Des Algorithmes morphologiques à l'intelligence artificielle

Michel Schmitt
Abstract : The aim of this thesis is to examine some aspects of mathematical morphology from special viewpoints. We first show how the notion of convergence of closed sets and that of random closed sets can be used in computational geometry. Then we describe a new technique which allows us to write efficient morphological algorithms for binary image processing by means of boundary coding with chains and loops. We describe among others the following algorithms: erosion, dilation, distance function (both in the Euclidean and the geodesic case), propagation function, (in the hexagonal and dodecagonal metrics), labeling, particle reconstruction, etc. We also tackle morphological measures such as diametrical variation, Ferret's diameter, perimeter, Euler's number, etc. The use of these transformations is then illustrated by the complete resolution of one special problem in material sciences, where we discuss the respective quality of about ten different solutions. Finally, the attempt to formalize the use of the morphological transformations led to an automatic programming system in mathematical morphology.
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Michel Schmitt. Des Algorithmes morphologiques à l'intelligence artificielle. Mathematics [math]. École Nationale Supérieure des Mines de Paris, 1989. English. ⟨pastel-00001572⟩

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