Abstract
In a recent paper we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued maps, provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we characterized the deletion of simple points, one of the most important processing operations in digital topology, as a particular kind of retraction.
In this work we give a simpler algorithm to define the retraction associated to the deletion of a simple point and we use this algorithm to characterize some well known parallel thinning algorithm as a particular kind of multivalued retraction, with the property that each point is retracted to its neighbors.
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Escribano, C., Giraldo, A., Sastre, M.A. (2009). Thinning Algorithms as Multivalued \({\mathcal{N}}\)-Retractions. In: Brlek, S., Reutenauer, C., Provençal, X. (eds) Discrete Geometry for Computer Imagery. DGCI 2009. Lecture Notes in Computer Science, vol 5810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04397-0_24
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DOI: https://doi.org/10.1007/978-3-642-04397-0_24
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