Superquadrics

Abstract: A physically-based approach is presented to fitting complex 3D shapes using a novel class of dynamic models. These models can deform both locally and globally. The authors formulate deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline. The local/global representational power of a deformable superquadric simultaneously satisfies the conflicting requirements of shape reconstruction and shape recognition. The model's six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models. Model fitting experiments involving 2D monocular image data and 3D range data are reported. >

Abstract: A method for recovery of compact volumetric models for shape representation of single-part objects in computer vision is introduced. The models are superquadrics with parametric deformations (bending, tapering, and cavity deformation). The input for the model recovery is three-dimensional range points. Model recovery is formulated as a least-squares minimization of a cost function for all range points belonging to a single part. During an iterative gradient descent minimization process, all model parameters are adjusted simultaneously, recovery position, orientation, size, and shape of the model, such that most of the given range points lie close to the model's surface. A specific solution among several acceptable solutions, where are all minima in the parameter space, can be reached by constraining the search to a part of the parameter space. The many shallow local minima in the parameter space are avoided as a solution by using a stochastic technique during minimization. Results using real range data show that the recovered models are stable and that the recovery procedure is fast. >

Abstract: A potential function based on superquadrics is presented that closely models a large class of object shapes. This potential function also prevents the creation of local minima when it is added to spherically symmetric attractive wells. Two compatible forms of the superquadric potential function are introduced: one for obstacle avoidance, and another for obstacle approach. The avoidance and approach potentials are implemented in simulations. In these simulations the end effector of the manipulator experiences an attractive force from a global spherical well, while the end effector and each of the links experience repulsive forces from all of the objects. The authors have also experimentally implemented the avoidance potentials on the CMU DDARM II system. The results demonstrate successful obstacle avoidance and approach, and exhibit an improvement over existing schemes. >

Abstract: List of Figures. List of Tables. Preface. Acknowledgments. Foreword. 1. Introduction. 2. Superquadrics and their Geometric Properties. 3. Extensions of Superquadrics. 4. Recovery of Individual Superquadrics. 5. Segmentation with Superquadrics. 6. Experimental Results. 7. Applications of Superquadrics. 8. Conclusions. Appendices. References. Author Index. Topic Index.