Directions of Motion Fields are Hardly Ever Ambiguous

If instead of the full motion field, we consider only the direction of the motion field due to a rigid motion, what can we say about the three-dimensional motion information contained in it? This paper provides a geometric analysis of this question based solely on the constraint that the depth of the surfaces in view is positive. The motivation behind this analysis is to provide a theoretical foundation for image constraints employing only the sign of flow in various directions and justify their utilization for addressing 3D dynamic vision problems.