Watermarking for Bézier Polynomial Surface Models

This paper presents a new method for embedding digital watermarks into Bézier polynomial patches. An object surface is supposed to be represented by multiple piecewise Bézier polynomial patches. A Bézier patch passes through its four-comer control points, which are called data points, and does not pass through the other control points. To embed a watermark, a Bézier patch is divided into two patches by PPM(Piecewise Parametric Modeling) method proposed in [4]. Since each subdivided patch shares two data points of the original patch, the subdivision apparently generates two additional data points on the boundaries of the original patch. We can generate the new data points in any position on the boundaries by changing the division parameters in the PPM. However, the additional data points can be removed if some parameters for subdividing the patch have been known. In order to improve the tolerance against such attack, we deform the boundary curve of subdivided patches. As a result, the others can not either perceive the deformation, nor delete the watermarking.