Microfacet Model and Material Appearancesungeui/GCG/Student_Presentations/... · SIGGRAPH 2016 [2]...

$: Microfacet Model and Material Appearancesungeui/GCG/Student_Presentations/... · SIGGRAPH 2016 [2] A Two-Scale Microfacet Reflectance Model Combining Reflection and Diffraction Nicolas$
Microfacet Model and

Material Appearance

19.05.14

Student Presentation

20193163 Hakyeong Kim

Review

• Light Transport for Participating Media (Joowon Lim)

– Point based light global illumination

– Higher-Dimensional photon samples for volumetric light transport

2

Microfacet theory

Surface light transport framework

• Assumption: Surface is made up of tiny flat microfacets

• Surface normal 𝝎𝒈 is average of microfacet normals 𝝎𝒎

3

𝝎𝒈𝝎𝒎

Microfacet theory




• Described by normal distribution function NDF 𝑫(𝝎𝒎)

4

𝜔𝑚

𝑫(𝝎𝒎)

Microfacet theory




• Described by normal distribution function NDF 𝑫(𝝎𝒎)

5

Papers

[1] Multiple Scattering Microfacet BSDFs

with the Smith ModelEric Heitz, Johannes Hanika, Eugene d’Eon

SIGGRAPH 2016

[2] A Two-Scale Microfacet Reflectance Model

Combining Reflection and DiffractionNicolas Holzschuch, Romain Pacanowski, SIGGRAPH 2017

6

Papers

[1] Multiple Scattering Microfacet BSDFs

with the Smith ModelEric Heitz, Johannes Hanika, Eugene d’Eon

SIGGRAPH 2016



7

Microfacet model

• The Smith Model

• Cook-Torrance Model

Volumetric Scattering

Microflake theory+

Single-Scattering BSDF/

Unphysical Multiple-Scattering

Multiple-Scattering BSDF

=

Papers



8

Microfacet model

• The Smith Model


Diffraction model

Harvey-Shack Theory+

New Reflectance model

that both considers

Reflection and Diffraction=

MULTIPLE SCATTERING MICROFACET BSDFS

WITH THE SMITH MODELERIC HEITZ, JOHANNES HANIKA, EUGENE D’EON

SIGGRAPH 2016

9

Overview

1. Background

• Smith Model

• Microflake Theory

2. Model

• Define medium

• Track intersection (Extinction coefficient & free-path distribution)

• Track light scatter (Phase function)

• Simulate random walk

• Define multiple-scattering BSDF (Expectation of random walk)

3. Evaluation

10

Smith Model

Statistical model of random microsurface described by

Distributions of Heights and Distributions of Normals

Main Assumption : 𝑃1 (ℎ) and 𝐷(𝜔𝑚) is independent

⟹ Final reflectance is independent of height distribution

𝑷𝟏 (𝒉) : Uniform, Gaussain

𝑫(𝝎𝒎) : Anisotropic Beckmann distribution, GGX distribution

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1

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𝜔𝑚 = 𝑥𝑚, 𝑦𝑚 , 𝑧𝑚

ℎ

Smith Model

Classic Single-Scattering BSDF(Bidirectional Scattering Distribution Function)

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3

2

1

( , , )

( , )( , ) ( , , ) , ( )i m o

ii m

G

i o m i m o o m m mGf f D d

Smith Model


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2

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3

2

1

( , , )

( , )( , ) ( , , ) , ( )i m o

ii m

G


Micro-BRDF

𝒇𝒎 of each materials :

• Rough dielectric

• Rough conductor 𝑓𝑟𝑑𝑖𝑒𝑙 + 0

• Rough diffuse𝑎

𝜋𝜔𝑜, 𝜔𝑚

BRDF(Reflection) BTDF(Transmission)

Smith Model


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3

2

1

( , , )

( , )( , ) ( , , ) , ( )i m o

ii m

G


Masking-shadowing function

Visible Normal Distribution

Masking function

Visibility to viewer

Shadowing function

Visibility to light

Multiple Scattering

Only allows single scattering

Masking-shadowing function Visible Normal Distribution

1 ( ) , ( )( )

cosi

dist

i i m m

m

i

G DD

1cos ( , ) ,i i m i m m mG D d

Smith-like masking function Microflake theory

Microflake theory

[Jakob et al. 2010]

• Framework that describes volumetric scattering

• Use oriented non-spherical particals defined by distribution of normals

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Microflake theory

Light Transport in Volume : Anisotropic Radiative Transfer Equation

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( ) ( ) ( ) ( ) ( ) ( ) ( )i i t i i s i p i o o o iL L f L d Q

Directional derivative of radiance

Microflake theory


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( ) ( )

( ) ( )

: volume density

: direction independent albedo

: microflake projected area

( ) , ( )

t i i

s i i

i i m m mD d

Attenuation

coefficientScattering

coefficient

Microflake theory


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Phase Function

1

, ,( )

p i o

m i o i m m m

i

f

p D d

Microflake theory


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Phase Function

1

, ,( )

p i o

m i o i m m m

i

f

p D d

“Smith-like” masking function


Without shadowing function Multiple Scattering

Recall Smith model

Multiple Scattering BSDF Model

1) Build medium

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1) Build medium

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3

1

1

1|Smith

h h P hh P h h h

C h

1

1

SmithP h

hC h

( ) , ( )microflake

r r m m mD d

( ) , ( ) ( ) cosSmith

r r m m m r rD d

( ) ( )microflake microflake microflake

t r r ( ) ( )Smith Smith Smith

t r r

Volume density

Projected area

Extinction coefficient


1) Build medium

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Multiple Scattering BSDF

2) Track intersection

• Microsurface intersection Probability

• Free-Path Distribution

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𝜏′ 𝜏′ + 𝑑𝜏′

1

0

( ) ( )1 1

1 1

1

, ,

exp , cot

( ) ( )

( cot ) ( )

r r

dist

r r

Smith

t r r r

r r r

G h

dh d

C h C h

C h C h

Probability that there is no intersection in [0, 𝜏]

1

, 1 1

0 if 0

1 , , if 0

1 if r r

dist

h r r rC h G h


2) Track intersection

• Free Path Sampling1

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3) Track light scatter

• Phase Function

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, , , ,ii o m m i o i m m mp f D d

, ( ) , ( )( )

( ), ( )i

i m m i m m

m Smith

ii m m m

D DD

D d


4) Simulate random walk

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3

Track intersection

Track light scatter


5) Define multiple scattering BSDF

: Expectation of random walk

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Random walk

Sequence of N heights, directions and energy throughput 𝜔1, ℎ1, 𝑒1 , … , 𝜔𝑁, ℎ𝑁, 𝑒𝑁 ,

Distribution

• Contribution of 𝑟𝑡ℎ bounce in direction 𝜔𝑂

• Total scattered energy by random walk

• Mutiple Scattering BRDF

1

( ) , ( , )dist

r o r r o o rE e p G h

1,...,

1

( ) ( )N

N o r o

r

E E

1

1,...,

1

( , ) cos ( )

, ( , )

i o o N o

Ndist

r r o o r

r

f E

e p G h


Result

- Practical rendering

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A TWO-SCALE MICROFACET REFLECTANCE MODEL

COMBINING REFLECTION AND DIFFRACTIONNICOLAS HOLZSCHUCH, ROMAIN PACANOWSKI

SIGGRAPH 2017

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Papers



30

Microfacet model

• The Smith Model


Diffraction model

Harvey-Shack Theory+

New Reflectance model

that both considers

Reflection and Diffraction=

Overview

1. Background


• Modified Harvey-Shack Theory

2. Model

• Two-scale BRDF model

• NDF

3. Evaluation

31

Cook-Torrance Model

Main Assumption:

1. Microfacet is larger than light wavelength Geometric optic applies

2. Each microfacet act as specular mirror

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1

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3

𝜔𝑚 𝑜

𝑖

( ( ), )( , ) ( , )

cosF

o

refl i oi o F i o

( , )F i o

Cook-Torrance Model

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𝑫(𝝎𝒎)

( ( ), )( , ) ( , )

cosF

o

refl i oi o F i o

Main Assumption:



( , )4cos cos

Cook Torrance i o

i o

DFG

𝜔𝑚 𝑜

𝑖

( , )F i o

1

•

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2

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3

Cook-Torrance Model

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𝑫(𝝎𝒎)

( ( ), )( , ) ( , )

cosF

o

refl i oi o F i o

Main Assumption:



( , )4cos cos

Cook Torrance i o

i o

DFG

𝜔𝑚 𝑜

𝑖

( , )F i o𝑭(𝜼, 𝜽𝒅) : Fresnel term• Defines material color

• Only wavelength determinant

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Harvey-Shack theory

• Based on optical path length (OPD) difference

• Phase difference:

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(cos cos ) ( , )i oOPD h x y

(2 / )(cos cos ) ( , )i o h x y 1

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3

Harvey-Shack theory



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(2 / )(cos cos ) ( , )i o h x y

( ( ), )( , ) ( , ) (1 ) ( , ) ( )

cos

i odiff i o i o i o HS

o

reflAF A Q S f

Specular lobe Scattered lobe

Average

1

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2

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3

Harvey-Shack theory



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(2 / )(cos cos ) ( , )i o h x y

( ( ), )( , ) ( , ) (1 ) ( , ) ( )

cos

i odiff i o i o i o HS

o

reflAF A Q S f

AverageMirror reflection direction

2

02 cos cossi

A e

𝝈𝒔: Surface roughness

= Variance of height distribution

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Two-Scale BRDF model

• Surface detail

– Micro-geometry : larger than light wavelength

– Nano-geometry : similar to light wavelength

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• Generic BRDF in original microfacet framework

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( , ) ( , , ) , ( , ) ( )i m o mi o s i m o o m i o m m

i n o n

f G D d

1

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2

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3



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( , ) ( , ) ( ( ), )F i o F i o refl i o

Recall) Cook- Torrance model if microfacet reflectance is Dirac,


i n o n

f G D d

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2

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3



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( , , ) ( , ) ( ( ), ) (1 ) ( , ) ( )s i o m i o i o i o HSf AF refl A Q S f

Diffraction model


i n o n

f G D d

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2

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3



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Standard Cook-Torrance Lobe

Diffraction model

Cook Torrance Diffraction Lobe

( , ) ( )i o spec d Cook Torrance Cook TorranceDiffractionA


i n o n

f G D d

1

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2

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3



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i n o n

f G D d


Diffraction model

4cos cosi o

DFG

2

2 reli m o m

e

( , ) ( )i o spec d Cook Torrance Cook TorranceDiffractionA

Approximation

Spherical convolution between

𝑫 and 𝑺𝑯𝑺

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i n o n

f G D d

• NDF 𝑫(𝝎𝒎): Exponential power distribution

• Shadow function 𝑮 𝜽𝒉 : 𝟏

𝟏+𝚲(𝜷+𝒕𝒂𝒏𝜽), computed by Smith’s method

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• Result

– Validation with measured materials(MERL database)

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• Result

– Validation with measured materials(Good performance)

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• Result

– Validation with measured materials (materials with larger RMSE)

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THANK YOU

48

Quiz

1. What is responsible for material appearance both in classical

microfacet and microflake theory?

① Height distribution function

② Normal distribution function

③ Extinction coefficient

④ Phase function

2. Which one is not microfacet model?

① Smith Model

② Cook-Torrance model

③ Harvey-Shack model

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ADDITIONAL SLIDES

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Microfacet Theory

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The Smith Model Single Scattering BSDF

Distribution of heights

Distribution of normals

Smith masking function


Distribution of visible normals

• Probability that 𝜔𝑛 is in 𝜔ℎ - X

•

• Projected surface area of the microfacets

above area is equal to dA

𝜔𝑛

𝑑𝜔ℎ

1( ) hD h n h d

hdA n h dA

h hdA D h d A

1

( 1) ( )h hn h dA D h n h dA

Microfacet Theory

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1 1 1( , , ) ( , ) ( , )local dist

i m i m iG h G G h

𝜔𝑛

𝜔𝑖

Visibility of a point on microsurface

Microfacet Theory

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1 1 1( , , ) ( , ) ( , )local dist

i m i m iG h G G h

𝜔𝑛

𝜔𝑖

1 ( , ) ( )local

i m i mG

Non-backfacing


Microfacet Theory

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1 1 1( , , ) ( , ) ( , )local dist

i m i m iG h G G h

𝜔𝑛

𝜔𝑖 ( )1

1 ( , ) ( ) idist

iG h C h

Probability that ray does not

intersect microsurface

Smith lambda function

CDF of heights


Microfacet Theory

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1

1 1

1( ) ( , ) ( )

1 ( )

dist dist

i i

i

G G h P h dh

Masking function averaged over all heights

1 1 1( , ) ( , ) ( )local dist

i m i m iG G G

Microfacet Theory

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22 1 1( , , ) ( , ) ( , ) ( , )local local dist

i m o i m o i oG G G h G

Visible to both ingoing and

outgoing direction

Height-correlated distant

masking-shadowing function

1

2 1 1( , ) ( , ) ( , ) ( )

1

1 ( ) ( )

(1 ( ),1 ( ))

dist dist dist

i o i o

i o

i o

G G h G h P h dh

B

Microfacet Theory

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DVNF of Smith model

1 ( ) , ( ) , ( )( )

cos cos (1 ( ))i

dist

i i m m i m m

m

i i i

G D DD


Normalization [1]

Visible microsurface

= Projected area of geometric surface

[1] Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs, Eric Heitz, 2014

Microfacet Theory

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Distribution of heights 𝑃1(ℎ)

Distribution of normal 𝐷(𝜔𝑚)

Smith masking function 𝐺1(𝜔𝑖 , 𝜔𝑜)

Masking-shadowing function 𝐺2(𝜔𝑖 , 𝜔𝑜, 𝜔𝑚)

Distribution of visible normals 𝐷𝜔𝑖(𝜔𝑚)

2

1

( , , )

( , )

( , )

( , , ) , ( )i m o

ii m

i o

G

m i m o o m m mG

f

f D d

Single-Scattering BSDF of Generic Rough Materials

Given visible for 𝜔𝑖, visible for 𝜔𝑜

Micro-BRDF

Derivable: Rough dielectric, rough conductor, rough diffuse

Microfacet Model and Material Appearancesungeui/GCG/Student_Presentations/... · SIGGRAPH 2016 [2]...

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