On using geometric distance fits to estimate 3D object shape, pose, and deformation from range, CT, and video images

The problems of automatically constructing algebraic surface models from sets of 3D and 2D images and using these models in pose computation, motion and deformation estimation, and object recognition are addressed. It is proposed that a combination of constrained optimization and nonlinear least-squares estimation techniques be used to minimize the mean-squared geometric distance between a set of points or rays and a parameterized surface. In modeling tasks, the unknown parameters are the surface coefficients, while in pose and deformation estimation tasks they represent the transformation mapping the observer´s coordinate system onto the modeled surface´s own coordinate system. This approach is applied to a variety of real range, computerized tomography (CT), and video images