Recognizing geons from superquadrics fitted to range data

This paper attempts to relate two influential families of 3D shape primitives, superquadrics and geons. Superquadric surfaces have attracted considerable interest recently as part models for representation of 3D objects. Here, we explore their utility for a different purpose, i.e. for shape discrimination. We investigate how well the estimated superquadric parameters can reflect certain intuitive geometric attributes of elongated objects, such as axis shape (straight or bent), type of cross-sectional edges (straight or curved), and variation of cross-section size along the axis (constant, tapered, or increasing-and-decreasing). Parameters of the best-fitting superquadric are estimated for real as well as synthetic range images, obtained from a large number of viewpoints, of models belonging to 12 shape classes based on the above geometric attributes. These shape classes correspond to a ‘collapsed’ set of 36 different geons. Five features derived from the estimated superquadric parameters are used to distinguish between these 12 shape classes. Classification error rates are estimated for k-nearest-neighbour and binary tree classifiers. The effects of varying the range image resolution, noise level and the model elongation are also investigated. The results indicate that existing methods of superquadric parameter estimation are quite sensitive to noise in range values and also do not work well for ‘rough’, coarse-surfaced objects. However, for low-noise real range images of objects with ‘smooth’ surfaces, numerical features derived from estimated superquadric parameters can be used with a binary tree classifier to infer qualitative shape properties with about 80% reliability.