Déformations homotopiques dans les images digitales n-aires

Loïc Mazo 1
1 MIV
LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection
Abstract : In a digital image, when performing processes such as registration, deformation or thinning, the preservation of the topological properties of the objects contained in the image (e.g., connected components, tunnels, cavities, etc.) is an important requirement. For 50 years, several tools enabling the analysis and the modification under topological constraints of binary images have been proposed and used. Nevertheless, in many fields an image is generally composed of several objects, and it is often important to understand or maintain their topological properties all together, that is the topology of each and the topology of the scene. In such images, the objects are characterised by specific labels on which there generally exists no meaningful order relation (unlike grey-level images for instance). In this thesis, we focus on homotopic deformations that preserve all the topological relations of such partitions of the space. After describing our theoretical framework for binary images, and its compatibility with usual approaches in digital imaging, we propose two models to be used with n-ary images. In these models, the regions of interest compose a sub-lattice of the power set of the labeled regions. Thereby, we can define some elementary modifications that preserve individual and "collective" topologies.
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Loïc Mazo. Déformations homotopiques dans les images digitales n-aires. Traitement des images [eess.IV]. Université de Strasbourg, 2011. Français. ⟨tel-00660049⟩

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