Crystal vision-applications of point groups in computer vision

Methods from the representation theory of finite groups are used to construct efficient processing methods for the special geometries related to the finite subgroups of the rotation group. We motivate the use of these subgroups in computer vision, summarize the necessary facts from the representation theory and develop the basics of Fourier theory for these geometries. We illustrate its usage for data compression in applications where the processes are (on average) symmetrical with respect to these groups. We use the icosahedral group as an example since it is the largest finite subgroup of the 3D rotation group. Other subgroups with fewer group elements can be studied in exactly the same way.