3-D SHAPE APPROXIMATION USING PARAMETRIC GEONS

This paper presents a new approach to 3D shape representation - approx imating the shapes of object parts by a set of prescribed volumetric m odels using single- and multi-view range data. We define a new ser of volumetric part models, called parametric geons. These are seven quali tative shapes, each of which is formulated by a restricted globally-de formed superellipsoid. Model recovery is performed by fitting all para metric geons to a part and selecting the best model for the part based on the minimum fitting residual. A newly-defined objective function a nd a fast global optimisation technique are employed to obtain robust model fitting results. Parametric geons provide a global shape constra int that allows model recovery to explicitly verify the resultant part descriptions. Through systematic experiments, we examine the efficien cy of the objective function, the discriminative ability of parametric geons, the effects of object shape imperfection to model recovery, an d the importance of multiview data for shape approximation. The experi mental results demonstrate that this approach can successfully recover qualitative shape models from object parts, especially when a part sh ape is not fully consistent with model shapes.