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Issue No.07 - July (2011 vol.17)

pp: 956-969

Adam Arbree , Autodesk® Corporation, San Francisco

Bruce Walter , Cornell University, Ithaca

Kavita Bala , Cornell University, Ithaca

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2010.117

ABSTRACT

Materials with visually important heterogeneous subsurface scattering, including marble, skin, leaves, and minerals are common in the real world. However, general, accurate, and efficient rendering of these materials is an open problem. In this paper, we describe a finite element (FE) solution of the heterogeneous diffusion equation (DE) that solves this problem. Our algorithm is the first to use the FE method to solve the difficult problem of heterogeneous subsurface rendering. To create our algorithm, we make two contributions. First, we correct previous work and derive an accurate and complete heterogeneous diffusion formulation with two key elements: the diffusive source boundary condition (DSBC)—an accurate model of the reduced intensity (RI) source—and its associated render query function. Second, we solve this formulation accurately and efficiently using the FE method. With these contributions, we can render subsurface scattering with a simple four step algorithm. To demonstrate that our algorithm is simultaneously general, accurate, and efficient, we test its performance on a series of difficult scenes. For a wide range of materials and geometry, it produces, in minutes, images that match path traced references, that required hours.

INDEX TERMS

Three-dimensional graphics and realism, color, shading, shadowing, texture, miscellaneous, subsurface scattering, partial differential equations, finite element methods.

CITATION

Adam Arbree, Bruce Walter, Kavita Bala, "Heterogeneous Subsurface Scattering Using the Finite Element Method",

*IEEE Transactions on Visualization & Computer Graphics*, vol.17, no. 7, pp. 956-969, July 2011, doi:10.1109/TVCG.2010.117REFERENCES

- [1] R.T. Ackroyd,
Finite Element Methods for Particle Transport: Applications to Reactor and Radiation Physics. Research Studies, 1997.- [2] A. Arbree, B. Walter, and K. Bala, "Single-Pass Scalable Subsurface Rendering with Lightcuts,"
Computer Graphics Forum, vol. 27, no. 2, pp. 507-516, Apr. 2008.- [3] A. Arbree, B. Walter, and K. Bala, "Diffusion Formulation for Heterogeneous Subsurface Scattering," technical report, Cornell Univ. Computing and Information Science, http://hdl.handle. net/181314199, 2009.
- [4] W. Bangerth and O. Kayser-Herold, "Data Structures and Requirements for $hp$ Finite Element Software," Technical Report ISC-07-04-MATH, Inst. for Scientific Computation, Texas A&M Univ., 2007.
- [5] N.A. Carr, J.D. Hall, and J.C. Hart, "GPU Algorithms for Radiosity and Subsurface Scattering,"
Proc. ACM SIGGRAPH/EUROGRAPHICS Conf. Graphics Hardware, pp. 51-59, 2003.- [6] C.-W. Chang, W.-C. Lin, T.-C. Ho, T.-S. Huang, and J.-H. Chuang, "Real-Time Translucent Rendering Using GPU-Based Texture Space Importance Sampling,"
Computer Graphics Forum, vol. 27, no. 2, pp. 517-526, Apr. 2008.- [7] Y. Chen, X. Tong, J. Wang, S. Lin, B. Guo, and H.-Y. Shum, "Shell Texture Functions,"
Proc. ACM SIGGRAPH '04, pp. 343-353, 2004.- [8] C. Dachsbacher and M. Stamminger, "Translucent Shadow Maps,"
Proc. 14th Eurographics Workshop Rendering Techniques, pp. 197-201, 2003.- [9] P. Debevec, "Image-Based Lighting,"
IEEE Computer Graphics and Application, vol. 22, no. 2, pp. 26-34, Mar./Apr. 2002.- [10] C. Donner and H.W. Jensen, "Light Diffusion in Multi-Layered Translucent Materials,"
Proc. ACM SIGGRAPH '05, pp. 1032-1039, 2005.- [11] C. Donner and H.W. Jensen, "Rendering Translucent Materials Using Photon Diffusion,"
Proc. Eurographics Symp. Rendering Techniques, pp. 243-251, 2007.- [12] C. Donner, T. Weyrich, E. d'Eon, R. Ramamoorthi, and S. Rusinkiewicz, "A Layered, Heterogeneous Reflectance Model for Acquiring and Rendering Human Skin,"
ACM Trans. Graphics, vol. 27, no. 5, pp. 1-12, 2008.- [13] J. Dorsey, A. Edelman, H.W. Jensen, J. Legakis, and H.K. Pedersen, "Modeling and Rendering of Weathered Stone,"
Proc. 26th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 225-234, 1999.- [14] L.C. Evans,
Partial Differential Equations. Am. Math. Soc., 1998.- [15] T.J. Farrell, M.S. Patterson, and B. Wilson, "A Diffusion Theory Model of Spatially Resolved, Steady-State Diffuse Reflectance for the Noninvasive Determination of Tissue Optical Properties In Vivo,"
Medical Physics, vol. 19, no. 4, pp. 879-888, 1992.- [16] R. Fattal, "Participating Media Illumination Using Light Propagation Maps,"
ACM Trans. Graphics, vol. 28, no. 1, pp. 1-11, 2009.- [17] A. Ghosh, T. Hawkins, P. Peers, S. Frederiksen, and P. Debevec, "Practical Modeling and Acquisition of Layered Facial Reflectance,"
ACM Trans. Graphics, vol. 27, no. 5, pp. 1-10, 2008.- [18] A.P. Gibson, J.C. Hebden, and S.R. Arridge, "Recent Advances in Diffuse Optical Imaging,"
Physics in Medicine and Biology, vol. 50, no. 4, pp. R1-R43, 2005.- [19] M. Goesele, H.P.A. Lensch, J. Lang, C. Fuchs, and H.-P. Seidel, "Disco: Acquisition of Translucent Objects,"
Proc. ACM SIGGRAPH '04, pp. 835-844, 2004.- [20] T. Haber, T. Mertens, P. Bekaert, and F.V. Reeth, "A Computational Approach to Simulate Subsurface Light Diffusion in Arbitrarily Shaped Objects,"
Proc. Graphics Interface Conf., pp. 79-86, 2005.- [21] P. Hanrahan and W. Krueger, "Reflection from Layered Surfaces Due to Subsurface Scattering,"
Proc. 20th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 165-174, 1993.- [22] X. Hao, T. Baby, and A. Varshney, "Interactive Subsurface Scattering for Translucent Meshes,"
Proc. 2003 Symp. Interactive 3D Graphics, pp. 75-82, 2003.- [23] X. Hao and A. Varshney, "Real-Time Rendering of Translucent Meshes,"
ACM Trans. Graphics, vol. 23, no. 2, pp. 120-142, 2004.- [24] A. Ishimaru,
Wave Propagation and Scattering in Random Media. Academic Press, 1978.- [25] H.W. Jensen and J. Buhler, "A Rapid Hierarchical Rendering Technique for Translucent Materials,"
Proc. 29th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 576-581, 2002.- [26] H.W. Jensen and P.H. Christensen, "Efficient Simulation of Light Transport in Scences with Participating Media Using Photon Maps,"
Proc. 25th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 311-320, 1998.- [27] H.W. Jensen, J. Legakis, and J. Dorsey, "Rendering of Wet Materials,"
Rendering Techniques, D. Lischinski and G. W. Larson, eds., pp. 273-282. Springer-Verlag, 1999.- [28] H.W. Jensen, S.R. Marschner, M. Levoy, and P. Hanrahan, "A Practical Model for Subsurface Light Transport,"
Proc. 28th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 511-518, 2001.- [29] B. Kirk, J.W. Peterson, R.H. Stogner, and G.F. Carey, "libMesh: A C++ Library for Parallel Adaptive Mesh Refinement/Coarsening Simulations,"
Eng. with Computers, vol. 22, nos. 3/4, pp. 237-254, 2006.- [30] J.J. Koenderink and A.J. van Doorn, "Shading in the Case of Translucent Objects,"
Proc. SPIE Human Vision and Electronic Imaging VI, pp. 312-320, 2001.- [31] V. Kolehmainen, "Novel Approaches to Image Reconstruction in Diffusion Tomography," PhD dissertation, Kuopio Univ., 2001.
- [32] H.P.A. Lensch, M. Goesele, P. Bekaert, J. Kautz, M.A. Magnor, J. Lang, and H.-P. Seidel, "Interactive Rendering of Translucent Objects,"
Proc. 10th IEEE Pacific Conf. Computer Graphics and Applications, p. 214, 2002.- [33] H. Li, F. Pellacini, and K.E. Torrance, "A Hybrid Monte Carlo Method for Accurate and Efficient Subsurface Scattering,"
Proc. 16th Eurographics Workshop Rendering Techniques, pp. 283-290, June 2005.- [34] T. Mertens, J. Kautz, P. Bekaert, F.V. Reeth, and H.-P. Seidel, "Efficient Rendering of Local Subsurface Scattering,"
Proc. 11th IEEE Pacific Conf. Computer Graphics and Applications, p. 51, 2003.- [35] T. Mertens, J. Kautz, P. Bekaert, H.-P. Seidelz, and F.V. Reeth, "Interactive Rendering of Translucent Deformable Objects,"
Proc. 14th Eurographics Workshop Rendering Techniques, pp. 130-140, 2003.- [36] K.W. Morton,
Numerical Solution of Convection-Diffusion Problems. Chapman and Hall, 1996.- [37] M. Pauly, T. Kollig, and A. Keller, "Metropolis Light Transport for Participating Media,"
Proc. Eurographics Workshop Rendering Techniques, pp. 11-22, 2000.- [38] P. Peers, K. vom Berge, W. Matusik, R. Ramamoorthi, J. Lawrence, S. Rusinkiewicz, and P. Dutré, "A Compact Factored Representation of Heterogeneous Subsurface Scattering,"
Proc. ACM SIGGRAPH, pp. 746-753, 2006.- [39] M. Pharr and P. Hanrahan, "Monte Carlo Evaluation of Non-Linear Scattering Equations for Subsurface Reflection,"
Proc. 27th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 75-84, 2000.- [40] M. Schweiger, S.R. Arridge, M. Hiraoka, and D.T. Delpy, "The Finite Element Method for the Propagation of Light in Scattering Media: Boundary and Source Conditions,"
Medical Physics, vol. 22, no. 11, pp. 1779-1792, 1995.- [41] H. Si and K. Gaertner, "Meshing Piecewise Linear Complexes by Constrained Delaunay Tetrahedralizations,"
Proc. 14th Int'l Meshing Roundtable, pp. 147-163, Sept. 2005.- [42] P.-P. Sloan, B. Luna, and J. Snyder, "Local, Deformable Precomputed Radiance Transfer,"
Proc. ACM SIGGRAPH, pp. 1216-1224, 2005.- [43] Y. Song, X. Tong, F. Pellacini, and P. Peers, "Subedit: A Representation for Editing Measured Heterogeneous Subsurface Scattering,"
ACM Trans. Graphics, vol. 28, no. 3, pp. 1-10, 2009.- [44] J. Stam, "Multiple Scattering as a Diffusion Process,"
Proc. Eurographics Workshop Rendering Techniques, pp. 41-50, 1995.- [45] M. Tarini, K. Hormann, P. Cignoni, and C. Montani, "Polycube-Maps,"
Proc. ACM SIGGRAPH, pp. 853-860, 2004.- [46] X. Tong, J. Wang, S. Lin, B. Guo, and H.-Y. Shum, "Modeling and Rendering of Quasi-Homogeneous Materials,"
Proc. ACM SIGGRAPH, pp. 1054-1061, 2005.- [47] B. Walter, A. Arbree, K. Bala, and D.P. Greenberg, "Multidimensional Lightcuts,"
Proc. ACM SIGGRAPH, pp. 1081-1088, 2006.- [48] B. Walter, S. Fernandez, A. Arbree, K. Bala, M. Donikian, and D.P. Greenberg, "Lightcuts: A Scalable Approach to Illumination,"
Proc. ACM SIGGRAPH, pp. 1098-1107, 2005.- [49] J. Wang, S. Zhao, X. Tong, S. Lin, Z. Lin, Y. Dong, B. Guo, and H.-Y. Shum, "Modeling and Rendering of Heterogeneous Translucent Materials Using the Diffusion Equation,"
ACM Trans. Graphics, vol. 27, no. 1, pp. 1-18, 2008.- [50] R. Wang, J. Tran, and D. Luebke, "All-Frequency Interactive Relighting of Translucent Objects with Single and Multiple Scattering,"
Proc. ACM SIGGRAPH, pp. 1202-1207, 2005.- [51] Y. Wang, J. Wang, N. Holzschuch, K. Subr, J.-H. Yong, and B. Guo, "Real-Time Rendering of Heterogeneous Translucent Objects with Arbitrary Shapes,"
Computer Graphics Forum, vol. 29, no. 2,pp. 497-506, 2010. |