Robust%20Mesh%20Watermarking

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Robust Mesh Watermarking
Emil Praun Hugues Hoppe Adam Finkelstein
Princeton University Microsoft Research Princeton
University
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Watermarking Applications

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

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Watermarking Applications

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

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Motivating Scenario

• 1. Alice creates a 3D shape,and publishes it on
  the web.

2. Bob sells it as his own.
3. How can Alice prove ownership?(and make Bob
pay her a lot of money)
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Digital Watermarks
kept secret
originaldocument
watermark
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Incidental Attacks

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

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Malicious Attacks

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

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Our Goal

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

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Previous Watermarking

• Cox et al. 97 Introduce spread-spectrum for
  images
• Ohbuchi et al. 98 3 schemes fragile under
  resampling
• Kanai et al. 98 Requires subdivision
  connectivity meshes
• Benedens 99 Redistributes face normals by
  moving vertices

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Spread-Spectrum Watermarking

• Transform to frequency space
• Cox et al. 97

DCT
frequency domain
image
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Spread-Spectrum
Salient features ? largest coefficients
Perturb coefficients slightly to embed signal

• Image basis function ? DCT coefficient

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Our Approach

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

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Replacing DCT Basis Functions
image
mesh
cosine basis

• Multiresolution ? frequency information
• Progressive mesh Hoppe 96

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Multiresolution Neighborhoods

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

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Scalar Basis Function ?i
amplitude? i
directiondi
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Watermark Insertion
Construct basis functions ? 1 ? m
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Watermark Insertion

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

basis function coefficient
watermark direction
watermark coefficient
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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

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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 )

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Process
(1) original mesh
(2) watermarked
(exaggerated)
(3) suspect mesh
(4) registered
(5) resampled
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Registration Resampling

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

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Global Deformation

• Deform original mesh to fit suspect mesh
• Minimize
• Inter-mesh distance( vertex springs )
• Deformation( edge springs )
• Penalty for flipped triangles
• Accurate, but slow

Suspect mesh
Optimized mesh
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Results
10-29
10-7
similarity
1/2 faces
watermarked mesh
10-6
10-7
watermarked mesh
2nd watermark
noise
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Results
0
10-13
watermarked mesh
cropped
1/8 faces
10-2
10-12
smoothing
all attacks
watermarked mesh
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Summary

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

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Future Work

• Consider other attacks
• General affine and projective transforms
• Free-form deformations! StirMark by Petitcolas
  
• Explore other basis functions
• e.g. Guskov et al. 99
• Fast mesh recognition ? web crawler