Representation issues in the ML estimation of camera motion
- 1 January 1999
- conference paper
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE) in Proceedings of the Seventh IEEE International Conference on Computer Vision
- Vol. 1, 640-647 vol.1
- https://doi.org/10.1109/iccv.1999.791285
Abstract
The computation of camera motion from image measurements is a parameter estimation problem. We show that for the analysis of the problem's sensitivity, the parameterization must enjoy the property of fairness, which makes sensitivity results invariant to changes of coordinates. We prove that Cartesian unit norm vectors and quaternions are fair parameterizations of rotations and translations, respectively, and that spherical coordinates and Euler angles are not. We extend the Gauss-Markov theorem to implicit formulations with constrained parameters, a necessary step in order to take advantage of fair parameterizations. We show how maximum likelihood (ML) estimation problems whose sensitivity depends on a large number of parameters, such as coordinates of points in the scene, can be partitioned into equivalence classes, with problems in the same class exhibiting the same sensitivity.Keywords
This publication has 9 references indexed in Scilit:
- 3D recovery of polyhedra by rectangularity heuristicsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Determining the Epipolar Geometry and its Uncertainty: A ReviewInternational Journal of Computer Vision, 1998
- Optimal motion and structure estimationIEEE Transactions on Pattern Analysis and Machine Intelligence, 1993
- Lower bounds for parametric estimation with constraintsIEEE Transactions on Information Theory, 1990
- Motion and structure from two perspective views: algorithms, error analysis, and error estimationIEEE Transactions on Pattern Analysis and Machine Intelligence, 1989
- Direct methods for recovering motionInternational Journal of Computer Vision, 1988
- Reliability analysis of parameter estimation in linear models with applications to mensuration problems in computer visionComputer Vision, Graphics, and Image Processing, 1987
- Facts on optic flowBiological Cybernetics, 1987
- A computer algorithm for reconstructing a scene from two projectionsNature, 1981