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Eigenfunctions of Ultrametric Morphological Openings and Closings

Abstract : This paper deals with the relationship between spectral analysis in min-max algebra and ultrametric morphological operators. Indeed, morphological semigroups in ultrametric spaces are essentially based on that algebra. Theory of eigenfunctionals in min-max analysis is revisited, including classical applications (preference analysis, percolation and hierarchical segmentation). Ultrametric distance is the fix point functional in min-max analysis and from this result, we prove that the ultrametric distance is the key ingredient to easily define the eigenfunctions of ultrametric morphological openings and closings.
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Contributor : Jesus Angulo Connect in order to contact the contributor
Submitted on : Friday, April 30, 2021 - 7:34:43 PM
Last modification on : Wednesday, August 24, 2022 - 11:41:35 AM

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Jesus Angulo. Eigenfunctions of Ultrametric Morphological Openings and Closings. IAPR International Conference on Discrete Geometry and Mathematical Morphology (DGMM), May 2021, Uppsala, Sweden. ⟨10.1007/978-3-030-76657-3_36⟩. ⟨hal-03108985v2⟩

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