DocumentCode :
3782075
Title :
Motion estimation in computer vision: optimization on Stiefel manifolds
Author :
Y. Ma;J. Kosecka;S. Sastry
Author_Institution :
Electron. Res. Lab., California Univ., Berkeley, CA, USA
Volume :
4
fYear :
1998
Firstpage :
3751
Abstract :
Motion recovery from image correspondences is typically a problem of optimizing an objective function associated with the epipolar (or Longuet-Higgins) constraint. This objective function is defined on the so called essential manifold. In the paper, the intrinsic Riemannian structure of the essential manifold is thoroughly studied. Based on existing optimization techniques on Riemannian manifolds, in particular on Stiefel manifolds, we propose a Riemannian Newton algorithm to solve the motion recovery problem, making use of the natural geometric structure of the essential manifold. Although only the Newton algorithm is studied in detail, the same ideas also apply to other typical conjugate gradient algorithms. It is shown that the proposed nonlinear algorithms converge very rapidly (with quadratic rate of convergence) as long as the conventional SVD based eight-point linear algorithm has a unique solution. Such Riemannian algorithms have also been applied to the differential (or continuous) case where the velocities are recovered from optical flows.
Keywords :
"Motion estimation","Computer vision","Nonlinear optics","Image motion analysis","Iterative algorithms","Optimization methods","Laboratories","Constraint optimization","Mathematics","Fluid flow measurement"
Publisher :
ieee
Conference_Titel :
Decision and Control, 1998. Proceedings of the 37th IEEE Conference on
ISSN :
0191-2216
Print_ISBN :
0-7803-4394-8
Type :
conf
DOI :
10.1109/CDC.1998.761802
Filename :
761802
Link To Document :
بازگشت