We present a method to improve watermark robustness by exploiting the masking effect of surface roughness on watermark visibility. Our idea is to adapt watermark strength to local surface roughness based on the knowledge that human eyes are less sensitive to changes on a rougher surface patch than those on a smoother surface. In order to quantify human sensitivity to surface roughness of polygonal meshes, we conducted a rigorous psychovisual experiment to obtain human watermark detection thresholds as a function of surface roughness. The results can be used to adaptively select watermark strength according to local surface roughness during the watermark embedding process. To test our idea, we applied it to the modified versions of two popular 3-D watermarking methods, one proposed by Benedens and one by Cayre and Macq. Experimental results showed that our approach improves watermark robustness as compared to the original algorithms. Further analyses indicated that the average watermark strength allowed by our roughness-adaptive method was larger than that by the original Benedens's and Cayre and Macq's methods while ensuring watermark imperceptibility. This was the main reason for the improved robustness observed in our experiments. We conclude that exploiting the masking property of human vision is a viable way to improve the robustness of 3-D watermarks, and can potentially be applied to other 3-D digital watermarking techniques.
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