Approaches dedicated to the modelling of complex shapes application to medical data

The way to model complex shapes has a significant influence depending on the context. Handling an object can be considerably increased if a good underlying model is used. On the contrary, preponderant problems can appear if an unsuited model is associated to the object. The main criterion to discriminate existing models is to determine the balance between: their ability to control global characteristics and the possibility to handle local features of the shape. The fact is very few models are adapted both to structure and to geometrical modelling. In this paper, we first describe an overview of existing approaches. They can be classified principally in two groups: skeleton based models, used to control the global aspect of the shape, and free form models, used to control local specificities of the object. Then, trying to keep the advantages of both techniques in mind, we present an original approach based on a multi-layer model to represent a 3D object. We focus on the ability to take into account both global and local characteristics of a complex shape, on topological and morphological levels, as well as on the geometric level. To do that, the proposed model is composed of three layers. We call the boundary mesh the external layer, including a multi-resolution feature. We enhance this representation by adding an internal structure: the inner skeleton, which is topologically equivalent to the input object. In addition to that, a third layer links the structural entity and the geometrical crust, to induce an intermediary level of representation. This approach is applied to classical and medical data through a specific algorithm.