Optimal Rigid Motion Estimation
and Performance Evaluation with Bootstrap
Bogdan Matei and Peter Meer
Department of Electrical and Computer Engineering
Rutgers University, Piscataway, NJ 08854-8058, USA
A new method for 3D rigid motion estimation is derived under
the most general assumption that the measurements are corrupted by
inhomogeneous and anisotropic, i.e., heteroscedastic noise.
This is the case, for example, when the motion of a
calibrated stereo-head is to be determined from image pairs.
Linearization in the quaternion
space transforms the problem into a multivariate, heteroscedastic
errors-in-variables (HEIV) regression,
from which the rotation and translation estimates are
obtained simultaneously. The significant performance improvement
is illustrated, for real data, by comparison with
the results of quaternion, subspace and
renormalization based approaches described in the literature.
Extensive use is made of bootstrap, an advanced numerical tool from
statistics, both to estimate the covariances of the 3D data
points and to obtain confidence regions for the rotation and
translation estimates. Bootstrap enables an accurate
recovery of these information using only the two image pairs serving
as input.
Appeared in,
1999 Computer Vision and Pattern Recognition Conference ,
Fort Collins, CO, June 1999, vol.1, 339-345.
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