Robust Mesh Watermarking

1
Robust Mesh Watermarking

• Emil Praun, Hugues Hoppe, and Adam Finkelstein.
• In Proceedings of the 26th annual conference on
  Computer graphics and interactive techniques,
  pages 49--56. ACM Press/Addison-Wesley Publishing
  Co., 1999.
• Princeton University, Microsoft Research
• Speaker J.B. Feng

2
Watermarking Applications

• Authentication / localization of changes
• Fragile watermarks
• Ownership protection
• Robust watermarks
• Tracing of distribution channels
• Fingerprints

3
Elements of 3D Models

• Point
• Vertex
• Line
• Edge
• Mesh
• Face, polygon, shape

4
Digital Watermarks
kept secret
originaldocument
watermark
5
Incidental Attacks

• Filtering smoothing
• A/D D/A conversions
• Scaling
• Rotation
• Cropping

6
Malicious Attacks

• Adding noise
• Adding another watermark
• Resampling
• Statistical analysis

7
Goal

• Watermarking scheme for 3D models
• Robust against attacks
• Works on arbitrary meshes
• Preserves original connectivity
• Imperceptible

8
Processing Domain

• Spatial Domain
• Low complexity
• Low robustness
• Frequency Domain
• High robustness
• High complexity

9
Spread-Spectrum Watermarking

• Transform to frequency space
• Cox et al. 97

DCT
IDCT
frequency domain
image
10
Approach

• Extend spread-spectrum method to meshes
• Problem no DCT
• Solution multiresolution representation
• Problem no natural sampling
• Solution registration resampling

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Multiresolution Neighborhoods

• Naturally correspond to important features
• Provide hints on allowable perturbation

12
Scalar Basis Function ?i
amplitude? i
directiondi
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Watermark Insertion

• Construct basis functions ? 1 ? m
• Perturb each vertex

basis function coefficient
watermark direction
watermark coefficient
14
Watermark Extraction

• Get points v on attacked mesh surface
  corresponding to original mesh vertices v
• Use same basis functions ? 1 ? m and hence
  same matrix B
• Solve least-squares system for w

15
False-Positive Probability

• Correlation ? lt w,w gt
• Pfp computed from ? and m using Students
  t-test
• Declare watermark present if Pfp lt Pthresh
  ( e.g. Pthresh 10-6 )

16
Registration Resampling

• Registration
• Chen Medioni 92
• Resampling choices
• Closest point projection
• Ray-casting along local normal
• Global deformation of original

17
Process
(1) original mesh
(2) watermarked
(exaggerated)
(3) suspect mesh
(4) registered
(5) resampled
18
Results
10-29
10-7
similarity
1/2 faces
watermarked mesh
10-6
10-7
watermarked mesh
2nd watermark
noise
19
Results
0
10-13
watermarked mesh
cropped
1/8 faces
10-2
10-12
smoothing
all attacks
watermarked mesh
20
Summary

• Robust watermarking for 3D meshes
• Spread-spectrum
• Basis functions from multiresolution analysis
• Resampling as global optimization
• Resilient to a variety of attacks