“Physical reproduction of materials with specified subsurface scattering” by Hasan, Fuchs, Matusik, Pfister and Rusinkiewicz

  • ©Milos Hasan, Martin Fuchs, Wojciech Matusik, Hanspeter Pfister, and Szymon Rusinkiewicz




    Physical reproduction of materials with specified subsurface scattering



    We investigate a complete pipeline for measuring, modeling, and fabricating objects with specified subsurface scattering behaviors. The process starts with measuring the scattering properties of a given set of base materials, determining their radial reflection and transmission profiles. We describe a mathematical model that predicts the profiles of different stackings of base materials, at arbitrary thicknesses. In an inverse process, we can then specify a desired reflection profile and compute a layered composite material that best approximates it. Our algorithm efficiently searches the space of possible combinations of base materials, pruning unsatisfactory states imposed by physical constraints. We validate our process by producing both homogeneous and heterogeneous composites fabricated using a multi-material 3D printer. We demonstrate reproductions that have scattering properties approximating complex materials.


    1. Cortat, F. 2004. The Kubelka-Munk theory, applications and modifications. Presentation for the graduate course on Optical properties of Paper, Linkoping University.Google Scholar
    2. 2010. Discrete Hankel Transforms. http://www.gnu.org/software/gsl/manual/html_node/Discrete-Hankel-Transforms.html.Google Scholar
    3. Dong, Y., Wang, J., Pellacini, F., Tong, X., and Guo, B. 2010. Fabricating Spatially-Varying Subsurface Scattering. ACM Transactions on Graphics. Google ScholarDigital Library
    4. Donner, C., and Jensen, H. W. 2005. Light Diffusion in Multi-Layered Translucent Materials. ACM Transactions on Graphics, Vol. 24, No. 3, 1032–1039. Google ScholarDigital Library
    5. Donner, C., Weyrich, T., d’Eon, E., Ramamoorthi, R., and Rusinkiewicz, S. 2008. A Layered, Heterogeneous Reflectance Model for Acquiring and Rendering Human Skin. ACM Transactions on Graphics, Vol. 27, No. 5 (Dec.). Google ScholarDigital Library
    6. Donner, C., Lawrence, J., Ramamoorthi, R., Hachisuka, T., Jensen, H. W., and Nayar, S. 2009. An Empirical BSSRDF Model. ACM Transactions on Graphics. Google ScholarDigital Library
    7. Fuchs, M., Raskar, R., Seidel, H.-P., and Lensch, H. P. A. 2008. Towards passive 6D reflectance field displays. In ACM Transactions on Graphics, ACM, New York, NY, USA, 1–8. Google ScholarDigital Library
    8. Ghosh, A., Hawkins, T., Peers, P., Frederiksen, S., and Debevec, P. 2008. Practical Modeling and Acquisition of Layered Facial Reflectance. ACM Transactions on Graphics, Vol. 27. Google ScholarDigital Library
    9. Goesele, M., Lensch, H. P. A., Lang, J., Fuchs, C., and Peter Siedel, H. 2004. DISCO: Acquisition of translucent objects. ACM Transactions on Graphics, Vol. 23, No. 3, 835–844. Google ScholarDigital Library
    10. Haase, C. S., and Meyer, G. W. 1992. Modeling pigmented materials for realistic image synthesis. ACM Transactions on Graphics, Vol. 11, No. 4, 305–335. Google ScholarDigital Library
    11. Hanrahan, P., and Krueger, W. 1993. Reflection from Layered Surfaces due to Subsurface Scattering. In Computer Graphics (Proceedings of SIGGRAPH 93), 164–174. Google ScholarDigital Library
    12. Hawkins, T., Einarsson, P., and Debevec, P. 2005. Acquisition of time-varying participating media. ACM Transactions on Graphics, Vol. 24, No. 3, 812–815. Google ScholarDigital Library
    13. Jensen, H. W., Marschner, S. R., Levoy, M., and Hanrahan, P. 2001. A practical model for subsurface light transport. In Proceedings of ACM SIGGRAPH 2001, 511–518. Google ScholarDigital Library
    14. Kubelka, P., and Munk, F. 1931. Ein Beitrag zur Optik der Farbanstriche. Zeitschrift für technische Physik, Vol. 12, 593–601. English translation by Steve Westin.Google Scholar
    15. Lorensen, W. E., and Cline, H. E. 1987. Marching cubes: A high resolution 3D surface construction algorithm. Computer Graphics (Proceedings of SIGGRAPH 87), Vol. 21, No. 4, 163–169. Google ScholarDigital Library
    16. Matusik, W., Ajdin, B., Gu, J., Lawrence, J., Lensch, H. P., Pellacini, F., and Rusinkiewicz, S. 2009. Printing Spatially-Varying Reflectance. ACM Transactions on Graphics, Vol. 28, No. 5. Google ScholarDigital Library
    17. Narasimhan, S. G., Gupta, M., Donner, C., Ramamoorthi, R., Nayar, S. K., and Jensen, H. W. 2006. Acquiring scattering properties of participating media by dilution. ACM Transactions on Graphics, Vol. 25, No. 3, 1003–1012. Google ScholarDigital Library
    18. Nicodemus, F. E., Richmond, J. C., Hsia, J. J., Ginsberg, I. W., and Limperis, T. 1977. Geometrical Considerations and Nomenclature for Reflectance. National Bureau of Standards.Google Scholar
    19. Peers, P., vom Berge, K., Matusik, W., Ramamoorthi, R., Lawrence, J., Rusinkiewicz, S., and Dutré, P. 2006. A compact factored representation of heterogeneous subsurface scattering. ACM Transactions on Graphics, Vol. 25, No. 3, 746–753. Google ScholarDigital Library
    20. Peng, J., Kristjansson, D., and Zorin, D. 2004. Interactive modeling of topologically complex geometric detail. ACM Transactions on Graphics, Vol. 23, No. 3. Google ScholarDigital Library
    21. Pharr, M., and Hanrahan, P. 2000. Monte Carlo evaluation of non-linear scattering equations for subsurface reflection. In Proceedings of ACM SIGGRAPH 2000, 75–84. Google ScholarDigital Library
    22. Saito, T., and Toriwaki, J. I. 1994. New algorithms for Euclidean distance transformations of an n-dimensional digitized picture with applications. Pattern Recognition, Vol. 27, 1551–1565.Google ScholarCross Ref
    23. Song, Y., Tong, X., Pellacini, F., and Peers, P. 2009. SubEdit: A Representation for Editing Measured Heterogeneous Subsurface Scattering. ACM Transactions on Graphics, Vol. 28, No. 3. Google ScholarDigital Library
    24. Stam, J. 1995. Multiple scattering as a diffusion process. In Rendering Techniques, 41–50.Google Scholar
    25. Stam, J. 2001. An Illumination Model for a Skin Layer Bounded by Rough Surfaces. In Rendering Techniques, 39–52. Google ScholarDigital Library
    26. Tariq, S., Gardner, A., Llamas, I., Jones, A., Debevec, P., and Turk, G. 2006. Efficient Estimation of Spatially Varying Subsurface Scattering Parameters. In Vision, Modeling, and Visualization.Google Scholar
    27. Tong, X., Wang, J., Lin, S., Guo, B., and Yeung Shum, H. 2005. Modeling and Rendering of Quasi-Homogeneous Materials. ACM Transactions on Graphics, Vol. 24, No. 3, 1054–1061. Google ScholarDigital Library
    28. 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 Transactions on Graphics, Vol. 27, No. 1, 1–18. Google ScholarDigital Library
    29. Weisstein, E. W., 2010. Hankel Transform. From Math-World – A Wolfram Web Resource. http://mathworld.wolfram.com/HankelTransform.html.Google Scholar
    30. Weyrich, T., Matusik, W., Pfister, H., Bickel, B., Donner, C., Tu, C., McAndless, J., Lee, J., Ngan, A., Jensen, H. W., and Gross, M. 2006. Analysis of Human Faces using a Measurement-Based Skin Reflectance Model. ACM Transactions on Graphics, Vol. 25, 1013–1024. Google ScholarDigital Library
    31. Weyrich, T., Peers, P., Matusik, W., and Rusinkiewicz, S. 2009. Fabricating Microgeometry for Custom Surface Reflectance. ACM Transactions on Graphics, Vol. 28, No. 3. Google ScholarDigital Library

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