Inverse problem of rotation of three-dimensional vector signals

This paper considers the problem of determining the rotation parameters such as the direction vector of the rotation axis and the rotation angle of a three-dimensional image whose surface points are specified by vectors. The initial and rotated vectors are considered known. An approach using a quaternion representation of vectors is proposed, whose computational efficiency is severalfold higher than the efficiency of known approaches. The mechanism of the effect of noise on the accuracy of determination of the parameters is studied, and recommendations on error minimization are given. Features of the solution of the inverse problem of rotation as applied to the image recognition system are considered.