Abstract
A novel 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 novel theorem.