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A novel blind method for 3D image watermarking, robust against geometric distortions, is proposed. A ternary watermark is embedded in a grayscale or a color 3D volume. Construction of watermarks having appropriate structure enables fast and robust watermark detection even after several geometric distortions of the watermarked volume. Simulation results indicate the ability of the proposed method to deal with the aforementioned attacks. The proposed method is also robust against lossy compression up to a certain compression ratio.