Abstract
Screen-space subsurface scattering is currently the most common approach to represent translucent materials in real-time rendering. However, most of the current approaches approximate the diffuse reflectance profile of translucent materials as a symmetric function, whereas the profile has an asymmetric shape in nature. To address this problem, we propose LinSSS, a numerical representation of heterogeneous subsurface scattering for real-time screen-space rendering. Although our representation is built upon a previous method, it makes two contributions. First, LinSSS formulates the diffuse reflectance profile as a linear combination of radially symmetric Gaussian functions. Nevertheless, it can also represent the spatial variation and the radial asymmetry of the profile. Second, since LinSSS is formulated using only the Gaussian functions, the convolution of the diffuse reflectance profile can be efficiently calculated in screen space. To further improve the efficiency, we deform the rendering equation obtained using LinSSS by factoring common convolution terms and approximate the convolution processes using a MIP map. Consequently, our method works as fast as the state-of-the-art method, while our method successfully represents the heterogeneity of scattering.
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Arbree, A., Walter, B., Bala, K.: Heterogeneous subsurface scattering using the finite element method. IEEE Trans. Vis. Comput. Graph. 17(7), 956–969 (2011). https://doi.org/10.1109/TVCG.2010.117
Chandrasekhar, S.: Radiative Transfer. Oxford University Press, Oxford (1960)
Chen, G., Peers, P., Zhang, J., Tong, X.: Real-time rendering of deformable heterogeneous translucent objects using multiresolution splatting. Vis. Comput. 28(6), 701–711 (2012). https://doi.org/10.1007/s00371-012-0704-1
Dachsbacher, C., Stamminger, M.: Translucent shadow maps. In: Proceedings of the Eurographics Workshop on Rendering, pp. 197–201 (2003). https://doi.org/10.2312/EGWR/EGWR03/197-201
Dachsbacher, C., Stamminger, M.: Reflective shadow maps. In: Proceedings of the Symposium on Interactive 3D Graphics and Games, pp. 203–231 (2005). https://doi.org/10.1145/1053427.1053460
d’Eon, E., Irving, G.: A quantized-diffusion model for rendering translucent materials. ACM Trans. Graph. 30(4), 56 (2011). https://doi.org/10.1145/2010324.1964951
d’Eon, E., Luebke, D., Enderton, E.: Efficient rendering of human skin. In: Proceedings of the Eurographics Conference on Rendering Techniques, pp. 147–157 (2007). https://doi.org/10.2312/EGWR/EGSR07/147-157
Donner, C., Jensen, H.W.: Light diffusion in multi-layered translucent materials. ACM Trans. Graph. 24(3), 1032–1039 (2005). https://doi.org/10.1145/1073204.1073308
Donner, C., Jensen, H.W.: Rendering translucent materials using photon diffusion. In: Proceedings of Eurographics Symposium on Rendering Techniques (EGSR), pp. 243–251 (2007)
Donner, C., Weyrich, T., d’Eon, E., Ramamoorthi, R., Rusinkiewicz, S.: A layered, heterogeneous reflectance model for acquiring and rendering human skin. ACM Trans. Graph. 27(5), 140:1–140:12 (2008). https://doi.org/10.1145/1409060.1409093
Elek, O., Krivánek, J.: Towards a principled kernel prediction for spatially varying BSSRDFs. In: Proceedings of the Eurographics Workshop on Material Appearance Modeling (2018). https://doi.org/10.2312/mam.20181200
Elek, O., Ritschel, T., Seidel, H.: Real-time screen-space scattering in homogeneous environments. IEEE Comput. Graph. Appl. 33(3), 53–65 (2013). https://doi.org/10.1109/MCG.2013.17
Elek, O., Sumin, D., Zhang, R., Weyrich, T., Myszkowski, K., Bickel, B., Wilkie, A., Křivánek, J.: Scattering-aware texture reproduction for 3d printing. ACM Trans. Graph. 36(6), 241:1–241:15 (2017). https://doi.org/10.1145/3130800.3130890
Frederickx, R., Dutré, P.: A forward scattering dipole model from a functional integral approximation. ACM Trans. Graph. 36(4), 109:1–109:13 (2017). https://doi.org/10.1145/3072959.3073681
Frisvad, J.R., Hachisuka, T., Kjeldsen, T.K.: Directional dipole model for subsurface scattering. ACM Trans. Graph. (2015). https://doi.org/10.1145/2682629
Goesele, M., Lensch, H.P.A., Lang, J., Fuchs, C., Seidel, H.P.: Disco: acquisition of translucent objects. ACM Trans. Graph. 23(3), 835–844 (2004). https://doi.org/10.1145/1186562.1015807
Habel, R., Christensen, P.H., Jarosz, W.: Photon beam diffusion: a hybrid Monte Carlo method for subsurface scattering. In: Proceedings of the Eurographics Symposium on Rendering (EGSR), pp. 27–37 (2013). https://doi.org/10.1111/cgf.12148
Hable, J., Borshukov, G., Hejl, J.: Fast skin shading. Shader X7, 161–173 (2009)
Hanrahan, P., Krueger, W.: Reflection from layered surfaces due to subsurface scattering. In: Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’93), pp. 165–174 (1993). https://doi.org/10.1145/166117.166139
High-resolution light probe image gallery. https://vgl.ict.usc.edu/Data/HighResProbes/. Accessed 22 July 2020
Jakob, W.: Mitsuba renderer (2010). http://www.mitsuba-renderer.org. Accessed 22 July 2020
Jensen, H.W., Buhler, J.: A rapid hierarchical rendering technique for translucent materials. ACM Trans. Graph. 21(3), 576–581 (2002). https://doi.org/10.1145/566654.566619
Jensen, H.W., Marschner, S.R., Levoy, M., Hanrahan, P.: A practical model for subsurface light transport. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’01), pp. 511–518 (2001). https://doi.org/10.1145/383259.383319
Jimenez, J., Gutierrez, D.: Faster rendering of human skin. In: Proceedings of Spanish Computer Graphics Conference (CEIG) (2008)
Jimenez, J., Gutierrez, D.: Screen-space subsurface scattering. In: GPU Pro: Advanced Rendering Techniques, pp. 335–351 (2010). https://doi.org/10.1201/b10648-26
Jimenez, J., Zsolnai, K., Jarabo, A., Freude, C., Auzinger, T., Wu, X.C., der Pahlen, J., Wimmer, M., Gutierrez, D.: Separable subsurface scattering. Comput. Graph. Forum 34(6), 188–197 (2015). https://doi.org/10.1111/cgf.12529
Lee, S., Kim, G.J., Choi, S.: Real-time depth-of-field rendering using anisotropically filtered mipmap interpolation. IEEE Trans. Vis. Comput. Graph. 15(3), 453–464 (2009). https://doi.org/10.1109/TVCG.2008.106
Lensch, H.P., Goesele, M., Bekaert, P., Kautz, J., Magnor, M.A., Lang, J., Seidel, H.P.: Interactive rendering of translucent objects. Comput. Graph. Forum 22(2), 195–205 (2003). https://doi.org/10.1111/1467-8659.00660
Mertens, T., Kautz, J., Bekaert, P., Seidelz, H.P., Van Reeth, F.: Interactive rendering of translucent deformable objects. In: Proceedings of the Eurographics Workshop on Rendering, pp. 130–140 (2003). https://doi.org/10.2312/EGWR/EGWR03/130-140
Mertens, T., Kautz, J., Bekaert, P., Van Reeth, F., Seidel, H.P.: Efficient rendering of local subsurface scattering. Comput. Graph. Forum 24(1), 41–49 (2005). https://doi.org/10.1111/j.1467-8659.2005.00827.x
Munoz, A., Echevarria, J.I., Seron, F.J., Lopez-Moreno, J., Glencross, M., Gutierrez, D.: Bssrdf estimation from single images. Comput. Graph. Forum 30(2), 455–464 (2011). https://doi.org/10.1111/j.1467-8659.2011.01873.x
Nocedal, J., Wright, S.J.: Numerical Optimization of Computer Models, 2nd edn. Springer, Berlin (2006)
Peers, P., vom Berge, K., Matusik, W., Ramamoorthi, R., Lawrence, J., Rusinkiewicz, S., Dutré, P.: A compact factored representation of heterogeneous subsurface scattering. ACM Trans. Graph. 25(3), 746–753 (2006). https://doi.org/10.1145/1179352.1141950
Ramamoorthi, R., Hanrahan, P.: An efficient representation for irradiance environment maps. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’01), pp. 497–500 (2001). https://doi.org/10.1145/383259.383317
Shah, M.A., Konttinen, J., Pattanaik, S.: Image-space subsurface scattering for interactive rendering of deformable translucent objects. IEEE Comput. Graph. Appl. 29(1), 66–78 (2009). https://doi.org/10.1109/MCG.2009.11
Sone, H., Hachisuka, T., Koike, T.: Parameter estimation of BSSRDF for heterogeneous materials. Eurograph. Short Pap. (2017). https://doi.org/10.2312/egsh.20171018
Song, Y., Tong, X., Pellacini, F., Peers, P.: Subedit: a representation for editing measured heterogeneous subsurface scattering. ACM Trans. Graph. 28(3), 31:1–31:10 (2009). https://doi.org/10.1145/1576246.1531337
Song, Y., Wang, W.: A data-driven model for anisotropic heterogeneous subsurface scattering. In: Proceedings of the Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, pp. 1–7 (2013). https://doi.org/10.1109/APSIPA.2013.6694333
Stam, J.: Multiple scattering as a diffusion process. In: Rendering Techniques, pp. 41–50 (1995). https://doi.org/10.1007/978-3-7091-9430-0_5
Wang, J., Zhao, S., Tong, X., Lin, S., Lin, Z., Dong, Y., Guo, B., Shum, H.Y.: Modeling and rendering of heterogeneous translucent materials using the diffusion equation. ACM Trans. Graph. 27(1), 9:1–9:18 (2008). https://doi.org/10.1145/1330511.1330520
Acknowledgements
We appreciate the anonymous reviewers for their helpful comments to significantly improve the quality of the paper. We thank Pietre Peers, Xin Tong, and Yue Dong for providing us their measured BSSRDF data. We also thank Hiroyuki Kubo, Takahito Aoto, and Hubert P. H. Shum for their constructive discussion on this study.
Funding
This project was jointly supported by JSPS KAKENHI (JP18K18075, JP20H04203, JP17H06101, and JP19H01129), JST ACCEL (JPMJAC1602), JST Mirai Project (JPMJMI19B2), and a Grant-in-Aid from the Waseda Institute of Advanced Science and Engineering.
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Yatagawa, T., Yamaguchi, Y. & Morishima, S. LinSSS: linear decomposition of heterogeneous subsurface scattering for real-time screen-space rendering. Vis Comput 36, 1979–1992 (2020). https://doi.org/10.1007/s00371-020-01915-4
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DOI: https://doi.org/10.1007/s00371-020-01915-4