Perceptual organization and the representation of natural form
Artificial Intelligence
Hyperquadrics: smoothly deformable shapes with convex polyhedral bounds
Computer Vision, Graphics, and Image Processing
Recovery of Parametric Models from Range Images: The Case for Superquadrics with Global Deformations
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Surface and volumetric segmentation of complex 3-D objects using parametric shape models
Surface and volumetric segmentation of complex 3-D objects using parametric shape models
Recognizing geons from superquadratics fitted to range data
Image and Vision Computing - Special issue: range image understanding
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
Darboux Frames, Snakes, and Super-Quadrics: Geometry from the Bottom Up
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Global and local deformations of solid primitives
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
DeepView: a channel for distributed microscopy and informatics
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
A Maximum-Likelihood Surface Estimator for Dense Range Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
IPMI '99 Proceedings of the 16th International Conference on Information Processing in Medical Imaging
An Integrated Approach for Surface Finding in Medical Images
MMBIA '96 Proceedings of the 1996 Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '96)
3-D shape approximation using parametric geons
Image and Vision Computing
Faithful recovering of quadric surfaces from 3D range data
3DIM'99 Proceedings of the 2nd international conference on 3-D digital imaging and modeling
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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.