Determination of parameters of quaternion signal transformation using filtering results

The solution of the problem of determining the parameters of transformation of the image of a spatial polyhedron using the results of its filtering is considered. The body is represented by the coordinates of its vertices and is described in the form of the quaternion signal. Each quaternion determines the vector connecting the pole with one of the vertices. The filter is related to the polyhedron of a certain class and produces the values of the measure of likelihood with the filtered polyhedron which is subject to the rotation transformation with unknown parameters before it is sent to the filter input. The expressions for determination of the parameters of each vector of the filtered signal in the spherical coordinate system and the values of the rotation angle and the axis of rotation common for the entire filtered signal are obtained. © 2008 Pleiades Publishing, Ltd.