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

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Watermarking Applications Authentication / localization of changesAuthentication / localization of changes Fragile watermarks Ownership protectionOwnership protection Robust watermarks Tracing of distribution channelsTracing of distribution channelsFingerprints Authentication / localization of changesAuthentication / localization of changes Fragile watermarks Ownership protectionOwnership protection Robust watermarks Tracing of distribution channelsTracing of distribution channelsFingerprints

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Watermarking Applications Authentication / localization of changesAuthentication / localization of changes Fragile watermarks Ownership protectionOwnership protection Robust watermarks Tracing of distribution channelsTracing of distribution channelsFingerprints Authentication / localization of changesAuthentication / localization of changes Fragile watermarks Ownership protectionOwnership protection Robust watermarks Tracing of distribution channelsTracing of distribution channelsFingerprints

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3.How can Alice prove ownership? (and make Bob pay her a lot of money) 2.Bob sells it as his own. Motivating Scenario 1. Alice creates a 3D shape, and publishes it on the web.

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Digital Watermarks original document watermark kept secret insertioninsertion Hidden in data! publishedpublished extractionextraction detected watermark suspect document attackattack ?

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Filtering & smoothingFiltering & smoothing A/D & D/A conversionsA/D & D/A conversions ScalingScaling RotationRotation CroppingCropping Filtering & smoothingFiltering & smoothing A/D & D/A conversionsA/D & D/A conversions ScalingScaling RotationRotation CroppingCropping Incidental Attacks

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Malicious Attacks Adding noiseAdding noise Adding another watermarkAdding another watermark ResamplingResampling Statistical analysisStatistical analysis Adding noiseAdding noise Adding another watermarkAdding another watermark ResamplingResampling Statistical analysisStatistical analysis

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Our Goal Watermarking scheme for 3D models: Robust against attacksRobust against attacks Works on arbitrary meshesWorks on arbitrary meshes Preserves original connectivityPreserves original connectivity ImperceptibleImperceptible Watermarking scheme for 3D models: Robust against attacksRobust against attacks Works on arbitrary meshesWorks on arbitrary meshes Preserves original connectivityPreserves original connectivity ImperceptibleImperceptible

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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 [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] Transform to frequency space [Cox et al. 97] frequency domain image DCT

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

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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 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 Multiresolution frequency information Progressive mesh [Hoppe 96] Multiresolution frequency information Progressive mesh [Hoppe 96] cosine basis image mesh ?

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Multiresolution Neighborhoods Naturally correspond to important features Provide hints on allowable perturbation Naturally correspond to important features Provide hints on allowable perturbation corresponding mesh region vertex neighborhood

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Scalar Basis Function i amplitude i direction d i radius displacement

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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: Construct basis functions 1 … m Perturb each vertex: watermark coefficient basis function coefficient watermark direction Matrix system:

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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*: 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 = Correlation = P fp computed from and m using Students t-test Declare watermark present if P fp < P thresh ( e.g. P thresh = ) Correlation = Correlation = P fp computed from and m using Students t-test Declare watermark present if P fp < P thresh ( e.g. P thresh = )

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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][Chen & Medioni 92] Resampling choices: Closest point projectionClosest point projection Ray-casting along local normalRay-casting along local normal Global deformation of originalGlobal deformation of originalRegistration: [Chen & Medioni 92][Chen & Medioni 92] Resampling choices: Closest point projectionClosest point projection Ray-casting along local normalRay-casting along local normal Global deformation of originalGlobal 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 Deform original mesh to fit suspect mesh Minimize: +Inter-mesh distance ( vertex springs ) +Deformation ( edge springs ) +Penalty for flipped triangles Accurate, but slow Optimized mesh Suspect mesh

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Results similarity 1/2 faces watermarked mesh watermarked mesh 2 nd watermark noise

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Results smoothing all attacks watermarked mesh cropped 1/8 faces

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

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Future Work Consider other attacks: General affine and projective transformsGeneral affine and projective transforms Free-form deformations! [StirMark by Petitcolas]Free-form deformations! [StirMark by Petitcolas] Explore other basis functions e.g. [Guskov et al. 99]e.g. [Guskov et al. 99] Fast mesh recognition web crawler Consider other attacks: General affine and projective transformsGeneral affine and projective transforms Free-form deformations! [StirMark by Petitcolas]Free-form deformations! [StirMark by Petitcolas] Explore other basis functions e.g. [Guskov et al. 99]e.g. [Guskov et al. 99] Fast mesh recognition web crawler

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