A novel theorem on symmetries of 2D images

A theorem linking reflectional symmetry and rotational symmetry of the 2D images has been established. This theorem shows that, for a rotationally symmetric image with K⩾1 fold(s) (K-RSI), its number of reflection-symmetric axes must be either K or zero. To the authors´ knowledge no previous studies have shown the constraint relationship between reflectional symmetry and rotational symmetry. Demonstrations on some typical images have shown the exactness of our theorem