Analysis of 3-D rotation fitting

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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>