ON THE GEOMETRY OF VISUAL CORRESPONDENCE

Image displacement fields-optical flow fields, stereo disparity fields , normal flow fields-due to rigid motion possess a global geometric st ructure which is independent of the scene in view. Motion vectors of c ertain lengths and directions are constrained to lie on the imaging su rface at particular loci whose location and form depends solely on the 3D motion parameters. If optical flow fields or stereo disparity fiel ds are considered, then equal vectors are shown to lie on conic sectio ns. Similarly, for normal motion fields, equal vectors lie within regi ons whose boundaries also constitute conics. By studying various prope rties of these curves and regions and their relationships, a character ization of the structure of rigid motion fields is given. The goal of this paper is to introduce a concept underlying the global structure o f image displacement fields. This concept gives rise to various constr aints that could form the basis of algorithms for the recovery of visu al information from multiple views.