Computational approaches for solving the bas-relief ambiguity under orthographic projection

Abstract Bas-relief ambiguity exists in point correspondences of two views. We present two algorithms that compute the rotation angle from two and three views. In the two view case with known rotation axis, a statistically unbiased least square approach is derived to compute the rotation angle uniquely. In three views, a numerical method is used to recover the rotation axis based on the assumption of equal rotations.

[1]  Sukhan Lee,et al.  A Kalman filter approach for accurate 3-D motion estimation from a sequence of stereo images , 1991, CVGIP Image Underst..

[2]  H. C. Longuet-Higgins,et al.  A computer algorithm for reconstructing a scene from two projections , 1981, Nature.

[3]  H. C. Longuet-Higgins Multiple interpretations of a pair of images of a surface , 1988, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[4]  K. S. Arun,et al.  Least-Squares Fitting of Two 3-D Point Sets , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Christopher G. Harris,et al.  Determination of Ego-Motion from Matched Points , 1987, Alvey Vision Conference.

[6]  Olivier D. Faugeras,et al.  Some Properties of the E Matrix in Two-View Motion Estimation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Kenichi Kanatani,et al.  Geometric computation for machine vision , 1993 .

[8]  A. Bandyopadhyay,et al.  Perception of Structure from Motion: Lower Bound Results , 1985 .

[9]  Kenichi Kanatani,et al.  Unbiased Estimation and Statistical Analysis of 3-D Rigid Motion from Two Views , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  S. Ullman,et al.  The interpretation of visual motion , 1977 .

[11]  Chris Harris,et al.  Resolution of the Bas-relief ambiguity in structure-from-motion under orthographic projection , 1990, BMVC.

[12]  Thomas S. Huang,et al.  Motion and structure from orthographic projections , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.