Uncertainty analysis of 3D reconstruction from uncalibrated views

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 assumptions, 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.