Modeling Anisotropic Surface Reflectance Modeling Anisotropic Surface Reflectance with Example-Based Microfacet Synthesiswith Example-Based Microfacet SynthesisModeling Anisotropic Surface Reflectance Modeling Anisotropic Surface Reflectance with Example-Based Microfacet Synthesiswith Example-Based Microfacet Synthesis

Jiaping WangJiaping Wang11, Shuang Zhao, Shuang Zhao22, Xin Tong, Xin Tong11

John SnyderJohn Snyder33, Baining Guo, Baining Guo11

Microsoft Research AsiaMicrosoft Research Asia11

Shanghai Jiao Tong UniversityShanghai Jiao Tong University22

Microsoft ResearchMicrosoft Research33

Surface ReflectanceSurface ReflectanceSurface ReflectanceSurface Reflectance

satin metal wood

Anisotropic Surface ReflectanceAnisotropic Surface ReflectanceAnisotropic Surface ReflectanceAnisotropic Surface Reflectance

anisotropicisotropic

Our GoalOur GoalOur GoalOur Goal

modeling spatially-varying anisotropic reflectance

Surface Reflectance in CGSurface Reflectance in CGSurface Reflectance in CGSurface Reflectance in CG

• 4D BRDF ρ(o,i)

– Bidirectional Reflectance Distribution Function

– how much light reflected wrt in/out directions

oi

Surface Reflectance in CGSurface Reflectance in CGSurface Reflectance in CGSurface Reflectance in CG

• 4D BRDF ρ(o,i)

– Bidirectional Reflectance Distribution Function

– how much light reflected wrt in/out directions

• 6D Spatially-Varying BRDF: SVBRDF ρ(x,o,i)

– BRDF at each surface point x

Related Work IRelated Work IRelated Work IRelated Work I

• parametric BRDF models

– compact representation

– easy acquisition and fitting

– lack realistic detailsgroundtruth

parametric model [Ward 92]

Related Work IIRelated Work IIRelated Work IIRelated Work II

• tabulated SVBRDF

– realistic

– large data set

– difficult to capture

• lengthy process

• expensive hardware

• image registration

light dome [Gu et al 06]

Related Work IIRelated Work IIRelated Work IIRelated Work II

• tabulated SVBRDF

– realistic

– large data set

– difficult to capture

• lengthy process

• expensive hardware

• image registration

light dome [Gu et al 06]

Microfacet BRDF ModelMicrofacet BRDF ModelMicrofacet BRDF ModelMicrofacet BRDF Model

[Cook & Torrance 82]

• surface modeled by tiny mirror facets

Microfacet BRDF ModelMicrofacet BRDF ModelMicrofacet BRDF ModelMicrofacet BRDF Model

• surface modeled by tiny mirror facets

shadow termshadow term fresnel termfresnel termnormal distributionnormal distribution

[Cook & Torrance 82]

Microfacet BRDF ModelMicrofacet BRDF ModelMicrofacet BRDF ModelMicrofacet BRDF Model

• based on Normal Distribution Function (NDF)

– NDF D is 2D function of the half-way vector h

– dominates surface appearance

Challenge: Partial DomainsChallenge: Partial DomainsChallenge: Partial DomainsChallenge: Partial Domains

• samples from a single viewing direction i

– cover only a sub-region h Ω of NDF

– How to obtain the full NDF?

partial regionpartial region

??

partial NDF complete NDFpartial NDF complete NDF

Solution: Exploit Spatial RedundancySolution: Exploit Spatial RedundancySolution: Exploit Spatial RedundancySolution: Exploit Spatial Redundancy

• find surface points with similar but differently similar but differently rotatedrotated NDFsNDFs

material sample material sample 　　　　 partial NDF at each surface pointpartial NDF at each surface point

Example-Based Microfacet SynthesisExample-Based Microfacet SynthesisExample-Based Microfacet SynthesisExample-Based Microfacet Synthesis

AlignAlign

++ ++ ==

partial NDFpartial NDFto completeto complete

completed NDFcompleted NDFrotated partial NDFsrotated partial NDFs

partial NDFs from partial NDFs from other surface pointsother surface points

ComparisonComparisonComparisonComparison

isotropic Ward modelisotropic Ward model anisotropic Ward modelanisotropic Ward model

ground truthground truth our modelour model

Overall PipelineOverall PipelineOverall PipelineOverall Pipeline

• BRDF Slice Capture

• Partial NDF Recovery

• Microfacet Synthesis

Overall PipelineOverall PipelineOverall PipelineOverall Pipeline

• BRDF Slice Capture

• Partial NDF Recovery

• Microfacet Synthesis

Device SetupDevice SetupDevice SetupDevice Setup

Camera-LED system, based on [Gardner et al 03]

•

Camera

Capturing ProcessCapturing ProcessCapturing ProcessCapturing Process

Overall PipelineOverall PipelineOverall PipelineOverall Pipeline

• BRDF Slice Capture

• Partial NDF Recovery

• Microfacet Synthesis

NDF RecoveryNDF RecoveryNDF RecoveryNDF Recovery

• invert the microfacet BRDF model

[Ashikhmin et al 00]

,

Unknown Unknown NDF Shadow Term

MeasuredBRDF

NDF Recovery (con’t)NDF Recovery (con’t)NDF Recovery (con’t)NDF Recovery (con’t)

• iterative approach [Ngan et al 05Ngan et al 05]

– solve for NDF, then shadow term

– works for complete 4D BRDF data

[Ashikhmin et al 00]

,1.

2.

[Ngan et al 05Ngan et al 05]

Partial NDF RecoveryPartial NDF RecoveryPartial NDF RecoveryPartial NDF Recovery

• biased result on incomplete BRDF data

ground truthground truth

NDFNDF shadow termshadow term

[Ngan et al. 05][Ngan et al. 05]

NDFNDF shadow termshadow term

Partial NDF Recovery (con’t)Partial NDF Recovery (con’t)Partial NDF Recovery (con’t)Partial NDF Recovery (con’t)

• minimize the bias

– isotropically constrain shadow term in each iteration

before constraintbefore constraint after constraintafter constraint

Recovered Partial NDFRecovered Partial NDFRecovered Partial NDFRecovered Partial NDF

ground truthground truth

[Ngan et al. 05][Ngan et al. 05]

our resultour result

Overall PipelineOverall PipelineOverall PipelineOverall Pipeline

• Capture BRDF slice

• Partial NDF Recovery

• Microfacet Synthesis

Microfacet SynthesisMicrofacet SynthesisMicrofacet SynthesisMicrofacet Synthesis

partial NDFpartial NDFto completeto complete

Merged partial NDFsMerged partial NDFs completed NDFcompleted NDF

Microfacet Synthesis (con’t)Microfacet Synthesis (con’t)Microfacet Synthesis (con’t)Microfacet Synthesis (con’t)

• straightforward implementation:

For N NDFs at each surface point

Match against (N-1) NDFs at other points

In M rotation angles for alignment

• number of rotations/comparisons:

N 2*M ≈ 5×1011 (N ≈ 640k, M ≈ 1k )

• a straightforward implementation:

For N NDFs in each surface point

Match with (N -1) NDFs in other location

In M rotation angles for alignment

• times of spherical function rotation and comparison

N 2* M ≈ 5×1011 ( N ≈ 640k )

Synthesis AccelerationSynthesis AccelerationSynthesis AccelerationSynthesis Acceleration

• Clustering [Matusik et al 03]

–complete representative NDFs only (1% of full set)

N'2* M ≈ 5×107 ( N' ≈ 6.4k )

• a straightforward implementation:

For N NDFs in each surface point

Match with (N -1) NDFs in other location

In M rotation angles for alignment

• times of spherical function rotation and comparison

N 2* M ≈ 5×1011 ( N ≈ 640k )

Synthesis AccelerationSynthesis AccelerationSynthesis AccelerationSynthesis Acceleration

• Clustering [Matusik et al 03]

–complete representative NDFs only (1% of full set)

• Search Pruning

–precompute all rotated candidates

–prune via hierarchical searching

N'2* M ≈ 5×107 ( N' ≈ 6.4k )N'* log(N'* M) ≈ 5×105

Performance Summary Performance Summary Performance Summary Performance Summary

• 5-10 hours for BRDF slice acquisition in HDR

– 1 Hour for acquisition in LDR

• 2-4 hours for image processing

• 2-3 hours for partial NDF recovery

• 2-4 hours for accelerated microfacet synthesis

On a PC with Intel CoreTM2 Quad 2.13GHz CPU and 4GB memory

Model Validation Model Validation Model Validation Model Validation

• full SVBRDF dataset [Lawrence et al. 06]

– data from one view for modeling

– data from other views for validation

Validation ResultValidation ResultValidation ResultValidation Result

LimitationsLimitationsLimitationsLimitations

• visual modeling, not physical accuracy

• single-bounce microfacet model

– retro-reflection not handled

• spatial redundancy of rotated NDFs

– easy fix by rotating the sample

Rendering Result: SatinRendering Result: SatinRendering Result: SatinRendering Result: Satin

Rendering Result: WoodRendering Result: WoodRendering Result: WoodRendering Result: Wood

Rendering Result: Brushed MetalRendering Result: Brushed MetalRendering Result: Brushed MetalRendering Result: Brushed Metal

ConclusionsConclusionsConclusionsConclusions

• model surface reflectance via microfacet synthesis

– general and compact representation

– high resolution (spatial & angular), realistic result

– easier acquisition:

single-view capture

cheap device

shorter capturing time

Future WorkFuture WorkFuture WorkFuture Work

• performance optimization

– capturing and data processing

• extension to non-flat objects

• extension to multiple light bounce

AcknowledgementsAcknowledgementsAcknowledgementsAcknowledgements

• Le Ma for electronics of the LED array

• Qiang Dai for capturing device setup

• Steve Lin, Dong Xu for valuable discussions

• Paul Debevec for HDR imagery

• Anonymous reviewers for their helpful suggestions and comments

Thank you!Thank you!Thank you!Thank you!