Robust watermarking for T-spline surfaces based on nonuniform B-spline wavelets transformation

T-spline surfaces are widely used in entertainment, engineering, science and medicine. Nonuniform B-spline wavelets transformation is introduced into T-spline surfaces watermarking, and a scheme is proposed for embedding watermarks into T-spline surfaces. In watermark embeding stage, firstly, the points are selected from the standard T-spline surfaces. Secondly, the points are decomposited by nonumiform B-spline wavelets transformation, then the watermarks are embedded into its lower resolution coefficients, and then the watermarked points are obtained by the B-spline wavelets reconstruction. Finally, the watermarked T-spline surfaces are obtained by modifing the T-spline control points. In watermark extracting stage, the same points selection and wavelets decomposition processes are performed to both the original surfaces and the watermarked surfaces, then the watermarks are obtained according to the differences of their lower resolution coefficients. Experimental results show that the proposed scheme is robust against attacks such as translation, rotation, uniform scaling, noise addition, control points modification, weights modification, local knot insertion and control point removal.