Directions of Motion Fields are Hardly Ever Ambiguous,
Abstract
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. It is shown that, considering as the imaging surface the whole sphere, independently of the scene in view, two different rigid motions cannot give rise to the same directional motion field. If we restrict the image to half of a sphere (or an infinitely large image plane) two different rigid motions with instantaneous translational and rotational velocities (t1,w1) and (t2, w2) cannot give rise to the same directional motion field unless the plane through t1 and t2 is perpendicular to the plane through W1 and w2 (i.e., (t1 x t2) - (w1 x w2) = 0). In addition, in order to give practical significance to these uniqueness results for the case of a limited field of view, we also characterize the locations on the image where the motion vectors due to the different motions must have different directions. If (w1 x w2). (t1 x t2) = 0 and certain additional constraints are met, then the two rigid motions could produce motion fields with the same direction. For this to happen the depth of each corresponding surface has to be within a certain range, defined by a second and a third order surface. Finally, as a byproduct of the analysis it is shown that if we also consider the constraint of positive depth the full motion field on a half sphere uniquely constrains 3D motion independently of the scene in view. (KAR) P.2
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1995
- Accession Number
- ADA297576
Entities
People
- Cornelia Fermüller
- Tomas Brodsky
- Yiannis Aloimonos
Organizations
- University of Maryland