Representations that uniquely characterize images modulo translation, rotation, and scaling

Representations that uniquely characterize images modulo the planar geometric similarity transformations are presented. Such representations are invariant with respect to translation, rotation, scaling, and their combination. We will first discuss basic invariants, that is, the invariants for translation, rotation, and scaling only. We will then discuss hybrid invariants, that is, invariants with respect to combinations of translation, rotation, and scaling.