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<p>In many applications of computer vision, the following problem is encountered. Two point patterns (sets of points) (x/sub i/) and (x/sub i/); i=1, 2, . . ., n are given in m-dimensional space, and the similarity transformation parameters (rotation, translation, and scaling) that give the least mean squared error between these point patterns are needed. Recently, K.S. Arun et al. (1987) and B.K.P. Horn et al. (1987) 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 proposed theorem is a strict solution of the problem, and it always gives the correct transformation parameters even when the data is corrupted.</p>
pattern recognition; parameter estimation; two point patterns; computer vision, ; transformation parameters; least mean squared error; computer vision; error analysis; least squares approximations; parameter estimation; pattern recognition

S. Umeyama, "Least-Squares Estimation of Transformation Parameters Between Two Point Patterns," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 13, no. , pp. 376-380, 1991.
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