Les travaux présentés et discutés dans cette thèse ont pour objectif de proposer plusieurs solutions au problème de l’analyse et du clustering de nuages de points en basse dimension. Ces solutions s’appuyent sur l’analyse de triangulations de Delaunay. Deux types d’approches sont présentés et discutés. Le premier type suit une approche en trois-passes classique: 1) la construction d’un graphe de proximité contenant une information topologique, 2) la construction d’une information statistique à partir de ce graphe et 3) la suppression d’éléments inutiles au regard de cette information statistique. L’impact de différentes measures sur le clustering ainsi que sur la reconnaissance de caractères est discuté. Ces mesures s’appuyent sur l’exploitation du complexe simplicial et non pas uniquement sur celle du graphe. Le second type d’approches est composé d’approches en une passe extrayant des clusters en même temps qu’une triangulation de Delaunay est construite. / This thesis aims at proposing and discussing several solutions to the problem of low-dimensional point cloudanalysis and clustering. These solutions are based on the analysis of the Delaunay triangulation.Two types of approaches are presented and discussed. The first one follows a classical three steps approach:1) the construction of a proximity graph that embeds topological information, 2) the construction of statisticalinformation out of this graph and 3) the removal of pointless elements regarding this information. The impactof different simplicial complex-based measures, i.e. not only based on a graph, is discussed. Evaluation is madeas regards point cloud clustering quality along with handwritten character recognition rates. The second type ofapproaches consists of one-step approaches that derive clustering along with the construction of the triangulation.

Performing tasks with a robotic hand often requires a complete knowledge of the manipulated object, including its properties (shape, rigidity, surface texture) and its location in the environment, in order to ensure safe and efficient manipulation. While well-established procedures exist for the manipulation of rigid objects, as well as several approaches for the manipulation of linear or planar deformable objects such as ropes or fabric, research addressing the characterization of deformable objects occupying a volume remains relatively limited. The fundamental objectives of this research are to track the deformation of non-rigid objects under robotic hand manipulation using RGB-D data, and to automatically classify deformable objects as either rigid, elastic, plastic, or elasto-plastic, based on the material they are made of, and to support recognition of the category of such objects through a robotic probing process in order to enhance manipulation capabilities. The goal is not to attempt to formally model the material of the object, but rather employ a data-driven approach to make decisions based on the observed properties of the object, capture implicitly its deformation behavior, and support adaptive control of a robotic hand for other research in the future. The proposed approach advantageously combines color image and point cloud processing techniques, and proposes a novel combination of the fast level set method with a log-polar mapping of the visual data to robustly detect and track the contour of a deformable object in a RGB-D data stream. Dynamic time warping is employed to characterize the object properties independently from the varying length of the detected contour as the object deforms. The research results demonstrate that a recognition rate over all categories of material of up to 98.3% is achieved based on the detected contour. When integrated in the control loop of a robotic hand, it can contribute to ensure stable grasp, and safe manipulation capability that will preserve the physical integrity of the object.