Modeling and Rendering Heterogeneous Translucent Materials using Diffusion Equation

Jiaping Wang Microsoft Research Asia
Shuang Zhao Shanghai Jiao Tong University
Xin Tong Microsoft Research Asia
Stephen Lin Microsoft Research Asia
Zhouchen Lin Microsoft Research Asia
Yue Dong Tsinghua University
Baining Guo Microsoft Research Asia and Tsinghua University
Heung-Yeung Shum Microsoft Research Asia and Tsinghua University


ACM Transactions on Graphics, Volume 27, Number 1


      In this paper, we propose techniques for modeling and rendering of heterogeneous translucent materials that enable acquisition from measured samples, interactive editing of material attributes, and real-time rendering. The materials are assumed to be optically dense such that multiple scattering can be approximated by a diffusion process described by the diffusion equation. For modeling heterogeneous materials, we present an algorithm for acquiring material properties from appearance measurements by solving an inverse diffusion problem. Our modeling algorithm incorporates a regularizer to handle the ill-conditioned inverse problem, an adjoint method to dramatically reduce the computational cost, and a hierarchical GPU implementation for further speedup. To display an object with known material properties, we present an algorithm that performs rendering by solving the diffusion equation with the boundary condition defined by the given illumination environment. This algorithm is centered around object representation by a polygrid, a grid with regular connectivity and an irregular shape, which facilitates the solution of the diffusion equation in arbitrary volumes. Because of the regular connectivity, our rendering algorithm can be implemented on the GPU for real-time performance. We demonstrate our techniques by capturing materials from physical samples and performing real-time rendering and editing with these materials.


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The snail in Figure 20 was modeled by Feiyang Tong. The authors thank Ming Jiang, Tie Zhou, Ruo Li and Guanquan Zhang for discussions on inverse diffusion, and the anonymous reviewers for their helpful suggestions and comments. This work was done when Shuang Zhao, and Yue Dong were visiting students in Microsoft Research Asia.

BibTex reference

   author    = {Jiaping Wang and Shuang Zhao and Xin Tong and Stephen Lin and Zhouchen Lin and 
                Yue Dong and Baining Guo and Heung-Yeung Shum},
   title     = {Modeling and rendering of heterogeneous translucent materials using the diffusion 
   journal   = {ACM Trans. Graph.},
   volume    = {27},
   number    = {1},
   year      = {2008},
   pages     = {1--18},
   publisher = {ACM},
   address   = {New York, NY, USA}