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      Double-sided probing by map of Aspl\"und's distances using Logarithmic Image Processing in the framework of Mathematical Morphology

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          Abstract

          We establish the link between Mathematical Morphology and the map of Aspl\"und's distances between a probe and a grey scale function, using the Logarithmic Image Processing scalar multiplication. We demonstrate that the map is the logarithm of the ratio between a dilation and an erosion of the function by a structuring function: the probe. The dilations and erosions are mappings from the lattice of the images into the lattice of the positive functions. Using a flat structuring element, the expression of the map of Aspl\"und's distances can be simplified with a dilation and an erosion of the image, these mappings stays in the lattice of the images. We illustrate our approach by an example of pattern matching with a non-flat structuring function.

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          The algebraic basis of mathematical morphology I. Dilations and erosions

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            Virtual double-sided image probing: A unifying framework for non-linear grayscale pattern matching

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              Logarithmic image processing for color images

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                Author and article information

                Journal
                2017-01-27
                Article
                1701.08092
                3769dd58-a9f9-4246-ab38-195015304ca1

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                cs.CV math.NA
                ccsd

                Numerical & Computational mathematics,Computer vision & Pattern recognition

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