Improving stability and invariance of Cartesian Zernike moments

Zernike moments are widely used in shape retrieval, recognition and classification. The rotational invariance property of Zernike moments is very simple to achieve, due to their separable magnitude-phase property. However, Zernike moments are not directly invariant to scale and translation. Recently Cartesian Zernike moments invariants (CZMI) were introduced to directly make Zernike moments invariant under translation and scale. Although CZMI reduced scale error considerably, they are inconsistent and scale error increases for high aspect ratio images. In this paper, we propose a new scale invariance parameter, which reduces scale errors, improves the stability of scale invariance and is more consistent and stable for processing all images including the ones with large aspect ratios.