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Shape is a fundamental image feature used in content-based image-retrieval systems. This paper proposes a robust and effective shape feature, which is based on a set of orthogonal complex moments of images known as Zernike moments (ZMs). As the rotation of an image has an impact on the ZM phase coefficients of the image, existing proposals normally use magnitude-only ZM as the image feature. In this paper, we compare, by using a mathematical form of analysis, the amount of visual information captured by ZM phase and the amount captured by ZM magnitude. This analysis shows that the ZM phase captures significant information for image reconstruction. We therefore propose combining both the magnitude and phase coefficients to form a new shape descriptor, referred to as invariant ZM descriptor (IZMD). The scale and translation invariance of IZMD could be obtained by prenormalizing the image using the geometrical moments. To make the phase invariant to rotation, we perform a phase correction while extracting the IZMD features. Experiment results show that the proposed shape feature is, in general, robust to changes caused by image shape rotation, translation, and/or scaling. The proposed IZMD feature also outperforms the commonly used magnitude-only ZMD in terms of noise robustness and object discriminability.