Optimal rigid motion estimation and performance evaluation with bootstrap

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 as 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.