Adaptive Shape Diagrams for Multiscale Morphometrical Image Analysis

Authors:
Séverine Rivollier;Johan Debayle;Jean-Charles Pinoli
Affiliations:
Ecole Nationale Supérieure des Mines, LGF UMR CNRS 5307, Saint-Etienne cedex 2, France 42023;Ecole Nationale Supérieure des Mines, LGF UMR CNRS 5307, Saint-Etienne cedex 2, France 42023;Ecole Nationale Supérieure des Mines, LGF UMR CNRS 5307, Saint-Etienne cedex 2, France 42023
Venue:
Journal of Mathematical Imaging and Vision
Year:
2014

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Abstract

Shape diagrams are integral geometric representations in the Euclidean plane introduced to study 2D connected compact sets. Such a set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. In addition, the General Adaptive Neighborhoods (GANs) are spatial neighborhoods defined around each point of the spatial support of a gray-tone image, that fit with the image local structures. The aim of this paper is to introduce and study the GAN-based shape diagrams, which allow a gray-tone image morphometrical analysis to be realized in a local, adaptive and multiscale way. The GAN-based shape diagrams will be illustrated on standard images and also applied in the biomedical and materials areas.