Translation and scale invariants of Tchebichef moments

Discrete orthogonal moments such as Tchebichef moments have been successfully used in the field of image analysis. However, the invariance property of these moments has not been studied mainly due to the complexity of the problem. Conventionally, the translation and scale invariant functions of Tchebichef moments can be obtained either by normalizing the image or by expressing them as a linear combination of the corresponding invariants of geometric moments. In this paper, we present a new approach that is directly based on Tchebichef polynomials to derive the translation and scale invariants of Tchebichef moments. Both derived invariants are unchanged under image translation and scale transformation. The performance of the proposed descriptors is evaluated using a set of binary characters. Examples of using the Tchebichef moments invariants as pattern features for pattern classification are also provided.