A computer vision system has been implemented that can recognize threedimensional objects from unknown viewpoints in single gray-scale images. Unlike most other approaches, the recognition is accomplished without any attempt to reconstruct depth information bottom-up from the visual input. Instead, three other mechanisms are used that can bridge the gap between the two-dimensional image and knowledge of three-dimensional objects. First, a process of perceptual organization is used to form groupings and structures in the image that are likely to be invariant over a wide range of viewpoints. Second, a probabilistic ranking method is used to reduce the size of the search space during model based matching. Finally, a process of spatial correspondence brings the projections of three-dimensional models into direct correspondence with the image by solving for unknown viewpoint and model parameters. A high level of robustness in the presence of occlusion and missing data can be achieved through full application of a viewpoint consistency constraint. It is argued that similar mechanisms and constraints form the basis for recognition in human vision. This paper has been published in Artificial Intelligence, 31, 3 (March 1987), pp. 355–395. 1 1

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