How to Make nD Functions Digitally Well-Composed in a Self-dual Way
International audience Latecki et al. introduced the notion of 2D and 3D well-composed images, i.e., a class of images free from the " connectivities paradox " of digital topology. Unfortunately natural and synthetic images are not a priori well-composed. In this paper we extend the notion...
Main Authors: | , , |
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Other Authors: | , , , , , , , |
Format: | Conference Object |
Language: | English |
Published: |
HAL CCSD
2015
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Subjects: | |
Online Access: | https://hal.archives-ouvertes.fr/hal-01168723 https://hal.archives-ouvertes.fr/hal-01168723/document https://hal.archives-ouvertes.fr/hal-01168723/file/article.pdf https://doi.org/10.1007/978-3-319-18720-4_47 |
Summary: | International audience Latecki et al. introduced the notion of 2D and 3D well-composed images, i.e., a class of images free from the " connectivities paradox " of digital topology. Unfortunately natural and synthetic images are not a priori well-composed. In this paper we extend the notion of " digital well-composedness " to nD sets, integer-valued functions (gray-level images), and interval-valued maps. We also prove that the digital well-composedness implies the equivalence of connectivities of the level set components in nD. Contrasting with a previous result stating that it is not possible to obtain a discrete nD self-dual digitally well-composed function with a local interpolation, we then propose and prove a self-dual discrete (non-local) interpolation method whose result is always a digitally well-composed function. This method is based on a sub-part of a quasi-linear algorithm that computes the morphological tree of shapes. |
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