Résumé en anglais

In many computer vision and image understanding problems, it is important to find previous termanext term smooth surface that previous termfits anext term set of given previous termunstructured 3D data.next term Although approaches based on general previous termdeformable modelsnext term give satisfactory results, in particular previous termanext term local description of the surface, they involve large linear systems to solve when dealing with high resolution previous term3Dnext term images. The advantage of previous termparametric deformablenext term templates like superquadrics is their small number of parameters to describe previous termanext term shape. However, the set of shapes described by superquadrics is too limited to approximate precisely complex surfaces. This is why hybrid previous termmodelsnext term have been introduced to refine the initial approximation. This article introduces previous terma deformablenext term superquadric previous termmodelnext term based on previous termanext term superquadric previous termfitnext term followed by previous termanext term free-form deformation (FFD) to previous termfit unstructured 3Dnext term points. At the expense of previous termanext term reasonable number of additional parameters, free-form deformations provide previous termanext term much closer previous termfit and anext term volumetric deformation field. We first present the mathematical and algorithmic details of the method. Then, since we are mainly concerned with applications for medical images, we present previous termanext term medical application consisting in the reconstruction of the left ventricle of the heart from previous termanext term number of various previous term3Dnext term cardiac images. The extension of the method to track anatomical structures in spatio-temporal images (4D previous termdata)next term is presented in previous termanext term companion article [9].