Fitting 3-D data using superquadrics and free-form deformations

Recovery of 3D 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 Barr (1994). It appears however that whilst superquadrics could describe a wide variety of forms, they are too simple to recover and describe complex shapes. This paper describes a two-step method to fit a parametric deformable surface to 3D points. We suppose that a 3D image has been segmented to get a set of 3D points. The first step consists in our version of a superquadric fit with global tapering. We then make use of the technique of free-form deformations, as in computer graphics. We present experimental results with synthetic and real 3D medical images where the original points are laid on an iso-surface.