Direct Computation of Qualitative 3-D Shape and Motion Invariants

Structure from motion often refers to the computation of 3-D structure from a matched sequence of images. However, a depth map of a surface is difficult to compute and may not be a good representation for storage and recognition. Given matched images, this correspondence will show that the sign of the normal curvature in a given direction at a given point in the image can be computed from a simple difference of slopes of line segments in one image. Using this result, local surface patches can be classified as convex, concave, cylindrical, hyperbolic (saddle point) or planar. At the same time, the translational component of the optical flow is obtained, from which the focus of expansion can be computed.