Implicit Invariants and Object Recognition

The use of traditional moment invariants in object recognition is limited to simple geometric transforms, such as rotation, scaling and affine transformation of the image. This paper presents a novel concept of so-called implicit moment invariants. Implicit invariants measure the similarity between two images factorized by admissible image deformations. For many types of image deformations traditional invariants do not exist but implicit invariants can be used as features for object recognition. In the paper we present implicit moment invariants with respect to polynomial transform of spatial coordinates, describe their stable and efficient implementation by means of orthogonal polynomials, and demonstrate their robustness as well as performance in a real life experiment.