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<p><it>Abstract</it>—This paper discusses the applications of hyperquadric models in computer vision and focuses on their recovery from range data. Hyperquadrics are volumetric shape models that include superquadrics as a special case. A hyperquadric model can be composed of any number of terms and its geometric bound is an arbitrary convex polytope. Thus, hyperquadrics can model more complex shapes than superquadrics. Hyperquadrics also possess many other advantageous properties (compactness, semilocal control, and intuitive meaning). Recovering hyperquadric parameters is difficult not only due to the existence of many local minima in the error function but also due to the existence of an infinite number of global minima (with zero error) that do not correspond to any meaningful shape. Our proposed algorithm starts with a rough fit using only six terms in 3D (four in 2D) and adds additional terms as necessary to improve fitting. Suitable constraints are used to ensure proper convergence. Experimental results with real 2D and 3D data are presented.</p>
Object modeling, hyperquadrics, surface fitting, object representation, volumetric models.

D. Goldgof, S. Han, S. Kumar and K. Bowyer, "On Recovering Hyperquadrics from Range Data," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 17, no. , pp. 1079-1083, 1995.
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