Mahdi M. Bagher / Cyril Soler / Nicolas Holzschuch Maverick, INRIA Grenoble-Rhône-Alpes and LJK (University of Grenoble and CNRS)

Mahdi M. Bagher / Cyril Soler / Nicolas Holzschuch Maverick, INRIA Grenoble-Rhône-Alpes and LJK (University of Grenoble and CNRS)

Wide variety of materials characterized by surface reflectance and scattering

There is room for improvement! Cook-Torrance BRDF Lab error Beckmann Distribution Gold-metallic-paint Ground truth

What is reflectance? How to acquire reflectance? How to represent reflectance? Tabulated BRDF Compression and factorization Analytical approximations

For each surface point: For each light direction: For each view direction: How much of the incident light is reflected? Depends on: Light properties Material properties Geometric profile of the surface

Rusinkiewicz's half-angle coordinate system BRDF measurement gantry [Matusik et al. 2003] MERL BRDF Database

Tabulating the full BRDF measurement Large memory footprint (33 MB for an isotropic MERL material) Impractical importance sampling Unreliable measurements near grazing angles Difficult reflectance editing [Bagher et al. 2012] [Pellacini et al. 2007] [Lawrence et al. 2006] [Ben-Artzi et al. 2006]

Use BRDF compression and factorization Smaller memory footprint Importance sampling can still be a problem Editability is still hard Potential loss of subtle or wavelength dependent effects [Romeiro et al. 2008] [Pacanowski et al. 2012] [Claustres et al. 2007] [Wang et al. 2009] [McCool et al. 2001] [Kautz et al. 1999]

Approximate reflectance using analytical expressions Some are physically-based models. (e.g. Cook-Torrance) Some other are empirical (e.g. Phong) Fast evaluation More practical importance sampling Editing by parameter tweaking Not accurate for highly glossy and specular materials [Ngan et al. 2005] The parameters can be used for fitting to measurements

[Ward 1992] [Duer 2004] [Blinn 1977] [Lafortune 1997] [Cook et al. 1981] [He et al. 1991] [Ashikhmin et al. 2000] Purple-paint [Ngan et al. 2005]

A rough surface is composed of many specular micro-facets Each micro-facet reflects light in a single direction according to its normal Micro-facets follow a Normal Distribution Function (D). view light m m m

Normal distribution function Shadowing and masking Fresnel [Cook & Torrance 1982]

Beckmann NDF (widely used in graphics) [Cook & Torrance 1982] Exponential NDF (used for radio wave propagation) [Brown 1980] & [Bourlier et al. 2002] Trowbridge-Reitz / GGX NDFs [Trowbridge et al. 1975] & [Walter et al. 2007] D(θ h ) θ h

Smith [Smith 1967] shadowing functions (G 1 ) is derived from the micro-facet distribution D. incoming outgoing θ o highly specular material θ o glossy material

Depends on the refraction index of the material Small at normal incidence and increases to unity at grazing angles Schlick s approximation to Fresnel is widely used [Schlick 1994] Fresnel [Lazanyi et al. 2005]: more accurate but complex Fresnel approximation for metals θ d

Existing models are not very accurate Specially for highly glossy and specular materials [Ngan et al. 2005] We need a more accurate model: Approach: Identify the problems (by looking at an example) Propose solutions to the identified problems

If, then Fresnel becomes a constant. For very small and specular materials, is almost constant and equal to 1. The extracted BRDF slice, for varying θ h with θ d = 0, varies with D only!

Requirements: 1. Non-zero slope at θ h = 0 2. Rapid decrease at the peak 3. Slow decrease at the tail

We are going to propose: A more accurate analytical expression In the case of Cook-Torrance BRDF A better normal distribution function (D) shadowing and masking function (G) is derived from D A better Fresnel function (F) A fast and efficient fitting algorithm An Importance sampling solution Validation (quantitative and qualitative)

Shifted Gamma Distribution where incomplete gamma function

Derived form the Shifted Gamma Distribution Sidedness agreement incomplete gamma function confluent hyper-geometric function of the second kind Numerically approximate the integral by Gauss Legendre quadrature

θ o Fruitewood-241

At grazing angles, Fresnel decreases to 0 instead of increasing to 1

For some materials, the measured Fresnel is different from Schlick s curve

Our Fresnel term is a generalization of Schlick s approximation Schlick new gold-paint nickel brass

No closed form expression available Importance sample the GGX distribution as an approximation Refer to supplemental for details

Each RGB channel is fitted separately wavelength dependent effects (e.g. Fresnel) Faster and efficient fitting with less constraints We only use two slices of the BRDF for fitting Inspired by previous work: It s automated (no manual tweaking) [Romeiro et al. 2008] [Pacanowski et al. 2012] Any non-linear optimization would work We used Levenberg-Marquardt [Lourakis 2004]

Two-step approach: 1. Fit the SGD parameters (α,p) and ρ d to the measured reflectance for varying θ h with θ d = 0 2. Fit the Fresnel parameters (F 0,F 1 ) and ρ s to the measured reflectance for varying θ d with θ h = 0

Cook-Torrance BRDF Cook-Torrance BRDF Beckmann Distribution Ground truth SGD (ours) Lab error Lab error

Cook-Torrance BRDF Cook-Torrance BRDF Beckmann Distribution Ground truth SGD (ours) Lab error Lab error

Cook-Torrance BRDF Cook-Torrance BRDF Beckmann Distribution Ground truth SGD (ours) Lab error Lab error

Lafortune BRDF Cook-Torrance BRDF With Beckmann Cook-Torrance BRDF With TR / GGX Cook-Torrance BRDF With SGD (ours) Ground truth Lafortune Lab error Cook-Torrance BRDF With Beckmann Lab error Cook-Torrance BRDF With TR / GGX Lab error Cook-Torrance BRDF With SGD (ours) Lab error

Lafortune BRDF Cook-Torrance BRDF With Beckmann Cook-Torrance BRDF With TR / GGX Cook-Torrance BRDF With SGD (ours) Ground truth Lafortune Lab error Cook-Torrance BRDF With Beckmann Lab error Cook-Torrance BRDF With TR / GGX Lab error Cook-Torrance BRDF With SGD (ours) Lab error

Nickel

specular-violet-phenolic

Fitting cost: Using only two slices of the BRDF made fitting extremely fast (2.5 min on average) 65% of the materials were fitted in less than a minute. Rendering cost: 2x more expensive than Beckmann because each RGB channel is evaluated separately

3 Multi-lobe materials out of 100 : two-layer-silver two-layer-gold alum-bronze two-layer-silver

Null Fresnel at normal incidence Did not pick the right shape for specular lobe white-paint

The shifted gamma micro-facet probability distribution for Cook-Torrance BRDF non-zero slope at θ h = 0 rapid decrease at the peak slow decrease at the tail approximated the measured distribution very well A generalized Fresnel term approximation approximates the measured Fresnel very well A fitting algorithm fitted each channel separately used two slices of the BRDF only kept the calculation tractable and stable

Apply the same principle to material acquisition Possible physical interpretation for our distribution

Mahdi M. Bagher / Cyril Soler / Nicolas Holzschuch Maverick, INRIA Grenoble-Rhône-Alpes and LJK (University of Grenoble and CNRS) Beckmann Lab Error Beckmann distribution Ground truth SGD distribution (ours) SGD Lab error (ours) Beckmann Lab Error Beckmann distribution Ground truth SGD distribution (ours) SGD Lab error (ours)