Fitting Parameterized Three-Dimensional Models to Images

Model-based recognition and motion tracking depends upon the ability to solve for projection and model parameters that will best fit a 3-D model to matching 2-D image features. This paper extends current methods of parameter solving to handle objects with arbitrary curved surfaces and with any number of internal parameters representing articulations, 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 LevenbergMarquardt 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. This paper has been published in IEEE Transactions on Pattern Analysis and Machine Intelligence, 13, 5 (May 1991), pp. 441–450.