A Comparison of Four Algorithms for Estimating 3-D Rigid Transformations

A common need in machine vision is to compute the 3-D rigid transformation that exists between two sets of points for which corresponding pairs have been determined. In this paper a comparative analysis of four popular and efficient algorithms is given. Each computes the translational and rotational components of the transform in closed-form as the solution to a least squares formulation of the problem. They differ in terms of the representation of the transform and the method of solution, using respectively: singular value decomposition of a matrix, orthonormal matrices, unit quaternions and dual quaternions. This comparison presents results of several experiments designed to determine the (1) accuracy in the presence of noise, (2) stability with respect to degenerate data sets, and (3) relative computation time of each approach.