Compactification of the Rigid Motions Group in Image Processing

Image processing problems in general, and particular the field of single-particle cryo-electron microscopy, often require considering images up to their rotations translations. Such were tackled successfully when only, using quantities which are invariant action on images. Extending these methods cases where translations involved is more complicated. Here we present a computationally feasible theoretically sound approximate It allows one approximately reduce image similar over sphere, compact domain acted by group three-dimensional rotations, group. We show that this induced family mappings deforming, thereby compactifying, structure plane, i.e., rigid motions, into rotations. Furthermore, demonstrate its viability two tasks: multireference alignment classification. To our knowledge, first instance quantity either exactly or both rests theoretical foundation applicable practice.