Computational Studies in the Interpretation of Structure and Motion: Summary and Extension
Computational studies of the interpretation of structure from motion examine the conditions under which three-dimensional structure can be recovered from motion in the image. The first part of this paper summarizes the main results obtained to date in these studies. The second part examines two issues: the robustness of the 3-D interpretation of perspective velocity fields, and the 3-D information contained in orthographic velocity fields. The two are related because, under local analysis, limitations on the interpretation of orthographic velocity fields also apply to perspective projection. The following results are established: When the interpretation is applied locally, the 3-D interpretation of the perspective velocity field is unstable. The orthographic velocity field determines the structure of the inducing object exactly up to a depth-scaling. For planar objects, the orthographic velocity field always admits two distinct solutions up to depth-scaling. The 3-D structure is determined uniquely by a "view and a half" of the orthographic velocity field.