Watermarking for Bézier Polynomial Surface Models

Kumiko Ikesako, Ken'ichi Morooka, Hiroshi Nagahashi

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 languageEnglish
Title of host publicationIASTED International Conference on Computer Graphics and Imaging
EditorsM.H. Hamza, M.H. Hamza
Number of pages7
Publication statusPublished - 2003
Externally publishedYes
EventSixth IASTED International Conference on Computer Graphics and Imaging - Honolulu, HI, United States
Duration: Aug 13 2003Aug 15 2003

Publication series

NameIASTED International Conference on Computer Graphics and Imaging


ConferenceSixth IASTED International Conference on Computer Graphics and Imaging
Country/TerritoryUnited States
CityHonolulu, HI


  • Bézier Patch
  • Piecewise Parametric Modeling
  • Watermark Embedding

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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