A Method for Watermarking to Bezier Polynomial Surface Models

Hiroshi NAGAHASHI; Rikima MITSUHASHI; Ken'ichi MOROOKA

A Method for Watermarking to Bezier Polynomial Surface Models

Hiroshi NAGAHASHI, Rikima MITSUHASHI, Ken'ichi MOROOKA

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This paper presents a new method for embedding digital watermarks into Bezier polynomial patches. An object surface 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 embed a watermark, a Bezier 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.

Publication: IEICE TRANSACTIONS on Information Vol.E87-D No.1 pp.224-232

Publication Date: 2004/01/01

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Type of Manuscript: PAPER

Category: Computer Graphics

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Hiroshi NAGAHASHI, Rikima MITSUHASHI, Ken'ichi MOROOKA, "A Method for Watermarking to Bezier Polynomial Surface Models" in IEICE TRANSACTIONS on Information, vol. E87-D, no. 1, pp. 224-232, January 2004, doi: .
Abstract: This paper presents a new method for embedding digital watermarks into Bezier polynomial patches. An object surface 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 embed a watermark, a Bezier 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.
URL: https://globals.ieice.org/en_transactions/information/10.1587/e87-d_1_224/_p

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@ARTICLE{e87-d_1_224,
author={Hiroshi NAGAHASHI, Rikima MITSUHASHI, Ken'ichi MOROOKA, },
journal={IEICE TRANSACTIONS on Information},
title={A Method for Watermarking to Bezier Polynomial Surface Models},
year={2004},
volume={E87-D},
number={1},
pages={224-232},
abstract={This paper presents a new method for embedding digital watermarks into Bezier polynomial patches. An object surface 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 embed a watermark, a Bezier 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.},
keywords={},
doi={},
ISSN={},
month={January},}

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TY - JOUR
TI - A Method for Watermarking to Bezier Polynomial Surface Models
T2 - IEICE TRANSACTIONS on Information
SP - 224
EP - 232
AU - Hiroshi NAGAHASHI
AU - Rikima MITSUHASHI
AU - Ken'ichi MOROOKA
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E87-D
IS - 1
JA - IEICE TRANSACTIONS on Information
Y1 - January 2004
AB - This paper presents a new method for embedding digital watermarks into Bezier polynomial patches. An object surface 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 embed a watermark, a Bezier 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.
ER -