MOTION ESTIMATION FROM 3-D POINT SETS WITH AND WITHOUT CORRESPONDENCES.

The authors estimate rigid-body motion from two 3-D point sets with and without correspondences. By utilizing properties of Fourier transformation, a frequency-domain approach for determining the motion without point correspondences is obtained. In the algorithm, the problem of estimating the translation is first separated by subtracting the coordinates of the centroids from the 3-D point coordinates in the point sets. The rotation parameters are estimated by correlating the Fourier transforms of two functions defined on the two sets of the 3-D points. With the point correspondence given, an algorithm for finding the least-squares solution to the motion parameters is applied. It is proved that the least-squares solution is such that the centroids of the two point sets coincide. The determination of rotation and translation can therefore be decoupled. An iterative procedure for obtaining the rotation parameters is described.