The precision of 3D reconstruction from uncalibrated views

Grossmann, Santos-Vicrot

Abstract:

We consider reconstruction algorithms using points tracked over a sequence
of (at least three) images, to estimate the positions of the cameras (motion
parameters), the 3D coordinates (structure parameters), and the calibration
matrix of the cameras (calibration parameters).
Many algorithms have been reported in literature, and there is a need to
know how well they may perform. We show how the choice of assumptions
on the camera intrinsic parameters (either fixed, or with a probabilistic prior)
influences the precision of the estimator.
We associate a Maximum Likelihood estimator to each type of assump-
tions, and derive analytically their covariance matrices, independently of any
specific implementation. We verify that the obtained covariance matrices are
realistic, and compare the relative performance of each type of estimator.