Images via HSF model, MTM2016-81030-P (AEI/FEDER,UE)). The last co-author gratefully acknowledges the support of the Austrian Science Fund FWF-P27516.
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Real, P., Diaz-del-Rio, F., Onchis, D. (2017). Toward Parallel Computation of Dense Homotopy Skeletons for nD Digital Objects. In: Brimkov, V., Barneva, R. (eds) Combinatorial Image Analysis. IWCIA 2017. Lecture Notes in Computer Science(), vol 10256. Springer, Cham. https://doi.org/10.1007/978-3-319-59108-7_12
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DOI: https://doi.org/10.1007/978-3-319-59108-7_12
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