Three-dimensional shape modeling with extended hyperquadrics

The shape representation and modeling based on implicit functions have received considerable attention in computer vision literature. In this paper, we propose extended hyperquadrics, as a generalization of hyperquadrics developed by Hanson, for modeling global geometric shapes. The extended hyperquadrics can strengthen the representation power of hyperquadrics, especially for thr object with concavities. We discuss the distance measures between extended hyperquadric surfaces and given data set and their minimization to obtain the optimum model parameters. We present several experimental results for fitting extended hyperquadrics to 3D real and synthetic data. We demonstrate that extended hyperquadrics can model more complex shapes than hyperquadrics, maintaining many desirable properties of hyperquadrics.