research-article

Multiple-scattering microfacet BSDFs with the Smith model

Authors:

Johannes Hanika,

Carsten DachsbacherAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 35, Issue 4

Article No.: 58, Pages 1 - 14

https://doi.org/10.1145/2897824.2925943

Published: 11 July 2016 Publication History

Abstract

Modeling multiple scattering in microfacet theory is considered an important open problem because a non-negligible portion of the energy leaving rough surfaces is due to paths that bounce multiple times. In this paper we derive the missing multiple-scattering components of the popular family of BSDFs based on the Smith microsurface model. Our derivations are based solely on the original assumptions of the Smith model. We validate our BSDFs using raytracing simulations of explicit random Beckmann surfaces.

Our main insight is that the microfacet theory for surfaces with the Smith model can be derived as a special case of the microflake theory for volumes, with additional constraints to enforce the presence of a sharp interface, i.e. to transform the volume into a surface. We derive new free-path distributions and phase functions such that plane-parallel scattering from a microvolume with these distributions exactly produces the BSDF based on the Smith microsurface model, but with the addition of higher-order scattering.

With this new formulation, we derive multiple-scattering micro-facet BSDFs made of either diffuse, conductive, or dielectric material. Our resulting BSDFs are reciprocal, energy conserving, and support popular anisotropic parametric normal distribution functions such as Beckmann and GGX. While we do not provide closed-form expressions for the BSDFs, they are mathematically well-defined and can be evaluated at arbitrary precision. We show how to practically use them with Monte Carlo physically based rendering algorithms by providing analytic importance sampling and unbiased stochastic evaluation. Our implementation is analytic and does not use per-BSDF precomputed data, which makes our BSDFs usable with textured albedos, roughness, and anisotropy.

Supplementary Material

MP4 File (a58.mp4)

Download
206.80 MB

References

[1]

Beckmann, P., and Spizzichino, A. 1963. The scattering of electromagnetic waves from rough surfaces. International series of monographs on electromagnetic waves. Pergamon Press.

[2]

Bourlier, C., and Berginc, G. 2004. Multiple scattering in the high-frequency limit with second-order shadowing function from 2d anisotropic rough dielectric surfaces: I. theoretical study. Waves in Random Media 14, 3, 229--252.

[3]

Cook, R. L., and Torrance, K. E. 1982. A reflectance model for computer graphics. ACM Transactions on Graphics 1, 1 (Jan.), 7--24.

Digital Library

[4]

Furfaro, R., and Ganapol, B. 2007. Spectral Theory for Photon Transport in Dense Vegetation Media: Caseology for the Canopy Equation. Transport Theory and Statistical Physics 36, 1, 107--135.

[5]

Heitz, E., and d'Eon, E. 2014. Importance sampling microfacet-based BSDFs using the distribution of visible normals. In Proc. Eurographics Symposium on Rendering, 103--112.

Digital Library

[6]

Heitz, E., and Dupuy, J. 2015. Implementing a simple anisotropic rough diffuse material with stochastic evaluation. Research report.

[7]

Heitz, E., Dupuy, J., Crassin, C., and Dachsbacher, C. 2015. The SGGX microflake distribution. ACM Transactions on Graphics (Proc. SIGGRAPH) 34, 4, 48:1--48:11.

Digital Library

[8]

Heitz, E. 2014. Understanding the masking-shadowing function in microfacet-based BRDFs. Journal of Computer Graphics Techniques 3, 2, 32--91.

[9]

Heitz, E. 2015. Generating procedural Beckmann surfaces. Research report.

[10]

Hill, S., Mcauley, S., Burley, B., Chan, D., Fascione, L., Iwanicki, M., Hoffman, N., Jakob, W., Neubelt, D., Pesce, A., and Pettineo, M. 2015. Physically based shading in theory and practice. In ACM SIGGRAPH Courses.

Digital Library

[11]

Jakob, W., Arbree, A., Moon, J. T., Bala, K., and Marschner, S. 2010. A radiative transfer framework for rendering materials with anisotropic structure. ACM Transactions on Graphics (Proc. SIGGRAPH) 29, 4, 53:1--53:13.

Digital Library

[12]

Jakob, W., d'Eon, E., Jakob, O., and Marschner, S. 2014. A comprehensive framework for rendering layered materials. ACM Transactions on Graphics (Proc. SIGGRAPH) 33, 4, 118:1--118:14.

Digital Library

[13]

Kelemen, C., and Szirmay-Kalos, L. 2001. A microfacet based coupled specular-matte brdf model with importance sampling. In Eurographics short presentations.

[14]

Koenderink, J., Van Doorn, A., Dana, K., and Nayar, S. 1999. Bidirectional reflection distribution function of thoroughly pitted surfaces. International Journal of Computer Vision 31, 2, 129--144.

Digital Library

[15]

Kuščer, I., and Summerfield, G. C. 1969. Symmetries in scattering of slow neutrons. Phys. Rev. 188, 3 (Dec), 1445--1449.

[16]

Li, H., Pinel, N., and Bourlier, C. 2011. A monostatic illumination function with surface reflections from one-dimensional rough surfaces. Waves in Random and Complex Media 21, 1, 105--134.

[17]

Li, H., Pinel, N., and Bourlier, C. 2013. Polarized infrared reflectivity of one-dimensional gaussian sea surfaces with surface reflections. Appl. Opt. 52, 25 (Sep), 6100--6111.

[18]

Li, H., Pinel, N., and Bourlier, C. 2014. Polarized infrared reflectivity of 2d sea surfaces with two surface reflections. Remote Sensing of Environment 147, 0, 145--155.

[19]

Oren, M., and Nayar, S. K. 1995. Generalization of the lambertian model and implications for machine vision. International Journal of Computer Vision 14, 3, 227--251.

Digital Library

[20]

Pinel, N., Bourlier, C., and Saillard, J. 2005. Energy conservation of the scattering from one-dimensional random rough surfaces in the high-frequency limit. Opt. Lett. 30, 15 (Aug), 2007--2009.

[21]

Raab, M., Seibert, D., and Keller, A. 2008. Unbiased global illumination with participating media. In Monte Carlo and Quasi-Monte Carlo Methods 2006, 591--606.

[22]

Smith, B. 1967. Geometrical shadowing of a random rough surface. IEEE Transactions on Antennas and Propagation 15, 668--671.

[23]

Stam, J. 2001. An illumination model for a skin layer bounded by rough surfaces. In Rendering Techniques, 39--52.

Digital Library

[24]

Torrance, K. E., and Sparrow, E. M. 1967. Theory for off-specular reflection from roughened surfaces. Journal of the Optical Society of America (JOSA) 57, 9, 1105--1112.

[25]

Walter, B., Marschner, S. R., Li, H., and Torrance, K. E. 2007. Microfacet models for refraction through rough surfaces. In Proc. Eurographics Symposium on Rendering, 195--206.

Digital Library

[26]

Williams, M. M. R. 1978. Transport theory in anisotropic media. In Mathematical Proceedings of the Cambridge Philosophical Society, vol. 84, Cambridge Univ Press, 549--567.

Cited By

Pranovich AHannemose MJensen JTran DAanæs HGooran SNyström DFrisvad J(2024)Digitizing the Appearance of 3D Printing Materials Using a SpectrophotometerSensors10.3390/s2421702524:21(7025)Online publication date: 31-Oct-2024
https://doi.org/10.3390/s24217025
Simonot L(2024)Bouguer and Lambert’s pioneering contributions to goniophotometric reflectance measurements and models: retrospectiveJournal of the Optical Society of America A10.1364/JOSAA.53858642:1(1)Online publication date: 2-Dec-2024
https://doi.org/10.1364/JOSAA.538586
Xu KCavalier ABringier BRibardière MMeneveaux D(2024)Virtually measuring layered material appearanceJournal of the Optical Society of America A10.1364/JOSAA.51460441:5(959)Online publication date: 25-Apr-2024
https://doi.org/10.1364/JOSAA.514604
Show More Cited By

Index Terms

Multiple-scattering microfacet BSDFs with the Smith model
1. Computing methodologies
  1. Computer graphics
    1. Rendering
      1. Reflectance modeling

Recommendations

Fast-MSX: Fast Multiple Scattering Approximation
SA '23: SIGGRAPH Asia 2023 Conference Papers

Classical microfacet theory suffers from energy loss on materials with high roughness due to the single bounce assumption of most microfacet models. When roughness is high, there is a large chance of multiple scattering occurring among the microfacets ...
Additional progress towards the unification of microfacet and microflake theories
EGSR '16: Proceedings of the Eurographics Symposium on Rendering: Experimental Ideas & Implementations

We study the links between microfacet and microflake theories from the perspective of linear transport theory. In doing so, we gain additional insights, find several simplifications and touch upon important open questions as well as possible paths ...
Simulating multiple scattering in hair using a photon mapping approach

Simulating multiple scattering correctly is important for accurate rendering of hair. However, a volume of hair is a difficult scene to simulate because scattering from an individual fiber is very structured and forward directed, and because the ...

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 35, Issue 4

July 2016

1396 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2897824

Issue’s Table of Contents

Copyright © 2016 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 11 July 2016

Published in TOG Volume 35, Issue 4

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

73
Total Citations
View Citations
1,313
Total Downloads

Downloads (Last 12 months)119
Downloads (Last 6 weeks)11

Reflects downloads up to 28 Dec 2024

Other Metrics

View Author Metrics

Citations

Cited By

Pranovich AHannemose MJensen JTran DAanæs HGooran SNyström DFrisvad J(2024)Digitizing the Appearance of 3D Printing Materials Using a SpectrophotometerSensors10.3390/s2421702524:21(7025)Online publication date: 31-Oct-2024
https://doi.org/10.3390/s24217025
Simonot L(2024)Bouguer and Lambert’s pioneering contributions to goniophotometric reflectance measurements and models: retrospectiveJournal of the Optical Society of America A10.1364/JOSAA.53858642:1(1)Online publication date: 2-Dec-2024
https://doi.org/10.1364/JOSAA.538586
Xu KCavalier ABringier BRibardière MMeneveaux D(2024)Virtually measuring layered material appearanceJournal of the Optical Society of America A10.1364/JOSAA.51460441:5(959)Online publication date: 25-Apr-2024
https://doi.org/10.1364/JOSAA.514604
Tran DJensen MSantafé-Gabarda PKällberg SFerrero AHannemose MFrisvad J(2024)Digitizing translucent object appearance by validating computed optical propertiesApplied Optics10.1364/AO.52197463:16(4317)Online publication date: 22-May-2024
https://doi.org/10.1364/AO.521974
Lucas SRibardière MPacanowski RBarla P(2024)A Fully-correlated Anisotropic Micrograin BSDF ModelACM Transactions on Graphics10.1145/365822443:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658224
Tokuyoshi YEto K(2024)Bounded VNDF Sampling for the Smith-GGX BRDFProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/36512917:1(1-18)Online publication date: 13-May-2024
https://dl.acm.org/doi/10.1145/3651291
Li SLiu ZXiong XLiu Y(2024)Reflection modeling of rough metal surfaces using statistical theoryOptical Engineering10.1117/1.OE.63.11.11410263:11Online publication date: 1-Nov-2024
https://doi.org/10.1117/1.OE.63.11.114102
Fang QHachisuka T(2024)Lossless Basis Expansion for Gradient‐Domain RenderingComputer Graphics Forum10.1111/cgf.1515343:4Online publication date: 24-Jul-2024
https://doi.org/10.1111/cgf.15153
Lanza DPadrón‐Griffe JPranovich AMuñoz AFrisvad JJarabo A(2024)Practical Appearance Model for Foundation CosmeticsComputer Graphics Forum10.1111/cgf.1514843:4Online publication date: 24-Jul-2024
https://doi.org/10.1111/cgf.15148
Salesin KKnobelspiesse KChowdhary JZhai PJarosz W(2024)Unifying radiative transfer models in computer graphics and remote sensing, Part I: A surveyJournal of Quantitative Spectroscopy and Radiative Transfer10.1016/j.jqsrt.2023.108847314(108847)Online publication date: Mar-2024
https://doi.org/10.1016/j.jqsrt.2023.108847
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Issue’s Table of Contents