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Compression and Real-time Rendering of Measured BTFs using local-PCA

Compression and Real-time Rendering of Measured BTFs using local-PCA. Mueller, Meseth, Klein Bonn University Computer Graphics Group. Motivation. (Real-time) Rendering of complex meso-structure: Shadowing Masking Light-Transport: inter-reflections sub-surface scattering etc.

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Compression and Real-time Rendering of Measured BTFs using local-PCA

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  1. Compression and Real-time Rendering of Measured BTFs using local-PCA Mueller, Meseth, Klein Bonn University Computer Graphics Group

  2. Motivation • (Real-time) Rendering of complex meso-structure: • Shadowing • Masking • Light-Transport: • inter-reflections • sub-surface scattering • etc. • Classical modeling andrendering approach infeasible VMV 2003  University of Bonn  Computer Graphics Group 2/25

  3. Motivation • Common „work around“: Meso-structure is rendered from one image • Texture mapping • Fast and simple • Hardware support • Flat appearance • Only simple relighting VMV 2003  University of Bonn  Computer Graphics Group 3/25

  4. Motivation • Improvement: Meso-structure is rendered from many images • Rendering measured BTF • Bidirectional-Texture-Function (Dana et al. 1999) • Light and view-dependent Texture • Apparent BRDF that varies per texel • Captures all light and view-dependent effects of a material VMV 2003  University of Bonn  Computer Graphics Group 4/25

  5. Problem • Accurate samplings of the 6-dimensional BTF(x, y, wi, wr) contain many images • e.g. Sattler et al.(Bonn University, 2003): • 81 directions for light and view each • 256x256 texel spatial extend • 6561 RGB-images ~1.2GB • Interpolation from sampled data impossible in real-time • Memory reduction required http://btf.cs.uni-bonn.de/ VMV 2003  University of Bonn  Computer Graphics Group 5/25

  6. Previous Work • McAllister et al. (2002) • Fitting analytical BRDF-model (generalized cosine lobes - Lafortune) to every texel • Fast rendering and high compression (~1:500) • Limited quality (depth impression!) • Non-linear fitting required (expensive, <5 lobes) McAllister 2002 VMV 2003  University of Bonn  Computer Graphics Group 6/25

  7. per-texel apparent BRDF Previous Work • Daubert et al. (2001) • Fitting Lafortune to synthetic cloth-BTFs • Including view-dependent scaling factor • Increased depth-impression and moderate memory requirements (~1:40) • Modeling abilities still limited: wr Daubert et al. 2001 wi Lafortune 2 lobes scale factor 2 lobes Lafortune 10 lobes scale factor 10 lobes white plaster VMV 2003  University of Bonn  Computer Graphics Group 7/25

  8. Meseth et al. (2003) Fitting of analytical functions (polynomials, lobes) for fixed measured view-direction (reflectance fields) Rendering employs view-interpolation Masking and shadowing captured High memory requirements (~1:15) Artificiality of the fitted analytical functions still notable wr wi original per-view polynomial Previous Work Meseth et al. 2003 VMV 2003  University of Bonn  Computer Graphics Group 8/25

  9. Suykens et al. (2003) Application of an improved BRDF-factorization technique (Chained-Matrix-Factorization, CMF) Clustering of resulting factors leads to compact representation Fast implementation on current graphics hardware Tested samples not representative for real measured BTFs wr wi CMF (four factors) no clustering original Previous Work Suykens et al. 2003 VMV 2003  University of Bonn  Computer Graphics Group 9/25

  10. Sattler et al. (2003) Perform PCA on images with fixed view direction Combine the resulting “Eigen-Textures” during rendering High quality Environmental lighting supported High memory requirements (~1:10) Real-time only for small meshes(CPU-operations per vertex) wr wi original 8 PCA components Previous Work Sattler et al. 2003 VMV 2003  University of Bonn  Computer Graphics Group 10/25

  11. Our Approach • Interpret the measured BTF as set of high-dimensional vectors (either images or per texel apparent BRDFs) • Expect correlation between vectors • Apply data analysis tools for dimensionality reduction wr wi reprojected images per-texel apparent BRDF VMV 2003  University of Bonn  Computer Graphics Group 11/25

  12. Our Approach • Generalize Sattler et al.: • Cluster data to subsets • Apply Principal Component Analysis (PCA) to data in that subsets • Piece-wise affine-linear approximation: affine-linear approximation 3 piece affine-linear approximation VMV 2003  University of Bonn  Computer Graphics Group 12/25

  13. PCA basis vector Our Approach • How should we cluster? • Generalized Lloyd-algorithm • Euclidean distance • Reconstruction errorLocal-PCA (Kambhatla, Leen [1997]) VMV 2003  University of Bonn  Computer Graphics Group 13/25

  14. Analysis images BRDFs no clustering original reconstruction (k=32, c=8) c=30,k=1 inverted difference cluster index map Average reconstruction error (proposte, c=8) • BRDF-arrangement performs superior • Represent BTF by sets of “Eigen-BRDF”s VMV 2003  University of Bonn  Computer Graphics Group 14/25

  15. original white plaster scale factor 2 lobes per-view PCA (c=8) LPCA (k=32, c=8) wr wr wi wi CMF (four factors) no clustering per-view polynomial Analysis - Comparison corduroy VMV 2003  University of Bonn  Computer Graphics Group 15/25

  16. Analysis - Results raw data compressed (k=32, c=8) VMV 2003  University of Bonn  Computer Graphics Group 16/25

  17. Analysis - Results raw data compressed (k=32, c=8) VMV 2003  University of Bonn  Computer Graphics Group 17/25

  18. Analysis - Results raw data compressed (k=32, c=8) VMV 2003  University of Bonn  Computer Graphics Group 18/25

  19. Real-Time Rendering • Rendering equation for n point-light sources • Evaluate on hardware: Eigen-BRDF (includes cosine factor) closest measured light/view-directions cluster look-up VMV 2003  University of Bonn  Computer Graphics Group 19/25

  20. Real-Time Rendering • Straight-Forward GeForce 5900 FX implementation: • ~15 Frames – 800x600, P-IV 2.4GHz • Arranging Eigen-BRDFs in parabolic-maps enables built-in view-interpolation • ~Factor 3 speed-up VMV 2003  University of Bonn  Computer Graphics Group 20/25

  21. Demo VMV 2003  University of Bonn  Computer Graphics Group 21/25

  22. Extensions • Mip-Mapping: • Assigning weights and cluster-indices to scaled versions of the BTF • Environmental Lighting • Extend “Bi-Scale Radiance Transfer” (Sloan et al. [2003]) • Memory savings enable large BTFs • Lighting integral (dot-product of Spherical Harmonics coefficients) could be pre-computed! VMV 2003  University of Bonn  Computer Graphics Group 22/25

  23. Preview VMV 2003  University of Bonn  Computer Graphics Group 23/25

  24. Conclusions • Using local-PCA for BTF-compression • exploits correlations in the materials structure • especially suited for materials with low- and high-frequency content (high spatial resolution required) • stable fitting algorithm • high quality with affordable memory requirements and runtime cost • implementation on current graphics hardware • easily extendable and combinable with other techniques VMV 2003  University of Bonn  Computer Graphics Group 24/25

  25. Acknowledgements • Funded by the European Union under the project RealReflect (www.realreflect.org) • Funded by the BMBF under the project VirtualTry-On (www.virtual-try-on.de) • HDR-Environments from www.debevec.org VMV 2003  University of Bonn  Computer Graphics Group 25/25

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