Directions of motion fields are hardly ever ambiguous

Recent literature [7, 10, 11, 9, 13, 17] provides a number of results regarding uniqueness aspects of motion fields and exact image displacements due to 3-D rigid motion. Here instead of the full motion field we consider only the direction of the motion field due to a rigid motion and ask 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 fact that the depth of the surfaces in view is positive (i.e. that the surface in view is in front of the camera). With this analysis we thus offer a theoretical foundation for image constraints employing only the sign of flow in various directions and provide a solid basis for their utilization in addressing 3D dynamic vision problems.