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
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Thank You!