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Analysis of 3-D Rotation Fitting
May 1994 (vol. 16 no. 5)
pp. 543-549

Computational techniques for fitting a 3-D rotation to 3-D data are recapitulated in a refined form as minimization over proper rotations, extending three existing methods-the method of singular value decomposition, the method of polar decomposition, and the method of quaternion representation. Then, we describe the problem of 3-D motion estimation in this new light. Finally, we define the covariance matrix of a rotation and analyze the statistical behavior of errors in 3-D rotation fitting.

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Index Terms:
image processing; minimisation; motion estimation; matrix algebra; error statistics; 3-D rotation fitting; minimization; proper rotations; singular value decomposition; polar decomposition; quaternion representation; covariance matrix; statistical behavior
K. Kanatani, "Analysis of 3-D Rotation Fitting," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 5, pp. 543-549, May 1994, doi:10.1109/34.291441
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