SURFACE SHAPE FROM THE DEFORMATION OF APPARENT CONTOURS

The spatiotemporal analysis of deforming silhouettes (apparent contours) is here extended using the mathematics of perspective projections and tools from differential geometry. Analysis of the image motion of a silhouette or apparent contour enables computation of local surface curvature along the corresponding contour generator on the surface, assuming viewer motion is known. To perform the analysis, a spatiotemporal parameterization of image-curve motion is needed, but is underconstrained (a manifestation of the well-known aperture problem). It is shown that an epipolar parameterization is most naturally matched to the recovery of surface curvature. One immediate facility afforded by the analysis is that surface patches can be reconstructed in the vicinity of contour generators. Once surface curvature is known, it is possible to discriminate extremal contours from other fixed curves in space. Furthermore, the known robustness of parallax as a cue to depth extends to the case of surface curvature. Its derivative-rate of parallax-is shown theoretically to be a curvature cue that is robust to uncertainties in the known viewer motion. This robustness has been confirmed in experiments. Finally, the power of the new analysis for robotics applications is demonstrated. Illustrations are given of an Adept robot, equipped with a CCD camera, circumnavigating curved obstacles. When further equipped with a suction gripper the robot manipulator can pick up an object by its curved surface, under visual guidance.