Estimation of a Rigid Body Motion in the Presence of Noise

摘要

The problem of estimating a rigid body motion from two noisy images of an object taken at two different times is studied. The available data consist of the unordered locations of some of the prominent points of the object. Because these points are not individually recognized and some of them may be missed in one or both of the images, it is not obvious which points of the two images correspond to one another. Moreover the observed locations are subject to error. A computational procedure, capitalizing on the rigidity of the object, is proposed for estimating the motion parameters of the object in the presence of Gaussian noise independently added to the positions in the images of the points observed. In principle, one might apply maximum likelihood to the estimation problem, but thee difficulty in formulating and calculating the likelihood function under the above mentioned assumptions if formidable. A simulation study has been carried out to compare the efficiency of the proposed estimator for the more complex problem with that of the maximum likelihood estimate in the favorable situation and to test the robustness of the proposed estimator under the misspecification of the value of -sigma.