產生視覺逼真的影像以及進行數值精確的科學模擬為電腦圖學技術的兩個重要目的，基於物理性質的渲染繪製(physically-based rendering)因為可以同時滿足這兩個目的而受到重視。為了能夠使用一套完整的理論來考慮各式各樣複雜的光線傳播路徑，其通常會採用蒙地卡羅光線追蹤法(Monte Carlo ray tracing)來進行模擬。雖然蒙地卡羅法能用簡潔的方式模擬多種光影效果，其收斂速度並不理想。當繪製一個擁有大量的三維模型、逼真的材質、以及複雜光源的場景時，蒙地卡羅光線追蹤法往往需要非常大量的取樣數才能才能得到一張沒有雜訊的影像。
在這篇博士論文中我們共提出三種取樣與重建技術來增進蒙地卡羅光線追蹤法的效率。首先，我們觀察到在繪製複雜的場景時，比起光源和材質，物體表面兩點的可視度(visibility) 計算通常是造成雜訊的主要原因。因此為了增加取樣的效率，我們提出了可適度群聚(VisibilityCluster)演算法來快速並準確地預測場景中的可視度。此演算法可以被整合進重要性取樣(importance sampling)的架構中並大量減少雜訊。接著為了加速繪製需要龐大計算量的半透明材質，我們首先提出一個雙重矩陣(Dual-matrix)表示法來詮釋渲染半透明材質的問題。同時，我們發展一套取樣與重建技術來減少不重要的計算，大幅加速半透明材質的繪製。最後，我們提出一個有效率的自適應取樣與重建(adaptive sampling and reconstruction) 架構來處理淺景深，動態模糊，以及全域照明等光線傳遞效果。藉著導入統計學中估計誤差的方法到三維繪製的領域，我們成功的決定每個像素需要的取樣數量，並估計出一個最好的濾波器(filter)來大幅減少雜訊。與之前的研究相比，以上的這三個方法皆能大幅改善蒙地卡羅光線追蹤法的繪製效率。

Two of the important tasks that computer graphics techniques try to solve are rendering photo-realistic images and performing numerically accurate simulation. Physically-based rendering can naturally satisfy these two goals. It is usually simulated by Monte Carlo ray tracing for handling a variety of sophisticated light transport paths in a unified manner. Despite its generality and simplicity, however, Monte Carlo integration converges slowly. Rendering scenes with a large number of complex geometries and realistic materials under complex illumination usually requires a large number of samples to produce a noise-free image.
In this dissertation, we proposed three advanced sampling and reconstruction algorithms for improving the performance of Monte Carlo integration. First, realizing that in complex scenes visibility is usually the major source of noise during sampling the shading function, we developed a method called VisibilityCluster for efficiently approximating visibility function. By integrating it into importance sampling framework, we achieve superior noise reduction
compared to previous approaches. Second, to reduce the computation overhead of rendering translucent materials, we proposed an algorithm, Dual-matrix sampling, to avoid evaluating unimportant surface samples which contribute
little to the final image. Finally, a general adaptive sampling and reconstruction framework named SURE-based optimization is proposed to render a wide range of distributed effects, including depth of field, motion blur, and global illumination. All of the three methods achieve significant performance improvement compared to the state-of-the-art rendering algorithms.

Abstract viii
List of Figures xiv
Chapter 1 Introduction 1
Chapter 2 Light Transport, Monte Carlo, and Path Integration 8
2.1 Light Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Monte Carlo Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Importance Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Path Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.1 Path integral formulation . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.2 Antialiasing, depth of field, and motion blur . . . . . . . . . . . . . 16
2.5 Path-based Rendering Algorithms . . . . . . . . . . . . . . . . . . . . . . . 17
2.5.1 Path tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5.2 Virtual point light . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Chapter 3 VisibilityCluster: Average Directional Visibility for Many-Light Rendering
20
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.1 Importance sampling . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.2 Visibility algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.3 Directional occlusion . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 VisibilityCluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4.1 Initial clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4.2 Average visibility estimation . . . . . . . . . . . . . . . . . . . . . 32
3.4.3 Local refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.4 Bias avoidance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.1 Triple-product importance sampling . . . . . . . . . . . . . . . . . 36
3.5.2 Directional occlusion . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.6 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Chapter 4 Dual-Matrix Sampling for Scalable Translucent Material Rendering 48
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.2.1 BSSRDF models for subsurface scattering . . . . . . . . . . . . . . 52
4.2.2 Subsurface scattering rendering . . . . . . . . . . . . . . . . . . . . 53
4.3 Algorithm Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3.1 Dual-matrix representation . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.2 Flow of the algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 Dual-Matrix Representation and Sampling . . . . . . . . . . . . . . . . . . 57
4.4.1 Light-to-Surface matrix reconstruction (the first pass) . . . . . . . 58
4.4.2 Surface-to-Camera matrix reconstruction (the second pass) . . . . 61
4.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5.1 Tested scenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5.2 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.6 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Chapter 5 SURE-based Optimization for Adaptive Sampling and Reconstruction
72
5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2.1 Adaptive sampling and reconstruction . . . . . . . . . . . . . . . . 75
5.2.2 Denoising using SURE . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.3 Stein’s Unbiased Risk Estimator (SURE) . . . . . . . . . . . . . . . . . . . 77
5.4 SURE-based Adaptive Rendering . . . . . . . . . . . . . . . . . . . . . . . 78
5.4.1 Initial samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.4.2 Filter selection using SURE . . . . . . . . . . . . . . . . . . . . . . 80
5.4.3 Adaptive sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.5.1 Parameter setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.5.2 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.5.3 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.5.4 Other filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.5.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.6 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Chapter 6 Conclusions 98
Chapter A Derivatives for Filters 1
Bibliography 2

[1] S. Agarwal, R. Ramamoorthi, S. Belongie, and H. W. Jensen. Structured importance sampling of environment maps. ACM Trans. Graph. (Proc. SIGGRAPH 03), 22(3):605–612, July 2003.
[2] M. Agrawala, R. Ramamoorthi, A. Heirich, and L. Moll. Efficient image-based methods for rendering soft shadows. In Proc. 27th annual conference on Computer graphics and interactive techniques (SIGGRAPH 00), pages 375–384, 2000.
[3] A. Arbree. Scalable And Heterogeneous Rendering Of Subsurface Scattering Materials. PhD thesis, Cornell University, Oct. 2009.
[4] A. Arbree, B.Walter, and K. Bala. Single-pass scalable subsurface rendering with lightcuts. Computer Graphics Forum (Proc. Eurographics 08), pages 507–516, 2008.
[5] K. Bala, B. Walter, and D. P. Greenberg. Combining edges and points for interactive high-quality rendering. ACM Trans. Graph. (Proc. SIGGRAPH 03), 22(3):631–640, 2003.
[6] F. Banterle and A. Chalmers. A fast translucency appearance model for real-time applications. In Proc. Spring Conference on Computer Graphics (SCCG 2006), April 2006.
[7] T. Bashford-Rogers, K. Debattista, C. Harvey, and A. Chalmers. Approximate visibility grids for interactive indirect illumination. In Proc. 3rd International Conference on Games and Virtual Worlds for Serious Applications, pages 55–62, 2011.
[8] P. Bauszat, M. Eisemann, and M. Magnor. Guided image filtering for interactive highquality global illumination. In Proc. 22nd Eurographics conference on Rendering (EGSR 11), pages 1361–1368, 2011.
[9] A. Ben-Artzi, R. Ramamoorthi, and M. Agrawala. Efficient shadows for sampled environment maps. J. Graphics Tools, pages 13–36, 2006.
[10] T. Blu and F. Luisier. The SURE-LET approach to image denoising. IEEE Transactions on Image Processing, 16(11):2778–2786, 2007.
[11] S. Boulos. How often do shadow rays hit? Ray Tracing News, 23(1), July 2010.
[12] A. Buades, B. Coll, and J.-M. Morel. A non-local algorithm for image denoising. In Proc. IEEE Computer Vision and Pattern Recognition (CVPR 05), pages 60–65, 2005.
[13] D. Burke, A. Ghosh, and W. Heidrich. Bidirectional importance sampling for direct illumination. In Proc. 16th Eurographics conference on Rendering Techniques (EGSR 05), pages 147–156, 2005.
[14] N. A. Carr, J. D. Hall, and J. C. Hart. GPU algorithms for radiosity and subsurface scattering. In Proc. of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware, pages 51–59, 2003.
[15] 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 (Proc. Eurographics 08), pages 517–526, 2008.
[16] J. Chen, B. Wang, Y. Wang, R. S. Overbeck, J.-H. Yong, and W. Wang. Efficient depth-of-field rendering with adaptive sampling and multiscale reconstruction. Comput. Graph. Forum, 30(6):1667–1680, 2011.
[17] Y. Chen, X. Tong, J.Wang, S. Lin, B. Guo, and H.-Y. Shum. Shell texture functions. ACM Trans. Graph. (Proc. SIGGRAPH 04), 23(3):343–353, Aug. 2004.
[18] E. Cheslack-Postava, R. Wang, O. Akerlund, and F. Pellacini. Fast, realistic lighting and material design using nonlinear cut approximation. ACM Trans. Graph. (Proc. SIGGRAPH Asia 08), 27(5):128:1–128:10, Dec. 2008.
[19] P. H. Christensen, G. Harker, J. Shade, B. Schubert, and D. Batali. Multiresolution radiosity caching for global illumination in movies. In ACM SIGGRAPH 2012 Talks, pages 47:1–47:1, 2012.
[20] P. Clarberg and T. Akenine-M‥oller. Exploiting visibility correlation in direct illumination. In Proc. 19th Eurographics conference on Rendering (EGSR 08), pages 1125–1136, 2008.
[21] P. Clarberg and T. Akenine-M‥oller. Practical product importance sampling for direct illumination. Computer Graphics Forum (Proc. Eurographics 08), 27(2):681–690, 2008.
[22] P. Clarberg, W. Jarosz, T. Akenine-M‥oller, and H. W. Jensen. Wavelet importance sampling: efficiently evaluating products of complex functions. ACM Trans. Graph. (Proc. SIGGRAPH 05), 24(3):1166–1175, July 2005.
[23] D. Cline, D. Adams, and P. Egbert. Table-driven adaptive importance sampling. In Proc. 19th Eurographics conference on Rendering (EGSR 08), pages 1115–1123, 2008.
[24] D. Cline, P. K. Egbert, J. F. Talbot, and D. L. Cardon. Two stage importance sampling for direct lighting. In Proc. 17th Eurographics conference on Rendering Techniques (EGSR 06), pages 103–113, 2006.
[25] C. Dachsbacher and M. Stamminger. Translucent shadow maps. In Proc. 14th Eurographics workshop on Rendering (EGRW 03), pages 197–201, 2003.
[26] C. Dachsbacher and M. Stamminger. Reflective shadow maps. In Proc. Symposium on Interactive 3D graphics and games, pages 203–231, 2005.
[27] C. Dachsbacher and M. Stamminger. Splatting indirect illumination. In Proc. Symposium on Interactive 3D graphics and games, pages 93–100, 2006.
[28] H. Dammertz, D. Sewtz, J. Hanika, and H. P. A. Lensch. Edge-avoiding A’-Trous wavelet transform for fast global illumination filtering. In Proc. the Conference on High Performance Graphics (HPG 10), pages 67–75, 2010.
[29] T. Davidoviˇc, J. Kˇriv’anek, M. Haˇsan, P. Slusallek, and K. Bala. Combining global and local virtual lights for detailed glossy illumination. ACM Trans. Graph. (Proc. SIGGRAPH Asia 10), 29(6):143:1–143:8, Dec. 2010.
[30] L. M. Delves and J. L. Mohamed, editors. Computational methods for integral equations. Cambridge University Press, New York, NY, USA, 1986.
[31] E. D’Eon. A better dipole. Technical report, 2012.
[32] E. D’Eon and G. Irving. A quantized-diffusion model for rendering translucent materials. ACM Trans. Graph. (Proc. SIGGRAPH 11), 30(4):56:1–56:14, July 2011.
[33] E. d’Eon, D. Luebke, and E. Enderton. Efficient rendering of human skin. In Proc. 18th Eurographics Conference on Rendering Techniques (EGSR 07), pages 147–157, 2007.
[34] Z. Dong, T. Grosch, T. Ritschel, J. Kautz, and H.-P. Seidel. Real-time indirect illumination with clustered visibility. In Vision, Modeling, and Visualization Workshop, 2009.
[35] M. Donikian, B. Walter, K. Bala, S. Fernandez, and D. P. Greenberg. Accurate direct illumination using iterative adaptive sampling. IEEE Transactions on Visualization and
Computer Graphics, 12(3):353–364, May 2006.
[36] C. Donner and H. W. Jensen. Light diffusion in multi-layered translucent materials. ACM Trans. Graph. (Proc. SIGGRAPH 05), 24(3):1032–1039, July 2005.
[37] C. Donner and H. W. Jensen. Rendering translucent materials using photon diffusion. In Proc. 18th Eurographics conference on Rendering Techniques (EGSR 07), pages 243–251, 2007.
[38] D. Donoho and I. M. Johnstone. Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association, 90:1200–1224, 1995.
[39] P. Dutr’e, P. Tole, and D. P. Greenberg. Approximate visibility for illumination computations using point clouds. Technical Report PCG-00-01, Cornell University, june 2000.
[40] K. Egan, F. Durand, and R. Ramamoorthi. Practical filtering for efficient ray-traced directional occlusion. ACM Trans. Graph. (Proc. SIGGRAPH Asia 11), 30(6):180:1–180:10, Dec. 2011.
[41] K. Egan, F. Hecht, F. Durand, and R. Ramamoorthi. Frequency analysis and sheared filtering for shadow light fields of complex occluders. ACM Trans. Graph., 30(2):9:1–9:13, 2011.
[42] K. Egan, Y.-T. Tseng, N. Holzschuch, F. Durand, and R. Ramamoorthi. Frequency analysis and sheared reconstruction for rendering motion blur. ACM Trans. Graph. (Proc. SIGGRAPH 09), 28(3):93:1–93:13, 2009.
[43] S. Fernandez, K. Bala, and D. P. Greenberg. Local illumination environments for direct lighting acceleration. In Proc. 13th Eurographics workshop on Rendering, pages 7–14, 2002.
[44] C. V. Fiorio. Confidence intervals for kernel density estimation. Stata Journal, 4(2):168–179, 2004.
[45] I. Georgiev, J. Kˇriv’anek, S. Popov, and P. Slusallek. Importance caching for complex illumination. Computer Graphics Forum (Proc. Eurographics 12), 31(2):701–710, May 2012.
[46] A. Ghosh and W. Heidrich. Correlated visibility sampling for direct illumination. Visual Computer, 22(9):693–701, Sept. 2006.
[47] Y. Gong, W. Chen, L. Zhang, Y. Zeng, and Q. Peng. GPU-based rendering for deformable translucent objects. Vis. Comput., 24(2):95–103, Jan. 2008.
[48] R. Habel, P. H. Christensen, and W. Jarosz. Photon beam diffusion: A hybrid monte carlo method for subsurface scattering. In Proc. 24th Eurographics conference on Rendering Techniques (EGSR 13), 2013.
[49] T. Hachisuka, W. Jarosz, and H. W. Jensen. A progressive error estimation framework for photon density estimation. ACM Trans. Graph. (Proc. SIGGRAPH Asia 10), 29(6):144:1–144:12, 2010.
[50] T. Hachisuka,W. Jarosz, R. P.Weistroffer, K. Dale, G. Humphreys, M. Zwicker, and H.W. Jensen. Multidimensional adaptive sampling and reconstruction for ray tracing. ACM Trans. Graph. (Proc. SIGGRAPH 08), 27(3):33:1–33:10, 2008.
[51] X. Hao and A. Varshney. Real-time rendering of translucent meshes. ACM Trans. Graph., 23(2):120–142, Apr. 2004.
[52] D. Hart, P. Dutr’e, and D. P. Greenberg. Direct illumination with lazy visibility evaluation. In Proc. 26th annual conference on Computer graphics and interactive techniques (SIGGRAPH 99), pages 147–154, 1999.
[53] M. Haˇsan, J. Kˇriv’anek, B. Walter, and K. Bala. Virtual spherical lights for many-light rendering of glossy scenes. ACM Trans. Graph. (Proc. SIGGRAPH Asia 09), 28(5):143:1–143:6, Dec. 2009.
[54] M. Haˇsan, F. Pellacini, and K. Bala. Matrix row-column sampling for the many-light problem. ACM Trans. Graph. (Proc. SIGGRAPH 07), 26(3), July 2007.
[55] T. Ize and C. D. Hansen. RTSAH traversal order for occlusion rays. Computer Graphics Forum (Proc. Eurographics 11), 30(2):297–305, 2011.
[56] W. Jarosz, N. A. Carr, and H.W. Jensen. Importance sampling spherical harmonics. Computer Graphics Forum (Proc. Eurographics 09), 28(2):577–586, Apr. 2009.
[57] H. W. Jensen and J. Buhler. A rapid hierarchical rendering technique for translucent materials. ACM Trans. Graph. (Proc. SIGGRAPH 02), 21(3):576–581, July 2002.
[58] H. W. Jensen, S. R. Marschner, M. Levoy, and P. Hanrahan. A practical model for subsurface light transport. In Proc. 28th annual conference on Computer graphics and interactive techniques (SIGGRAPH 01), pages 511–518, 2001.
[59] J. T. Kajiya. The rendering equation. In Proc. 13th annual conference on computer graphics and interactive techniques (SIGGRAPH 86), pages 143–150, 1986.
[60] A. Keller. Instant radiosity. In Proc. 24th annual conference on Computer graphics and interactive techniques (SIGGRAPH 97), pages 49–56, 1997.
[61] S.-L. Keng, W.-Y. Lee, and J.-H. Chuang. An efficient caching-based rendering of translucent materials. Vis. Comput., 23(1):59–69, Dec. 2006.
[62] A. King, C. Kulla, A. Conty, and M. Fajardo. BSSRDF importance sampling. In ACM SIGGRAPH 2013 Talks, pages 48:1–48:1, 2013.
[63] T. Kollig and A. Keller. Efficient illumination by high dynamic range images. In Proc. 14th Eurographics workshop on Rendering, pages 45–50, 2003.
[64] T. Kollig and A. Keller. Illumination in the presence of weak singularities. In MCQMC Methods, 2004.
[65] J. Lawrence, S. Rusinkiewicz, and R. Ramamoorthi. Efficient BRDF importance sampling using a factored representation. ACM Trans. Graph. (Proc. SIGGRAPH 04), 23(3):496–505, Aug. 2004.
[66] J. Lehtinen, T. Aila, J. Chen, S. Laine, and F. Durand. Temporal light field reconstruction for rendering distribution effects. ACM Trans. Graph. (Proc. SIGGRAPH 11), 30(4):55:1–55:12, 2011.
[67] J. Lehtinen, T. Aila, S. Laine, and F. Durand. Reconstructing the indirect light field for global illumination. ACM Trans. Graph. (Proc. SIGGRAPH 12), 31(4):51:1–51:10, 2012.
[68] J. Lehtinen, M. Zwicker, E. Turquin, J. Kontkanen, F. Durand, F. X. Sillion, and T. Aila. A meshless hierarchical representation for light transport. ACM Trans. Graph. (Proc. SIGGRAPH 08), 27(3):37:1–37:9, Aug. 2008.
[69] H. P. A. Lensch, M. Goesele, P. Bekaert, J. Kautz, M. A. Magnor, J. Lang, and H.-P. Seidel. Interactive rendering of translucent objects. In Proc. 10th Pacific Conference on Computer Graphics and Applications (PG 02), 2002.
[70] H. Li, F. Pellacini, and K. E. Torrance. A hybrid monte carlo method for accurate and efficient subsurface scattering. In Proc. Sixteenth Eurographics conference on Rendering Techniques (EGSR 05), pages 283–290, 2005.
[71] T. Mertens, J. Kautz, P. Bekaert, F. Van Reeth, and H.-P. Seidel. Efficient rendering of local subsurface scattering. In Proc. 11th Pacific Conference on Computer Graphics and Applications (PG 03), 2003.
[72] D. P. Mitchell. Generating antialiased images at low sampling densities. In Proc. 14th annual conference on Computer graphics and interactive techniques (SIGGRAPH 87), pages 65–72, 1987.
[73] D. P. Mitchell. Spectrally optimal sampling for distribution ray tracing. In Proc. 18th annual conference on Computer graphics and interactive techniques (SIGGRAPH 91), pages 157–164, 1991.
[74] A. Mu&;#732;noz, J. I. Echevarria, F. J. Ser’on, and D. Gutierrez. Convolution-based simulation of homogeneous subsurface scattering. Comput. Graph. Forum, 30(8):2279–2287, 2011.
[75] S. G. Narasimhan, M. Gupta, C. Donner, R. Ramamoorthi, S. K. Nayar, and H. W. Jensen. Acquiring scattering properties of participating media by dilution. ACM Trans. Graph. (Proc. SIGGRAPH 06), 25(3):1003–1012, July 2006.
[76] G. Nichols and C. Wyman. Multiresolution splatting for indirect illumination. In Proc. Symposium on Interactive 3D graphics and games, pages 83–90, 2009.
[77] F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis. Radiometry. chapter Geometrical considerations and nomenclature for reflectance, pages 94–145. 1992.
[78] J. Nov’ak, T. Engelhardt, and C. Dachsbacher. Screen-space bias compensation for interactive high-quality global illumination with virtual point lights. In Proc. Symposium on Interactive 3D graphics and games, pages 119–124, 2011.
[79] J. Ou. Sampling for Complexity in Rendering. PhD thesis, Dartmouth college, Hanover, New Hampshire, May 2013.
[80] J. Ou and F. Pellacini. LightSlice: matrix slice sampling for the many-lights problem. ACM Trans. Graph. (Proc. SIGGRAPH Asia 11), 30(6):179:1–179:8, Dec. 2011.
[81] R. S. Overbeck, C. Donner, and R. Ramamoorthi. Adaptive wavelet rendering. ACM Trans. Graph. (Proc. SIGGRAPH Asia 09), 28(5):140:1–140:12, 2009.
[82] M. Pharr and G. Humphreys. Physically Based Rendering, Second Edition: From Theory To Implementation. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 2nd edition, 2010.
[83] R. Ramamoorthi, J. Anderson, M. Meyer, and D. Nowrouzezahrai. A theory of monte carlo visibility sampling. ACM Trans. Graph., 31(5):121:1–121:16, Sept. 2012.
[84] T. Ritschel, T. Grosch, M. H. Kim, H.-P. Seidel, C. Dachsbacher, and J. Kautz. Imperfect shadow maps for efficient computation of indirect illumination. ACM Trans. Graph. (Proc. SIGGRAPH Asia 08), 27(5):129:1–129:8, Dec. 2008.
[85] T. Ritschel, T. Grosch, and H.-P. Seidel. Approximating dynamic global illumination in image space. In Proc. Symposium on Interactive 3D graphics and games, pages 75–82, 2009.
[86] F. Rousselle, P. Clarberg, L. Leblanc, V. Ostromoukhov, and P. Poulin. Efficient product sampling using hierarchical thresholding. Visual Computer, 24(7):465–474, July 2008.
[87] F. Rousselle, C. Knaus, and M. Zwicker. Adaptive sampling and reconstruction using greedy error minimization. ACM Trans. Graph. (Proc. SIGGRAPH Asia 11), 30(6):159:1-159:12, 2011.
[88] B. Segovia, J. C. Iehl, R. Mitanchey, and B. P’eroche. Non-interleaved deferred shading of interleaved sample patterns. In Proc. 21st ACM SIGGRAPH/EUROGRAPHICS Symposium on Graphics Hardware, pages 53–60, 2006.
[89] P. Sen and S. Darabi. On filtering the noise from the random parameters in Monte Carlo rendering. ACM Trans. Graph., 31(3):18:1–18:15, 2012.
[90] M. A. Shah, J. Konttinen, and S. Pattanaik. Image-space subsurface scattering for interactive rendering of deformable translucent objects. IEEE Comput. Graph. Appl., 29(1):66–78, Jan. 2009.
[91] Y. Sheng, Y. Shi, L. Wang, and S. G. Narasimhan. A practical analytic model for the radiosity of translucent scenes. In Proc. symposium on Interactive 3D graphics, 2013.
[92] P. Shirley, T. Aila, J. Cohen, E. Enderton, S. Laine, D. Luebke, and M. McGuire. A local image reconstruction algorithm for stochastic rendering. In Proc. Symposium on Interactive 3D graphics and games, pages 9–14, 2011.
[93] P. Shirley, C.Wang, and K. Zimmerman. Monte Carlo techniques for direct lighting calculations. ACM Trans. Graph., 15(1):1–36, Jan. 1996.
[94] P.-P. Sloan, J. Hall, J. Hart, and J. Snyder. Clustered principal components for precomputed radiance transfer. ACM Trans. Graph. (Proc. SIGGRAPH 03), 22(3):382–391, July 2003.
[95] P.-P. Sloan, B. Luna, and J. Snyder. Local, deformable precomputed radiance transfer. ACM Trans. Graph. (Proc. SIGGRAPH 05), 24(3):1216–1224, July 2005.
[96] C. Soler, K. Subr, F. Durand, N. Holzschuch, and F. Sillion. Fourier depth of field. ACM Trans. Graph., 28(2):18:1–18:12, 2009.
[97] C. M. Stein. Estimation of the mean of a multivariate normal distribution. Annals of Statistics, 9(6):1135–1151, 1981.
[98] J. Steinhurst and A. Lastra. Global importance sampling of glossy surfaces using the photon map. In Proc. IEEE Symposium on Interactive Ray Tracing, pages 133–138, 2006.
[99] A. J. Stewart and T. Karkanis. Computing the approximate visibility map, with applications to form factors and discontinuity meshing. In Proc. 9th Eurographics workshop on Rendering, pages 57–68, 1998.
[100] J. F. Talbot, D. Cline, and P. Egbert. Importance resampling for global illumination. In Proc. 16th Eurographics conference on Rendering Techniques (EGSR 05), pages 139–146, 2005.
[101] R. Tamstorf and H. W. Jensen. Adaptive sampling and bias estimation in path tracing. In Proc. 8th Eurographics workshop on Rendering, pages 285–295, 1997.
[102] X. Tong, J. Wang, S. Lin, B. Guo, and H.-Y. Shum. Modeling and rendering of quasihomogeneous materials. ACM Trans. Graph. (Proc. SIGGRAPH 05), 24(3):1054–1061, July 2005.
[103] D. Van De Ville and M. Kocher. SURE-based non-local means. IEEE Signal Processing Letters, 16(11):973–976, 2009.
[104] E. Veach. Robust Monte Carlo Methods for Light Transport Simulation. PhD thesis, 1998.
[105] E. Veach and L. Guibas. Bidirectional estimators for light transport. In Proc. 5th Eurographics workshop on Rendering”, pages 147–162, June 1994.
[106] B. Walter, A. Arbree, K. Bala, and D. P. Greenberg. Multidimensional lightcuts. ACM Trans. Graph. (Proc. SIGGRAPH 06), 25(3):1081–1088, July 2006.
[107] B. Walter, S. Fernandez, A. Arbree, K. Bala, M. Donikian, and D. P. Greenberg. Lightcuts: a scalable approach to illumination. ACM Trans. Graph. (Proc. SIGGRAPH 05), 24(3):1098–1107, July 2005.
[108] B. Walter, P. Khungurn, and K. Bala. Bidirectional lightcuts. ACM Trans. Graph. (Proc. SIGGRAPH 12), 31(4):59:1–59:11, July 2012.
[109] R. Wang and O. A° kerlund. Bidirectional importance sampling for unstructured direct illumination. Computer Graphics Forum (Proc. Eurographics 09), 28(2):269–278, Apr. 2009.
[110] R. Wang, J. Tran, and D. Luebke. All-frequency interactive relighting of translucent objects with single and multiple scattering. ACM Trans. Graph. (Proc. SIGGRAPH 05), 24(3):1202–1207, July 2005.
[111] Y.-T.Wu and Y.-Y. Chuang. VisibilityCluster: Average directional visibility for many-light rendering. IEEE Transactions on Visualization and Computer Graphics, 19(9):1566–1578, Sept. 2013.
[112] R. Xu and S. N. Pattanaik. A novel Monte Carlo noise reduction operator. IEEE Computer Graphics and Applications, 25(2):31–35, 2005.
[113] L.-Q. Yan, Y. Zhou, K. Xu, and R. Wang. Accurate translucent material rendering under spherical gaussian lights. Comp. Graph. Forum, 31(7pt2):2267–2276, Sept. 2012.
[114] I. Yu, A. Cox, M. H. Kim, T. Ritschel, T. Grosch, C. Dachsbacher, and J. Kautz. Perceptual influence of approximate visibility in indirect illumination. ACM Trans. Appl. Percept., 6(4):24:1–24:14, Oct. 2009.