skip to main content
research-article

High-order similarity relations in radiative transfer

Published: 27 July 2014 Publication History

Abstract

Radiative transfer equations (RTEs) with different scattering parameters can lead to identical solution radiance fields. Similarity theory studies this effect by introducing a hierarchy of equivalence relations called "similarity relations". Unfortunately, given a set of scattering parameters, it remains unclear how to find altered ones satisfying these relations, significantly limiting the theory's practical value. This paper presents a complete exposition of similarity theory, which provides fundamental insights into the structure of the RTE's parameter space. To utilize the theory in its general high-order form, we introduce a new approach to solve for the altered parameters including the absorption and scattering coefficients as well as a fully tabulated phase function. We demonstrate the practical utility of our work using two applications: forward and inverse rendering of translucent media. Forward rendering is our main application, and we develop an algorithm exploiting similarity relations to offer "free" speedups for Monte Carlo rendering of optically dense and forward-scattering materials. For inverse rendering, we propose a proof-of-concept approach which warps the parameter space and greatly improves the efficiency of gradient descent algorithms. We believe similarity theory is important for simulating and acquiring volume-based appearance, and our approach has the potential to benefit a wide range of future applications in this area.

Supplementary Material

ZIP File (a104-zhao.zip)
Supplemental material.
MP4 File (a104-sidebyside.mp4)

References

[1]
Arbree, A., Walter, B., and Bala, K. 2011. Heterogeneous subsurface scattering using the finite element method. IEEE Trans. on Visualization and Computer Graphics 17, 7, 956--969.
[2]
Arfken, G. B., Weber, H.-J., and Ruby, L. 1985. Mathematical methods for physicists. Academic press New York.
[3]
Chandrasekhar, S. 1960. Radiative transfer. Courier Dover Publications.
[4]
Chatigny, S., Morin, M., Asselin, D., Painchaud, Y., and Beaudry, P. 1999. Hybrid Monte Carlo for photon transport through optically thick scattering media. Applied optics 38, 28, 6075--6086.
[5]
Curto, R. E., and Fialkow, L. A. 1991. Recursiveness, positivity, and truncated moment problems. Houston J. Math 17, 4, 603--635.
[6]
Dachsbacher, C., KÅŹivÃąnek, J., HaÅąan, M., Arbree, A., Walter, B., and NovÃąk, J. 2014. Scalable realistic rendering with many-light methods. Computer Graphics Forum 33, 1, 88--104.
[7]
Debevec, P. 1998. Rendering synthetic objects into real scenes: Bridging traditional and image-based graphics with global illumination and high dynamic range photography. In Proceedings of SIGGRAPH 1998, 189--198.
[8]
D'Eon, E., and Irving, G. 2011. A quantized-diffusion model for rendering translucent materials. ACM Trans. Graph. 30, 4, 56:1--56:14.
[9]
Dobashi, Y., Iwasaki, W., Ono, A., Yamamoto, T., Yue, Y., and Nishita, T. 2012. An inverse problem approach for automatically adjusting the parameters for rendering clouds using photographs. ACM Trans. Graph. 31, 6, 145:1--145:10.
[10]
Donner, C., and Jensen, H. W. 2007. Rendering translucent materials using photon diffusion. In Proceedings of the 18th Eurographics Conference on Rendering Techniques, EGSR'07, 243--251.
[11]
Frisvad, J. R., Christensen, N. J., and Jensen, H. W. 2007. Computing the scattering properties of participating media using Lorenz-Mie theory. ACM Trans. Graph. 26, 3, 60:1--60:10.
[12]
Gkioulekas, I., Xiao, B., Zhao, S., Adelson, E. H., Zickler, T., and Bala, K. 2013. Understanding the role of phase function in translucent appearance. ACM Trans. Graph. 32, 5, 147:1--147:19.
[13]
Gkioulekas, I., Zhao, S., Bala, K., Zickler, T., and Levin, A. 2013. Inverse volume rendering with material dictionaries. ACM Trans. Graph. 32, 6, 162:1--162:13.
[14]
Gurobi, 2013. Gurobi optimization libraries. www.gurobi.com.
[15]
Habel, R., Christensen, P. H., and Jarosz, W. 2013. Photon beam diffusion: A hybrid monte carlo method for subsurface scattering. In Computer Graphics Forum, vol. 32, 27--37.
[16]
Hachisuka, T., Jarosz, W., Bouchard, G., Christensen, P., Frisvad, J. R., Jakob, W., Jensen, H. W., Kaschalk, M., Knaus, C., Selle, A., and Spencer, B. 2012. State of the art in photon density estimation. In ACM SIGGRAPH 2012 Courses, SIGGRAPH '12, 6:1--6:469.
[17]
Hašan, M., Fuchs, M., Matusik, W., Pfister, H., and Rusinkiewicz, S. 2010. Physical reproduction of materials with specified subsurface scattering. ACM Trans. Graph. 29, 4, 61:1--61:10.
[18]
Henyey, L. G., and Greenstein, J. L. 1941. Diffuse radiation in the galaxy. The Astrophysical Journal 93, 70--83.
[19]
Ishimaru, A. 1978. Wave propagation and scattering in random media, vol. 2. Academic press New York.
[20]
Jakob, W., Arbree, A., Moon, J. T., Bala, K., and Marschner, S. 2010. A radiative transfer framework for rendering materials with anisotropic structure. ACM Trans. Graph. 29, 4, 53:1--53:13.
[21]
Jakob, W., 2010. Mitsuba renderer. www.mitsuba-renderer.org.
[22]
Jensen, H. W., Marschner, S. R., Levoy, M., and Hanrahan, P. 2001. A practical model for subsurface light transport. In Proceedings of SIGGRAPH 2001, 511--518.
[23]
Kajiya, J. T., and Von Herzen, B. P. 1984. Ray tracing volume densities. SIGGRAPH Comput. Graph. 18, 3, 165--174.
[24]
Kozlov, M. K., Tarasov, S. P., and Khachiyan, L. G. 1980. The polynomial solvability of convex quadratic programming. USSR Computational Mathematics and Mathematical Physics 20, 5, 223--228.
[25]
Lafortune, E. P., and Willems, Y. D. 1996. Rendering participating media with bidirectional path tracing. In Rendering TechniquesâĂŹ 96. Springer, 91--100.
[26]
Li, H., Pellacini, F., and Torrance, K. E. 2005. A hybrid Monte Carlo method for accurate and efficient subsurface scattering. In Proceedings of EGSR 2005, 283--290.
[27]
Mantiuk, R., Kim, K. J., Rempel, A. G., and Heidrich, W. 2011. HDR-VDP-2: A calibrated visual metric for visibility and quality predictions in all luminance conditions. ACM Trans. Graph. 30, 4, 40:1--40:14.
[28]
Papas, M., Regg, C., Jarosz, W., Bickel, B., Jackson, P., Matusik, W., Marschner, S., and Gross, M. 2013. Fabricating translucent materials using continuous pigment mixtures. ACM Trans. Graph. 32, 4, 146:1--146:12.
[29]
Pauly, M., Kollig, T., and Keller, A. 2000. Metropolis light transport for participating media. In Proceedings of EGWR 2000, 11--22.
[30]
Stam, J. 1995. Multiple scattering as a diffusion process. In Rendering TechniquesâĂŹ 95. 41--50.
[31]
Walter, B., Marschner, S. R., Li, H., and Torrance, K. E. 2007. Microfacet models for refraction through rough surfaces. In Proceedings of EGSR 2007, 195--206.
[32]
Wang, J., Zhao, S., Tong, X., Lin, S., Lin, Z., Dong, Y., Guo, B., and Shum, H.-Y. 2008. Modeling and rendering of heterogeneous translucent materials using the diffusion equation. ACM Trans. Graph. 27, 1, 9:1--9:18.
[33]
Wyman, D. R., Patterson, M. S., and Wilson, B. C. 1989. Similarity relations for anisotropic scattering in Monte Carlo simulations of deeply penetrating neutral particles. Journal of Computational Physics 81, 1, 137--150.
[34]
Wyman, D. R., Patterson, M. S., and Wilson, B. C. 1989. Similarity relations for the interaction parameters in radiation transport. Applied optics 28, 24, 5243--5249.

Cited By

View all
  • (2024)Spatial and Surface Correspondence Field for Interaction TransferACM Transactions on Graphics10.1145/365816943:4(1-12)Online publication date: 19-Jul-2024
  • (2024)Spin-Weighted Spherical Harmonics for Polarized Light TransportACM Transactions on Graphics10.1145/365813943:4(1-24)Online publication date: 19-Jul-2024
  • (2024)ZH3: Quadratic Zonal HarmonicsProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/36512947:1(1-15)Online publication date: 13-May-2024
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Graphics
ACM Transactions on Graphics  Volume 33, Issue 4
July 2014
1366 pages
ISSN:0730-0301
EISSN:1557-7368
DOI:10.1145/2601097
Issue’s Table of Contents
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: 27 July 2014
Published in TOG Volume 33, Issue 4

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. radiative transfer
  2. subsurface scattering

Qualifiers

  • Research-article

Funding Sources

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)20
  • Downloads (Last 6 weeks)2
Reflects downloads up to 17 Jan 2025

Other Metrics

Citations

Cited By

View all
  • (2024)Spatial and Surface Correspondence Field for Interaction TransferACM Transactions on Graphics10.1145/365816943:4(1-12)Online publication date: 19-Jul-2024
  • (2024)Spin-Weighted Spherical Harmonics for Polarized Light TransportACM Transactions on Graphics10.1145/365813943:4(1-24)Online publication date: 19-Jul-2024
  • (2024)ZH3: Quadratic Zonal HarmonicsProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/36512947:1(1-15)Online publication date: 13-May-2024
  • (2024)Navigating the Manifold of Translucent AppearanceComputer Graphics Forum10.1111/cgf.1503543:2Online publication date: 27-Apr-2024
  • (2024)Practical Measurements of Translucent Materials with Inter-Pixel Translucency Prior2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR52733.2024.01978(20932-20942)Online publication date: 16-Jun-2024
  • (2024)Efficient participating media rendering with differentiable regularizationComputational Visual Media10.1007/s41095-023-0372-210:5(937-948)Online publication date: 7-Oct-2024
  • (2023)Non-Newtonian ViRheometry via Similarity AnalysisACM Transactions on Graphics10.1145/361831042:6(1-16)Online publication date: 5-Dec-2023
  • (2023)State of the Art in Efficient Translucent Material Rendering with BSSRDFComputer Graphics Forum10.1111/cgf.1499843:1Online publication date: 22-Dec-2023
  • (2023)Accelerating Hair Rendering by Learning High‐Order Scattered RadianceComputer Graphics Forum10.1111/cgf.1489542:4Online publication date: 26-Jul-2023
  • (2022)Direct acquisition of volumetric scattering phase function using speckle correlationsSIGGRAPH Asia 2022 Conference Papers10.1145/3550469.3555379(1-9)Online publication date: 29-Nov-2022
  • Show More Cited By

View Options

Login options

Full Access

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media