Robust Mesh Watermarking by yurtgc548

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									 Robust Mesh Watermarking

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

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

• Authentication / localization of changes
    Fragile watermarks
• Ownership protection
    Robust watermarks
• Tracing of distribution channels
    Fingerprints
         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)
            Digital Watermarks
    kept secret         Hidden in data!
                                     published
 original
document                 insertion



watermark
                                          “attack”
                  ?
                      extraction              suspect
     detected
    watermark                                document
      Incidental Attacks

• Filtering & smoothing

• A/D & D/A conversions

• Scaling
• Rotation
• Cropping
     Malicious Attacks

• Adding noise

• Adding another watermark

• Resampling

• Statistical analysis
              Our Goal

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

Transform to frequency space
[Cox et al. ’97]



                   DCT



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




Image basis function  DCT coefficient
              Our Approach

Extend spread-spectrum method to meshes


Problem: no DCT
Solution: multiresolution representation

Problem: no natural sampling
Solution: registration & resampling
Replacing DCT Basis Functions
 image                  mesh




                                  ?
         cosine basis

Multiresolution  frequency information
Progressive mesh [Hoppe ’96]
 Multiresolution Neighborhoods




     vertex            corresponding
 neighborhood           mesh region


Naturally correspond to important features
Provide hints on allowable perturbation
Scalar Basis Function                     i


                      amplitude
                         i       direction
                                      di

       displacement




                              radius
        Watermark Insertion

Construct basis functions  1 …  m
        Watermark Insertion

Construct basis functions  1 …  m
                                         m
Perturb each vertex: v j '  v j         d w
                                         i 1
                                                i
                                                j   i   i


            basis function coefficient
            watermark direction

            watermark coefficient

      Matrix system:         v'  v  Bw
       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*:
              B w   (v   v )
 False-Positive Probability

Correlation  = < w*,w >

Pfp computed from  and m
     using Student’s t-test

Declare watermark present if
  Pfp < Pthresh ( e.g. Pthresh = 10-6 )
                    Process




(1) original mesh   (2) watermarked   (exaggerated)




(3) suspect mesh     (4) registered   (5) resampled
   Registration & Resampling

Registration:
• [Chen & Medioni ’92]


Resampling choices:
• Closest point projection
• Ray-casting along local normal
• Global deformation of original
          Global Deformation

Deform original mesh to fit suspect mesh
Minimize:                           Suspect mesh

+ Inter-mesh distance
  ( vertex springs )
+ Deformation
  ( edge springs )
+ Penalty for flipped triangles   Optimized mesh
Accurate, but slow
                   Results
                              10-7             10-29




watermarked mesh     1/2 faces         similarity
                              10-6                  10-7




watermarked mesh      noise          2nd watermark
                   Results
                             10-13                 0




watermarked mesh     1/8 faces       cropped

                            10-12              10-2




watermarked mesh    smoothing        all attacks
                Summary

Robust watermarking for 3D meshes
• Spread-spectrum
• Basis functions from multiresolution analysis
• Resampling as global optimization

Resilient to a variety of attacks
                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

								
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