Estimation of motion parameters for a deformable object from range data

If the correspondence between two sets of points representing the coordinates of different points of an object undergoing rotational motion and deformation is known, the parameters can be estimated using different least-squares estimators. The total-least-squares (TLS) method is very appropriate when the observation and the data matrices are both perturbed by random noise. For Gaussian-distributed noise, the TLS solution is equivalent to maximum-likelihood estimation. The mean-square error in TLS is always smaller than in an ordinary least-squares (LS) estimator. The scope is analyzed of TLS in estimating the generalized motion parameters, as is the feasibility of decomposing the generalized motion parameters in terms of rotation and deformation parameters. The performance of TLS is compared to that of the LS estimator