Determining the rotational variables of a spatial group point object from the object's filtering results

Solution of the problem of finding the rotational variables of the image of a spatial group point object (SGPO) from the results of filtering of this object is considered. The spatial group point object is represented both in the form of coordinates of its points and in the form of a quaternion signal. A filter that forms a similarity measure between the filtered SGPO with unknown rotational variables and the desired signal of a certain class is studied. Expressions for determining the parameters of each vector of the filtered signal are obtained. Expressions for determining the values of the angle of rotation and the rotation axis, which are common for the entire filtered signal, are obtained as well.