A Parametric Deformable Model to T Unstructured 3d Data a Parametric Deformable Model to T Unstructured 3d Data

Recovery of unstructured 3D data with deformable models has been the subject of many studies over the last ten years. In particular, in medical image understanding, deformable models are useful to get a precise representation of anatomical structures. However, general deformable models involve large linear systems to solve when dealing with high resolution 3D images. The advantage of parametric deformable models like superquadrics is their small number of parameters to describe a shape combined with a better robustness in the presence of noise or sparse data. Also, at the expense of a reasonable number of additional parameters, free form deformations provide a much closer t and a volumetric deformation eld. This article introduces such a model to t unstructured 3D points with a parametric deformable surface based on a superquadric t followed by a free form deformation to describe the cardiac left ventricle. We present the mathematical and algorithmic details of the method, as well as three experimental studies in a various number of 3D medical images. The extension of the method to track anatomical structures in spatio-temporal images (4D data) will be presented in a companion article [9]. Key-words: Parametric models, Deformable models, Superquadrics, 3D Splines, Free-form deformations, Regularization, Surface Reconstruction.