3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials

Abstract In this paper, we introduce new sets of separable discrete moments for 3D image analysis, named: TKKM (Tchebichef-Krawtchouk-Krawtchouk Moments) and TTKM (Tchebichef-Tchebichef-Krawtchouk Moments). Firstly, we present a detailed comparative study between the proposed separable 3D moments and the classical ones in terms of global feature extraction capability under noisy and noise-free conditions. Also, their local feature extraction ability is examined. Secondly, our study investigates the ability of the proposed separable 3D moments in pattern recognition. For this, new sets of separable 3D discrete moment invariants are introduced. The proposed rotation, scaling and translation 3D moment invariants have been rigorously tested under different sets of mixed transforms. The obtained results show that the representation capability, in comparison with traditional Krawtchouk and Tchebichef moments, has been significantly improved by using the new proposed 3D separable moments and can be highly useful in the field of 3D image analysis.

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