The Stability and Noise Tolerance of Cartesian Zernike Moments Invariants

Abstract

In real applications, it is quite common that shapes may have changes in orientation, scale, and viewpoint; a shape retrieval method should be unaffected by translation, rotation, and scaling. Zernike moments are widely used in shape retrieval, due to its rotation invariance. However, Zernike moments are not directly invariant under scaling and translation. Recently, Cartesian Zernike Moments Invariants (CZMI) were introduced to make Zernike moments directly invariant under scaling and translation. Although CZMI reduce the scale errors considerably, they are inconsistent and the scale errors increase for high aspect ratio shapes. In this paper, we introduce a scale invariance parameter which reduces the scale errors, improves the stability of the scale invariance and is more robust for wide range of shapes; even if the shapes are corrupted by different kinds of noises, such as Gaussian, Salt & Pepper and Speckle noise, our combined scale invariance parameter still has good performances.