This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Least-Squares Estimation of Transformation Parameters Between Two Point Patterns
April 1991 (vol. 13 no. 4)
pp. 376-380

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.

[1] B. K. P. Horn, "Closed-form solution of absolute orientation using orthonormal matrices,"J. Opt. Soc. Amer. A, vol. 5, no. 7, pp. 1127-1135, 1987.
[2] T. S. Huang, S. D. Blostein, and E. A. Margerum, "Least-squares estimation of motion parameters from 3-D point correspondences," inProc. IEEE Conf. Computer Vision and Pattern Recognition, Miami Beach, FL, 1986, pp. 24-26.
[3] B. K. P. Horn, "Closed-form solution of absolute orientation using unit quaternions,"J. Opt. Soc. Amer. A, vol. 4, no. 4, pp. 629-642, 1987.
[4] K. S. Arun, T. S. Huang, and S. D. Blostein, "Least-squares fitting of two 3-D point sets,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, no. 5, pp. 698-700, 1987.
[5] M. Athans, "The matrix minimum principle,"Inform. Contr., vol. 11, pp. 592-606, 1967.
[6] R. Bellman,Introduction to Matrix Analysis. New York: McGraw-Hill, 1960, p. 56.
[7] D. Holder and H. Buxton, "AVC89: Polyhedral object recognition with sparse data-Validation of interpretations," inProc. Fifth Alvey Vision Conf., 1989, pp. 19-24.

Index Terms:
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
Citation:
S. Umeyama, "Least-Squares Estimation of Transformation Parameters Between Two Point Patterns," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 4, pp. 376-380, April 1991, doi:10.1109/34.88573
Usage of this product signifies your acceptance of the Terms of Use.