Topology-preserving conditions for 2D digital images under rigid transformations

Abstract : In the continuous domain R^n, rigid transformations are topology-preserving operations. Due to digitization, this is not the case when considering digital images, i.e., images defined on Z^n. In this article, we begin to investigate this problem by studying conditions for digital images to preserve their topological properties under all rigid transformations on Z^2. Based on (i) the recently introduced notion of DRT graph, and (ii) the notion of simple point, we propose an algorithm for evaluating digital images topological invariance.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00838183
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Submitted on : Tuesday, September 23, 2014 - 4:45:31 PM
Last modification on : Thursday, July 19, 2018 - 3:34:01 PM
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Phuc Ngo, Yukiko Kenmochi, Nicolas Passat, Hugues Talbot. Topology-preserving conditions for 2D digital images under rigid transformations. Journal of Mathematical Imaging and Vision, Springer Verlag, 2014, 49 (2), pp.418-433. ⟨10.1007/s10851-013-0474-z⟩. ⟨hal-00838183v2⟩

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