Watermarking for Bézier Polynomial Surface Models

K. Ikesako, K. Morooka, and H. Nagahashi (Japan)


Watermark Embedding, Bezier Patch, Piecewise Paramet ric Modeling


This paper presents a new method for embedding digital watermarks into Bezier polynomial patches. An object sur face is supposed to be represented by multiple piecewise Bezier polynomial patches. A Bezier patch passes through its four-corner control points, which are called data points, and does not pass through the other control points. To em bed a watermark, a Bezier 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 posi tion on the boundaries by changing the division parame ters 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.

Important Links:

Go Back