Efficient Translation, Rotation, and Scale Invariants of Discrete Tchebichef Moments

Abstract

Translation rotation and scale invariants of Tchebichef moments are commonly used descriptors in image analysis. Existing invariant algorithms either indirectly compute from geometric moments or directly using Tchebichef moments. The former approach is relatively simple, but inefficient, especially when the system consists only of Tchebichef moments. Likewise, the latter approach is complicated, mainly because of the method used to formulate the invariant algorithm. Hence, in this paper, we introduce a new set of translation, rotation and scale Tchebichef moment invariants (TRSI) using moment normalization, which is much computationally efficient and accurate. This is achieved by formulating the recurrence relationship of the descriptors and successfully resolve uniqueness issues of principal axis normalization. Experimental studies show that the proposed method is computationally much faster and possesses higher discriminative power in classification when compared with present invariant algorithms. The main contribution of this paper is a novel fast computational algorithm that simplifies translation, rotation and scale invariant algorithms of Tchebichef moments and a novel normalization scheme that preserve invariants' orthogonality from the moment functions. The technique can be deployed to derive affine invariants of Tchebichef moments, and invariants for other orthogonal moments like Krawtchouk, Hahn, Racah moments etc.