Semi-regular 3D mesh progressive compression and transmission based on an adaptive wavelet decomposition 21 st January 2009 Wavelet Applications in Industrial Processing VI IS&T/SPIE Symposium on Electronic Imaging C. ROUDET, F. DUPONT & A. BASKURT croudet, fdupont,

2 Context 3D objects  Used in various applications  Lots of different models Triangular meshes  More and more detailed  Adapted to heterogeneous resources  Irregularly sampled

3 Triangular meshes 4 bytes x3 coordinates 4 bytes x3 indexes Mesh regularity  Link to vertex valence (σ) V : {V i = (x i, y i, z i ) є R 3 / 0 ≤ i <|V|} F : {F i = j, k, l є Z 3 / 0 ≤ i <|F|} I - Context II - WT III – Our approach IV - Results irregular regular semi-regular Mesh M = (V, F) Geometry Connectivity Triangular mesh 36 bytes / vertex 288 bits / vertex  3 types of meshes : 1. irregular 2. semi-regular :  W V |  V i,V j є W : σ ( V i ) ≠ σ ( V j ) 3. regular :  V i,V j є V : σ ( V i ) = σ ( V j ) ∩

4 Progressive representations Advantages :  Efficient rendering  Data adapted to heterogeneous devices and networks Various possible representations :  Subdivision surfaces [Doo & Sabin, 78] + wavelets [Lounsbery, 97] ≈ bits / v  Irregular refinements [Hoppe, 96], [Gandoin & Devillers, 02] ≈ 2 bytes / v

5 Multiresolution analysis L 2 H L L H 1/4 1/2 f L H L H L H … details M0M0 M m-1 MmMm H [½ ½] [1 -1]

6 Geometric wavelets Filter bank generalization  Spatial multiresolution analysis Advantages :  Reduce computation costs  Simplified filters  Analysis & synthesis in linear time [Sweldens, 95] [Lounsbery, 97] S : Split P : Predict U : Update reconstructed signal coarse signal details signal even odd [Mallat, 89] coarse signal details signal reconstructed signal

7 MnMn M n-1 On meshes Update Predict even odd coarse signal details reconstructed signal

8 Overview of our approach CHANNELCHANNEL Global analysis Multiresolution segmentation Local analysis Local encoding Local decoding binary flow Remesh wavelet coefficients irregular 3D model semi-regular 3D model clusters patches Coarse gluing Local synthesis binary flow resolution levels Visualization Classification

9 A n-3 MnMn A n-2 A n-1 D n-1 D n-2 D n-3 Multiresolution representation Level n-1Level n-2Level n-3Level n-1 … Level n original vertices vertices vertices vertices Multiresolution weighting 01 Wavelet magnitude x10

10 Classification and region growing Magnitude Polar angle vertices Classification (K-means) 2 clusters Magnitude Polar angle Magnitude Polar angle vertices facets K=2 Region growing Global analysis Level n original Level n-1

11 Cluster « coarse » projection Coarse projection Region extraction Level n (original) Level n-1 Level n-5 Level n-2 … Level n-4Level n-5 Fine projection t0t0 t2t2

12 Cluster « fine » projection Initial classification Level n-2Level n-4 …Level n-5 Coarse projection Region extraction Level n (original) Level n-1 Level n-5 Fine projection

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14 Different possible segmentations Multiresolution weighting on the finest approximation + « coarse » & « fine » projections Multiresolution weighting on the coarsest level + « fine » projection 5 regions 6 regions 5 regions 11 regions 9 regions

15 Independent analysis and coding CHANNELCHANNEL + Coding of partitioning information :  nb regions, cluster type, filters used, … : losslessly compressed zerotree Connectivity Arithmetic coding symbol list Quantization Geometry [Touma & Gotsman, 98] … [Khodakovsky et al., 00] Arithmetic coding Arithmetic coding symbol list Quantization [Touma & Gotsman, 98] Arithmetic coding Connectivity Geometry

16 Global vs local analysis PSNR = 20.log 10 BBdiag / d BBdiag = Bounding Box diagonal d = Hausdorff distance Rate / distortion curves (unique prediction scheme used) Local analysis (2 nd weighting) additional cost Local analysis (1 st weighting) Global analysis Remeshing error Bitrate (bits / irregular vertex)

17 Progressivity of the reconstruction 0,23 bit / vertex 0,68 bit / vertex 1,66 bit / vertex 6,54 bit / vertex

18 Other applications Adaptive denoising & watermarking View-dependent transmission & reconstruction (ROI) Error-resilient coding e : error ( x ) Global analysis Classification Adaptive reconstructions: with prédiction without 554 KB e: 0,203 36% rough 218 KB e: 10,3 218 KB e: 17, bytes bytes

19 Conclusion and future work Adaptive multiresolution framework  Used to propose view-dependent transmission & visualization  Based on a multiresolution segmentation  Patch-independent analysis, quantization & encoding Future work:  Design new prediction schemes adapted to non-smooth regions  Optimize patch-quantization and binary allocation