Double-sided probing by map of Asplund's distances using Logarithmic Image Processing in the framework of Mathematical Morphology

Abstract

We establish the link between Mathematical Morphology and the map of Asplund'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 Asplund'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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References in corpus (4)

• Morphological segmentation of hyperspectral images
• Aspl{ü}nd's metric defined in the Logarithmic Image Processing (LIP) framework for colour and multivariate images
• Multivariate mathematical morphology for DCE-MRI image analysis in angiogenesis studies
• Spatio-Colour Asplünd 's Metric and Logarithmic Image Processing for Colour Images (LIPC)

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• Region homogeneity in the Logarithmic Image Processing framework: application to region growing algorithms
• Logarithmic Mathematical Morphology: Theory and applications