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Contourlet transform is a very efficient anisotropy analysis tool in high dimensions, which can not only possess the main features of directionality and anisotropy, but also effectively capture the intrinsic geometrical structures such as smooth contours (at different scales and directions) in natural images. In this paper, an image normalization based robust digital watermarking scheme in contourlet domain is proposed. Firstly, the geometrically invariant space is constructed by using image normalization and the significant region is obtained from the normalized image by utilizing the invariant centroid theory. Then, the contourlet transform is performed on the significant region. Finally, the digital watermark is adaptively embedded into the significant region by quantizing the low-frequency contourlet coefficients according to the Human Visual System (HVS). Especially, the predistortion compensation technique is applied to reduce image distortion generated by image normalization. Experimental results show that the proposed scheme is not only invisible and robust against common signals processing such as noise adding, and JPEG2000 compression, but also robust against the geometric distortion such as rotation, translation, scaling, row or column removal, cropping.