Abstract
Zernike moments are one of the most commonly implemented feature extractors among the family of moment invariants. Their popularity stems from the fact that they are robust in the presence of noise. Their rotational invariance property is inherited from the angular dependence of Zernike polynomials; however the scale and translation invariance cannot be explicitly achieved. One of the indirect approaches to achieve scale and translation invariance is through expressing Zernike moments using centralized and normalized regular moments. In this paper Zernike moments are expressed in Cartesian coordinates to explicitly make them invariant to scale, translation and rotation directly without the need to use the regular moments. These Cartesian Zernike moment invariants are extensively tested using several gray level images. The results clearly demonstrate the effectiveness of the Cartesian Zernike moment invariants and superiority over the indirect approach of expressing Zernike moments using the regular moments.
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