Superquadrics and free-form deformations: A global model to fit and track 3D medical data

Abstract

Recovery of 3-D data with simple parametric models has been the subject of many studies over the last ten years. Many have used the notion of superquadrics, introduced for graphics in [4]. It appears, however, that although superquadrics can describe a wide variety of forms, they are too simple to recover and describe complex shapes. This paper describes a method to fit to 3-D points and then track a parametric deformable surface. We suppose that a 3-D image has been segmented to get a set of 3-D points. A first estimate consists of our version of a superquadric fit with global tapering. We then apply the technique of free-form deformations, as introduced by [9] in computer graphics to refine the estimate. We present experimental results with real 3-D medical images, where the original points are laid on an iso-surface. This is also applied to give efficient tracking of the deformation of the myocardium.