Bogdan Matei (1), Bogdan Georgescu (2) and Peter Meer (1)
(1) ECE Department, (2) CS Department
Rutgers University, Piscataway, NJ 08854-8058, USA
Reliable estimation of the trifocal tensor is crucial
for 3D reconstruction from uncalibrated cameras.
The estimation process is based on minimizing
the geometric distances between
the measurements and the corrected data points, the underlying
nonlinear optimization problem being most often solved with the
Levenberg-Marquardt (LM) algorithm. We employ for this task
the heteroscedastic errors-in-variables (HEIV) estimator and take into
account both the singularity of the multivariate tensor constraint
and the bifurcation which can appear for noisy data.
In comparison to the Gold Standard method,
the new approach is significantly faster while
having the same performance, and
it is less sensitive to initialization when the data is close to
degenerate.
Analytical expressions for the covariances of the parameter
and corrected image point estimates are available for the
HEIV estimator, and thus the confidence regions of the corrected
measurements can be delineated in the images.
8th International Conference on Computer Vision,
Vancouver, BC, Canada, July 2001, vol. II, 578-585.
Return to Research: Estimation under heteroscedasticity
