Zhejiang University

Wavelet-based 3D mesh model watermarking

Shi Jiao-Ying

State Key Laboratory of CAD&CG, Zhejiang University,

Hangzhou 310027

Zhejiang University Introduction

•Digital watermarking —an effective way of copyright protection

• Current watermarking technology focuses on media types like still images,and video and audio streams

• Research about 3D mesh model watermarking began in 1998

Zhejiang University

The challenges of mesh watermarking

(1)In watermark insertion process, arbitrary meshes lack a natural parameterization for frequency-based decomposition.

(2) In watermark detection process, simplification and other attacks may modify the connectivity of the mesh.

Introduction

Zhejiang University Introduction

• We construct a planar parameterization for arbitrary meshes. Geometric signals are transformed into 2D signals. Then we can apply any image watermarking algorithms for our geometry signals.

Our Solutions

Zhejiang University Introduction

• We obtain a mesh with the topology of the original and the geometry of the attacked object. We use an optimization technique similar to E.Praun’s method to resample an attacked mesh using the original mesh connectivity.

Our Solutions

Zhejiang University

(1) The watermark can be embedded in all mesh attributes, including position coordinates, normal, color and texture coordinates etc.

(2) All kinds of image frequency-domain watermarking algorithms can be applied to 3D models directly.

Introduction

The two advantages of our method:

Zhejiang University 3D Mesh Model Watermark System

OriginalSignalFM

RectangleSignalFD

RegularSampleSignalFU

WatermarkRegularSample

Signal F’U

WatermarkSignalF’M

PlaneParameterization Sampling

ImageWatermarkAlgorithms

Resampling &Inverse Mapping

Figure 1: 3D mesh model watermark system framework. Processing stages are depicted as rectangles; rounded

boxes represent input/output data of each stage.

Zhejiang University

Figure 2: The progressive planar parameterization. The up line depicts the simplification process which transfers the original mesh Mn into a tetrahedron M0; then M0 is mapped into a square D0; then using the information generated during mesh simplification, such as Spn, … ,Spi, Spi-1, … to generate an square mesh with original resolution Dn.

Planar parameterization

OriginalSignalFM

RectangleSignalFD

PlaneParameterization

Zhejiang University Sampling

Sampling: The 2D signal FD is adaptively sampled

into a regular signal FU

under the user specified precision threshold.Rectangle

SignalF0

RegularSampleSignalFU

Sampling

Zhejiang University Watermark Insertion

Figure 3: Watermark insertion process

2D original regular signal FU

2D watermarked regular signal F ‘U

Search significant subband coefficients

DWT

Inserting watermark

Generating watermark

IDWT

(1) DWT of the 2D original regular signal

(2) Significant coefficient search

(3) Watermark insertion

(4) IDWT of the coefficients with watermarks

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RegularSampleSignalFU

WatermarkRegularSample

Signal F’U

ImageWatermarkAlgorithms

Zhejiang University Resampling & Inverse Mapping

• M0- Original Mesh

• Ms- Mesh, which topology has been changed after attacks, needs to be resampled

• Mr- Result Mesh after resampling and inverse mapping which topology has been recovered with that of M0 by using optimization method.

WatermarkRegularSample

Signal F’U

WatermarkSignalF’M

Resampling &Inverse Mapping

Zhejiang University Watermark Detection

(1) DWT of original 2D regular signal and watermarked 2D regular signal

(2) Watermark extraction

(3) Calculation of the correlation

DWT

DWT

Calculating correlation

2D detected regular signal

2D original regular signal

Extracted watermark

Watermark

Watermark detection

Figure 4: Watermark detection process

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Zhejiang University Detection threshold analysis • First set the correlation threshold experimentally.

• 10000 watermark vectors with length of 50 randomly generated.

• The original watermark is the 5000th.

• The maximum correlation is around 0.47.

• We can set the correlation threshold to 0.5.

Figure 5: Detection threshold analysis

Zhejiang University Results and Attack Analysis We implemented our algorithm in MSVC++ 6.0 on a PⅡ350 machine. The test result in this section were obtained using a watermark length of m=50 coefficients, the scaling factors =0.2,=0.4. We ran each 5 times, using different random seeds, and report the median value. Table 1 shows the detection results for a host of attacks.

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A B C D E F F1 G H I J K L M N O P Q R S T

at tack type

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Venus Model Cat Model

Figure 6 ： Median of 5 tests for various attacks

Zhejiang University

Figure 7 ： Watermarked models and some attacked models.

Results and Attack Analysis

Zhejiang University Summary and Future work

Our 3D mesh models watermark system framework has following characteristics:

• Watermark can be embedded in all mesh attributes, including position coordinates, normal, color and texture coordinates etc.

• All kinds of image frequency-domain watermarking algorithms can be applied to 3D models directly.

Future work includes:

• Embedding the watermark in other mesh attributes, such as normal, color and texture coordinates etc;

• Appling more image frequency-domain watermark algorithms to 3D mesh models;

• Inserting the watermark in user specified position of 3D mesh models

Zhejiang University

Thank You!