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Zernike moments constitute a powerful shape descriptor in terms of robustness and description capability. However the classical way of comparing two Zernike descriptors only takes into account the magnitude of the moments and loses the phase information. The novelty of our approach is to take advantage of the phase information in the comparison process while still preserving the invariance to rotation. This new Zernike comparator provides a more accurate similarity measure together with the optimal rotation angle between the patterns, while keeping the same complexity as the classical approach. This angle information is particularly of interest for many applications, including 3D scene understanding through images. Experiments demonstrate that our comparator outperforms the classical one in terms of similarity measure. In particular the robustness of the retrieval against noise and geometric deformation is greatly improved. Moreover, the rotation angle estimation is also more accurate than state of the art algorithms.