TY - GEN

T1 - Watermarking for Bézier Polynomial Surface Models

AU - Ikesako, Kumiko

AU - Morooka, Ken'ichi

AU - Nagahashi, Hiroshi

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - Bézier Patch

KW - Piecewise Parametric Modeling

KW - Watermark Embedding

UR - http://www.scopus.com/inward/record.url?scp=1542299587&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542299587&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:1542299587

SN - 0889863768

T3 - IASTED International Conference on Computer Graphics and Imaging

SP - 193

EP - 199

BT - IASTED International Conference on Computer Graphics and Imaging

A2 - Hamza, M.H.

A2 - Hamza, M.H.

T2 - Sixth IASTED International Conference on Computer Graphics and Imaging

Y2 - 13 August 2003 through 15 August 2003

ER -