Experimental Analysis of BRDF Models Addy Ngan 1
Experimental Analysis of BRDF Models Addy Ngan 1 Frédo Durand 1 Wojciech Matusik 2 MIT CSAIL 1 Eurographics Symposium on Rendering 2005 MERL 2
Goal o Evaluate the performance of analytical reflectance models o Based on measured data
Background o Bidirectional Reflectance Distribution Function
BRDF o Bidirectional Reflectance Distribution Function n ρ(θi , i ; θo, o)
BRDF o Bidirectional Reflectance Distribution Function n ρ(θi , i ; θo, o) o Isotropic material n Invariant when material is rotated n BRDF is 3 D
Previous Measurements o Columbia-Utrecht Reflectance and Texture Database n ~60 materials, 205 measurements per BRDF o Cornell’s measurements n ~10 materials, 1439 measurements per BRDF o Bonn BTF Database n 6 materials, 6561 view/light combinations o Matusik’s image-based measurements n ~100 materials, ~106 measurements per BRDF n Include metals, plastic, paints, fabrics.
BRDF Models o Phenomenological n Phong [75] o Blinn-Phong [77] n Ward [92] n Lafortune et al. [97] n Ashikhmin et al. [00] Lafortune [97] o Physical n Cook-Torrance [81] n He et al. [91] Cook-Torrance [81]
Outline o o o Background BRDF Measurements BRDF Fitting Isotropic materials results Anisotropic materials results Conclusion
BRDF Measurements o Isotropic : Data from Matusik [03] n 100 materials chosen n Reprocessed to remove unreliable data o Flare o Near grazing angle o Anisotropic : New acquisition
Anisotropic Measurements o Similar to Lu et al. [00]
Anisotropic Measurements o 4 materials measured (brushed aluminum, satins, velvet) n Each: 18 hours acquisition time, 30 GB raw data n Tabulated into bins in 2° intervals (~108 bins) n 10 -20% bins populated
Outline o o o Background BRDF Measurements BRDF Fitting Isotropic materials results Anisotropic materials results Conclusion
BRDF Fitting o Target models: Blinn-Phong, Cook. Torrance, He et al. , Lafortune et al. , Ward, Ashikhmin-Shirley o Metric: n RMS of (ρmeasured– M(p)) (cos θi) n Linear w. r. t. diffuse/specular intensity
BRDF Fitting o Other potential metrics n Logarithmic remapping o Arbitrary scale o Highlights overly blurry n Perceptual metrics o Context dependent o Costly to compute/fit o Intensity parameters become nonlinear – optimization less stable
Outline o o o Background BRDF Measurements BRDF Fitting Isotropic materials results Anisotropic materials results Conclusion
Fitting Errors Dark blue paint Very diffuse Mirror-like
Dark blue paint Acquired data Material – Dark blue paint Environment map
Dark blue paint Acquired data Cook-Torrance Material – Dark blue paint
Dark blue paint Acquired data Blinn-Phong Material – Dark blue paint
Dark blue paint Acquired data Ward Material – Dark blue paint
Dark blue paint Acquired data Lafortune Material – Dark blue paint
Dark blue paint – error plots Ward Lafortune Blinn-Phong Cook-Torrance
Dark blue paint o Cook-Torrance fit, incidence plane, 4 different incident angles Material – Dark blue paint
Dark blue paint Cook-Torrance Ward Lafortune Ashikhmin Material – Dark blue paint
Dark blue paint Original Cook-Torrance Lafortune Ashikhmin Material – Dark blue paint
Lafortune Lobe o Distorted highlights near grazing angle Acquired data – gold paint Lafortune fit
Lafortune Lobe o Distorted highlights near grazing angle Acquired data – nickel Lafortune fit
Lobe Comparison o Half vector lobe n Gradually narrower when approaching grazing o Mirror lobe n Always circular Half vector lobe Mirror lobe
Half vector lobe o Consistent with what we observe in the dataset. o More details in the paper Example: Plot of “PVC” BRDF at 55° incidence
Observations - numerical o Rough order of quality n n Good fit He, Cook-Torrance, Ashikhmin Lafortune Ward Blinn-Phong Poor fit
Observations - visual o Mirror-like n metals, some plastics n All models match well visually o Glossy n paints, some metals, some wood n Fresnel effect n Distorted shape for Lafortune highlight o Near diffuse n fabrics, paints n Fresnel effect
Observations o Some materials impossible to represent with a single lobe Acquired data Cook-Torrance Material – Red Christmas Ball
Adding a second lobe o Some materials impossible to represent with a single lobe Acquired data Cook-Torrance 2 lobes Material – Red Christmas Ball
Outline o o o Background BRDF Measurements BRDF Fitting Isotropic materials results Anisotropic materials results Conclusion
Anisotropic Materials
Brushed Aluminum o Reasonable qualitative fit Acquired data Ward
Yellow Satin o Reasonable qualitative fit Acquired data Ward
Purple Satin o Split highlights ?
Outline o o o Background BRDF Measurements BRDF Fitting Isotropic materials results Anisotropic materials results n Estimation of microfacet distribution o Conclusion
Microfacet Theory o [Torrance & Sparrow 1967] n Surface modeled by tiny mirrors n Value of BRDF at o # of mirrors oriented halfway between L and o Modulated by Fresnel, shadowing/masking [Shirley 97]
Estimating the MF distribution o Ashikhmin’s microfacet-based BRDF generator [00] MF-distribution Fresnel Normalization Constant ~ Shadowing/Masking (Depend on the full distribution)
Estimating the MF distribution o Rearranging terms: Measurements
Estimating the MF distribution Measurements o depends on the distribution o Iterate to solve for n Compute n Estimate using current estimate given o Converges quickly in practice
Purple Satin o Split specular reflection microfacet distribution
Purple Satin Acquired data microfacet distribution fit
Brushed Aluminum Acquired data microfacet distribution fit
Brushed Aluminum measured data microfacet distribution fit Ward fit
MF-based BRDF generator o Expressive o Easy to estimate n No optimization necessary o Inexpensive to compute
Outline o o o Background BRDF Measurements BRDF Fitting Isotropic materials results Anisotropic materials results Conclusion
Conclusion o Isotropic materials n He, Cook-Torrance, Ashikhmin perform well o Explicit Fresnel o *multiple lobes help n Half-vector based lobe performs better n Most materials can be well-represented o Anisotropic materials n Cases where analytical models cannot match qualitatively n Estimation of the microfacet distribution is straightforward n Ashikhmin’s MF-based BRDF generator does well
Future Work o Metric o Generalized lobe based on half vector o Efficient acquisition based on the microfacet distribution
Acknowledgement o Eric Chan, Jan Kautz, Jaakko Lehtinen, Daniel Vlasic o NSF CAREER award 0447561 o NSF CISE Research Infrastructure Award (EIA 9802220) o Singapore-MIT Alliance
Questions?
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