Connection between internal representation of rigid transformation and cortical activity paths

A canonical unitary representation of the Euclidean group on the range space of the Gabor transform is constructed from mathematical properties of the Euclidean group and the quaternions. The visual cortical activity pattern corresponding to a given retinal image is represented by a point in the range space of the Gabor transform. Paths experienced in apparent motion and mental rotation are represented by paths in the Euclidean group. The key hypothesis of the paper is that an action of the Euclidean group on the Gabor transform space brings the perceived paths into relation with corresponding successive neural microstructure activity patterns. Possible experimental tests are suggested.