Explicit Separable two dimensional Moment Invariants for object recognition

Image moment invariants has been widely used in the fields of pattern recognition and computer vision, since they are able to represent pattern features independently of geometric transformations. Currently, Separable Moments and their invariants are gaining more interest, due to their capability for combining the basic properties of different orthogonal moments. However, most of the existing separable moment invariants are derived indirectly from the geometric invariants, based on the relationship orthogonal polynomials and the geometric basis. Therefore, in this paper, we propose a direct approach to construct a set of discrete separable Tchebichef-Krawtchouk Moment Invariants which are simultaneously invariant to Rotation, Scaling and Translation transformation, based on the explicit form of the Tchebichef and Krawtchouk polynomials. Consequently, the experimental and theoretical results validate the effectiveness of the proposed method and show their superiority in image classification and pattern recognition in comparison with the existing methods.