3-D shape approximation using parametric geons

This paper presents a new approach to 3D shape representation { approximating the shapes of object parts by a set of prescribed volumetric models using single-and multi-view range data. We deene a new set of volumetric part models , called parametric geons. These are seven qualitative shapes, each of which is formulated by a restricted globally-deformed superellipsoid. Model recovery is performed by tting all parametric geons to a part and selecting the best model for the part based on the minimum tting residual. A newly-deened objective function and a fast global optimisation technique are employed to obtain robust model tting results. Parametric geons provide a global shape constraint that allows model recovery to explicitly verify the resultant part descriptions. Through systematic experiments, we examine the eeciency of the objective function, the discriminative ability of parametric geons, the eeects of object shape imperfection to model recovery, and the importance of multiview data for shape approximation. The experimental results demonstrate that this approach can successfully recover qualitative shape models from object parts, especially when a part shape is not fully consistent with model shapes.