LEAST-SQUARES ESTIMATION OF TRANSFORMATION PARAMETERS BETWEEN 2 POINT PATTERNS

In many applications of computer vision, the following problem is encountered. Two point patterns (sets of points) {x(i)} and {y(i)}; i = 1,2,...,n are given in m-dimensional space, and we want to find the similarity transformation parameters (rotation, translation, and scaling) that give the least mean squared error between these point patterns. Recently Arun et al. and Horn et al. have presented a solution of this problem. Their solution, however, sometimes fails to give a correct rotation matrix and gives a reflection instead when the data is severely corrupted. The theorem given in this correspondence is a strict solution of the problem, and it always gives the correct transformation parameters even when the data is corrupted.