A versatile method for trifocal tensor estimation

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.