A Photometric Approach for Estimating Normals and

TangentsMichael Holroyd

University of Virginia

Jason LawrenceUniversity of

Virginia

Greg HumphreysUniversity of

Virginia

Todd ZicklerHarvard University

. . .

Input: Images under varying point lighting

Output: Estimate of surface orientation

Normal Field Tangent Field

Related Work Lambertian photometric stereo

[Woodham 1980]

Discard specular highlight[Coleman and Jain 1982; Mallick et al. 2005]

[Klette et al. 1998]

Fit to low-dimensional parametric models[Georghiades 2003; Goldman et al. 2005]

Fit non-parametric curves (isotropic only)[Alldrin et al. 2008]

Locate mirror direction[Wang and Dana 2006; Chen et al. 2006; Ma et al. 2007; Francken et al. 2008; Nehab et al. 2008]

Image: Ma et al. 2007

Our Approach

Our Approach

Our Approach

Half-angle parameterization

2D slice of the BRDF (fixed view)

Our Approach

Half-angle parameterization

2D slice of the BRDF (fixed view)

Our Approach

Analysis of microfacet-based models:

Microfacet distributionAlmost all analytic and measured distributions exhibit these symmetries.

Analysis of microfacet-based models:

Images: Ngan et al. 2005

Analysis of microfacet-based models:

1

-90° 90°

Fresnel TermWell approximated by , and is asymmetric only at grazing angles.

Shadowing/MaskingSmooth and can be greatly simplified.

Analysis of microfacet-based models:

Shadowing/Masking functionfrom Wang et al. 2008

[Torrance1987; Ashikhmin et al. 2000;

Ngan et al. 2005; Wang et al. 2008]

Restrict light positions

Symmetry Distance

Symmetry Distance

viewview

normal

Restriction of light positions

view

normal

Restriction of light positions

Restriction of light positions

view

normal

Validation

Normal Error Tangent Error

BRDF from Ngan et al. 2005

Normal Error Tangent Error

BRDF from Ngan et al. 2005

Validation

Anisotropic Ward

PurpleSatin

YellowSatin

BrushedMetal

Measured

Ngan et al. 2005

Error Analysis (Torrance-Sparrow)N

orm

al E

rror

(D

egre

es) Our approach

Photometric stereoSpecularity stereo

Diffuse Shiny

Acquisition

Calibrated spherical gantry

1,500 1024x1024 HDR images

2.3 GB

45 minutes

1. Reconstruct a continuous 2D slice of the BRDF at each pixel using barycentric interpolation of the original data.

2. Estimate by optimizing

3. Estimate by holding fixed and optimizing

Algorithm

Implementation

Independent at each pixel

42x Dual 1.6 Ghz Opertons

10 minutes

(~7 hours for single machine)

Limitations

Interreflections

Limitations: Sampling density

1,512 743 380 172

Limitations

Non-symmetric microfacet distributions

Red velvet dataset from Ngan et al. [2005]

Conclusion

Main advantages: General, does not rely on parametric model First technique to directly recover tangent field

Acknowledgments Jiajun Zhu for help with data capture NSF CAREER award CCF-0747220 NSF grant CCF-0811493 NVIDIA Professor Partnership award Fellowship from the Sloan Foundation

Thank You