### Abstract

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.

Original language | English |
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Title of host publication | IASTED International Conference on Computer Graphics and Imaging |

Editors | M.H. Hamza, M.H. Hamza |

Pages | 193-199 |

Number of pages | 7 |

Publication status | Published - Dec 1 2003 |

Externally published | Yes |

Event | Sixth IASTED International Conference on Computer Graphics and Imaging - Honolulu, HI, United States Duration: Aug 13 2003 → Aug 15 2003 |

### Other

Other | Sixth IASTED International Conference on Computer Graphics and Imaging |
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Country | United States |

City | Honolulu, HI |

Period | 8/13/03 → 8/15/03 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Graphics and Computer-Aided Design

### Cite this

*IASTED International Conference on Computer Graphics and Imaging*(pp. 193-199)

**Watermarking for Bézier Polynomial Surface Models.** / Ikesako, Kumiko; Morooka, Kenichi; Nagahashi, Hiroshi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IASTED International Conference on Computer Graphics and Imaging.*pp. 193-199, Sixth IASTED International Conference on Computer Graphics and Imaging, Honolulu, HI, United States, 8/13/03.

}

TY - GEN

T1 - Watermarking for Bézier Polynomial Surface Models

AU - Ikesako, Kumiko

AU - Morooka, Kenichi

AU - Nagahashi, Hiroshi

PY - 2003/12/1

Y1 - 2003/12/1

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.

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

SP - 193

EP - 199

BT - IASTED International Conference on Computer Graphics and Imaging

A2 - Hamza, M.H.

A2 - Hamza, M.H.

ER -