A Method for Watermarking to Bezier 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-corner 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. 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 subdivision parameters. The additional data points can not be removed without knowing some parameters for subdividing and deforming the patch, hence the patch subdivision enables us to embed a watermark into the surface. key words: Bézier Patch, Subdivision, Watermark Embedding