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Robust Mesh Watermarking

Robust Mesh Watermarking. Emil Praun Hugues Hoppe Adam Finkelstein. Princeton University Microsoft Research Princeton University. Watermarking Applications. Authentication / localization of changes Fragile watermarks Ownership protection Robust watermarks

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Robust Mesh Watermarking

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

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

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

  4. 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)

  5. Hidden in data! published insertion “attack” ? suspectdocument extraction detectedwatermark Digital Watermarks kept secret originaldocument watermark

  6. Incidental Attacks • Filtering & smoothing • A/D & D/A conversions • Scaling • Rotation • Cropping

  7. Malicious Attacks • Adding noise • Adding another watermark • Resampling • Statistical analysis

  8. Our Goal • Watermarking scheme for 3D models: • Robust against attacks • Works on arbitrary meshes • Preserves original connectivity • Imperceptible

  9. 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

  10. Spread-Spectrum Watermarking • Transform to frequency space • [Cox et al. ’97] DCT image frequencydomain

  11. Spread-Spectrum • Salient features largest coefficients • Perturb coefficients slightly to embed signal • Image basis function DCT coefficient

  12. Our Approach • Extend spread-spectrum method to meshes • Problem: no DCT • Solution: multiresolution representation • Problem: no natural sampling • Solution: registration & resampling

  13. ? Replacing DCT Basis Functions image mesh • Multiresolution  frequency information • Progressive mesh [Hoppe ’96] cosine basis

  14. correspondingmesh region vertexneighborhood Multiresolution Neighborhoods • Naturally correspond to important features • Provide hints on allowable perturbation

  15. displacement radius Scalar Basis Function i amplitudei directiondi

  16. Watermark Insertion Construct basis functions 1 … m

  17. Matrix system: Watermark Insertion • Construct basis functions 1 … m • Perturb each vertex: basis function coefficient watermark direction watermark coefficient

  18. Watermark Extraction • Get points v* on attacked mesh surface corresponding to original mesh verticesv • Use same basis functions 1 … m and hence same matrix B • Solve least-squares system for w*:

  19. False-Positive Probability • Correlation  = < w*,w > • Pfp computed from  and m using Student’s t-test • Declare watermark present ifPfp < Pthresh ( e.g. Pthresh = 10-6 )

  20. Process (1) original mesh (2) watermarked (exaggerated) (3) suspect mesh (4) registered (5) resampled

  21. Registration & Resampling • Registration: • [Chen & Medioni ’92] • Resampling choices: • Closest point projection • Ray-casting along local normal • Global deformation of original

  22. 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 Optimizedmesh

  23. Results 10-7 10-29 watermarked mesh 1/2 faces similarity 10-6 10-7 watermarked mesh noise 2nd watermark

  24. Results 0 10-13 watermarked mesh 1/8 faces cropped 10-2 10-12 watermarked mesh smoothing all attacks

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

  26. 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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