Model-based recognition and motion tracking depend upon the ability to solve for projection and model parameters that will best fit a 3-D model to matching 2-D image features. The author extends current methods of parameter solving to handle objects with arbitrary curved surfaces and with any number of internal parameters representing articulation, variable dimensions, or surface deformations. Numerical stabilization methods are developed that take account of inherent inaccuracies in the image measurements and allow useful solutions to be determined even when there are fewer matches than unknown parameters. The Levenberg-Marquardt method is used to always ensure convergence of the solution. These techniques allow model-based vision to be used for a much wider class of problems than was possible with previous methods. Their application is demonstrated for tracking the motion of curved, parameterized objects.
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