基于物理的可微渲染综述

邢健开; 徐昆

doi:10.11834/jig.230715

混合现实 | 浏览量 : 0 下载量: 3178 CSCD: 0

PDF
导出
分享
收藏
专辑

基于物理的可微渲染综述
Physically based differentiable rendering： a survey
2024年29卷第10期页码：2912-2925
收稿：2023-10-07，

修回：2024-02-06，

纸质出版：2024-10-16
DOI： 10.11834/jig.230715
稿件说明：

移动端阅览

邢健开，徐昆. 2024. 基于物理的可微渲染综述. 中国图象图形学报， 29(10):2912-2925 DOI： 10.11834/jig.230715.

Xing Jiankai， Xu Kun. 2024. Physically based differentiable rendering： a survey. Journal of Image and Graphics， 29(10):2912-2925 DOI： 10.11834/jig.230715.

摘要

可微渲染技术是当前计算机图形学与计算机视觉方向的研究热点，其目标是将计算机图形学中的渲染流水线进行可微化改造以支持计算渲染的输出图像关于输入参数如几何、材质等参数的梯度。结合渲染图像与目标图像之间的损失函数，可微渲染允许在生成式分析的框架中，通过梯度下降的方式从图像中推理出场景参数，是解决三维重建、逆向渲染等领域问题的有效方法，并在虚拟现实、自动驾驶等领域有着广泛的应用前景。基于物理的可微渲染旨在对基于物理的渲染管线进行可微化改造，主要涉及对场景几何和材质的表达，以及光路传输模拟过程的梯度计算方法。本文对近年来基于物理的可微渲染领域的发展情况进行了调研，总结了基于物理的可微渲染研究进展。首先总体介绍正向渲染和可微渲染的计算方法；然后介绍如何针对具体的几何、材质以及相机的表达方式进行梯度计算；讨论如何提高可微渲染的效率和鲁棒性；展示可微渲染如何应用于实际任务中；最后本文展望了可微渲染的发展趋势，期望推动该领域的进一步发展。

Abstract

Rendering has been a prominent subject in the field of computer graphics for an extended period. It can be regarded as a function that accepts an abstract scene description as input and typically generates a 2D image as output. The theory and practice of rendering have remarkably advanced through years of research. In recent years， inverse rendering has emerged as a new research focus in the field of computer graphics due to the development of digital technology. The objective of inverse rendering is to reverse the rendering process and deduce scene parameters from the output image， which is equivalent to solving the inverse function of the rendering function. This process plays a crucial role in addressing perception problems in diverse advanced technological domains， including virtual reality， autonomous driving， and robotics. Numerous methods exist for implementing inverse rendering， with the current mainstream framework being optimization through “analysis by synthesis”. First， it estimates a set of initial scene parameters， then performs forward rendering on the scene， compares the rendered result with the target image， and then minimizes the difference （loss function） by optimizing the scene parameters using gradient descent-based method. This pipeline necessitates the ability to compute the derivatives of the output image in forward rendering with respect to the input parameters. Consequently， differentiable rendering has emerged to fulfill this requirement. Specifically， the research topic of differentiable rendering is to convert the forward rendering pipeline in computer graphics into a differentiable form， enabling the differentiation of the output image with respect to input parameters such as geometry， material， light source， and camera. Currently， forward rendering can be broadly categorized into three types： rasterization-based rendering， physically based rendering， and the emerging neural rendering. Rasterization-based rendering is a fundamental technique in computer graphics that converts geometric shapes into pixels for display. It involves projecting 3D objects onto a 2D screen， performing hidden surface removal， shading， and texturing to create realistic images efficiently. While rasterization is fast and suitable for real-time applications， it may lack physical accuracy in simulating light interactions. By contrast， physically based rendering aims to simulate real-world light behavior accurately by considering the physical properties of materials， light sources， and the environment. It calculates how light rays interact with surfaces， accounting for reflections， refractions， and scattering to produce photorealistic visual results. This method prioritizes realism and is widely used in industries， such as animation， gaming， and visual effects. Neural rendering is an emerging rendering technique in recent years， mainly used for image-based rendering tasks. In contrast to traditional graphics rendering， image-based rendering does not require any explicit 3D scene information （geometry， materials， lighting， etc.）， but instead implicitly encodes scenes through a sequence of 2D images sampled from different viewpoints， enabling the generation of images of the scene from any viewpoint. Accordingly， differentiable rendering can also be categorized into three types： differentiable rasterization， physically based differentiable rendering， and differentiable neural rendering. In differentiable rasterization， many works employ approximate methods to compute approximate derivatives of the rasterization process for backpropagation of gradients or modify steps in the traditional rendering pipeline （usually rasterization and testing/blending steps） to make pixels differentiable with respect to vertices. Neural rendering is naturally differentiable because its rendering process is conducted through neural networks. For physically based differentiable rendering， accurately calculating the gradient of the image concerning scene parameters is challenging because of the intricate nature of geometry， material， and light transmission processes. Therefore， this study concentrates on recent research in the field of physically based differentiable rendering. The article is organized into the following sections： Section 1 introduces the computational methods of forward rendering and differentiable rendering from an abstract standpoint and two types of method for correctly computing boundary integral： edge sampling and reparameterization. Section 2 explores the attainment of differentiable rendering for distinct representations of geometry， such as volumetric representation， signed distance field， height field， and vectorized geometry； materials， such as volumetric material； parameterized bidirectional reflectance distribution function， bidirectional surface scattering reflectance distribution function， and continuously varying refractive index fields； and camera-related parameters， such as pixel reconstruction filter and time-of-flight camera. Section 3 focuses on enhancing the efficiency and robustness of differentiable rendering， including efficient sampling， high-efficiency system and framework， language for differentiable rendering and several techniques， to enhance the robustness of differentiable rendering. Section 4 showcases the application of differentiable rendering in practical tasks， which can be generally divided in three types： single-object reconstruction， object and environment light reconstruction， and scene reconstruction. Section 5 discusses the future development trends of differentiable rendering， including improving efficiency， robustness of differentiable rendering， and combining differentiable rendering with other methods.

关键词

Keywords

references

Azinovic D ， Li T M ， Kaplanyan A and Nießner M . 2019 . Inverse path tracing for joint material and lighting estimation // Proceedings of 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition （CVPR） . Long Beach， USA ： IEEE： 2442 - 2451 ［ DOI： 10.1109/CVPR.2019.00255 http://dx.doi.org/10.1109/CVPR.2019.00255 ］

Balint M ， Myszkowski K ， Seidel H P and Singh G . 2023 . Joint sampling and optimisation for inverse rendering // Proceedings of 2023 SIGGRAPH Asia Conference Papers . New York， USA ： Association for Computing Machinery： 1 - 10 ［ DOI： 10.1145/3610548.3618244 http://dx.doi.org/10.1145/3610548.3618244 ］

Bangaru S P ， Gharbi M ， Luan F J ， Li T M ， Sunkavalli K ， Hasan M ， Bi S ， Xu Z X ， Bernstein G and Durand F . 2022 . Differentiable rendering of neural SDFs through reparameterization // Proceedings of 2023 SIGGRAPH Asia Conference Papers . New York， USA ： Association for Computing Machinery： 1 - 9 ［ DOI： 10.1145/3550469.3555397 http://dx.doi.org/10.1145/3550469.3555397 ］

Bangaru S P ， Li T M and Durand F . 2020 . Unbiased warped-area sampling for differentiable rendering . ACM Transactions on Graphics ， 39 （ 6 ）： # 245 ［ DOI： 10.1145/3414685.3417833 http://dx.doi.org/10.1145/3414685.3417833 ］

Bangaru S P ， Michel J ， Mu K ， Bernstein G ， Li T M and Ragan-Kelley J . 2021 . Systematically differentiating parametric discontinuities . ACM Transactions on Graphics ， 40 （ 4 ）： # 107 ［ DOI： 10.1145/3450626.3459775 http://dx.doi.org/10.1145/3450626.3459775 ］

Bangaru S P ， Wu L F ， Li T M ， Munkberg J ， Bernstein G ， Ragan-Kelley J ， Durand F ， Lefohn A and He Y . 2023 . SLANG.D： fast， modular and differentiable shader programming . ACM Transactions on Graphics ， 42 （ 6 ）： # 264 ［ DOI： 10.1145/3618353 http://dx.doi.org/10.1145/3618353 ］

Cai G Y ， Yan K ， Dong Z ， Gkioulekas I and Zhao S . 2022 . Physics-based inverse rendering using combined implicit and explicit geometries . Computer Graphics Forum ， 41 （ 4 ）： 129 - 138 ［ DOI： 10.1111/cgf.14592 http://dx.doi.org/10.1111/cgf.14592 ］

Chang W ， Sivaram V ， Nowrouzezahrai D ， Hachisuka T ， Ramamoorthi R and Li T M . 2023 . Parameter-space ReSTIR for differentiable and inverse rendering // Proceedings of 2023 ACM SIGGRAPH Conference Proceedings . New York， USA ： Association for Computing Machinery： 1 - 10 ［ DOI： 10.1145/3588432.3591512 http://dx.doi.org/10.1145/3588432.3591512 ］

Czerninski I and Schechner Y Y . 2023 . PARS-Path recycling and sorting for efficient cloud tomography . Intelligent Computing ， 2 ： # 0007 ［ DOI： 10.34133/icomputing.0007 http://dx.doi.org/10.34133/icomputing.0007 ］

Deng X ， Luan F J ， Walter B ， Bala K and Marschner S . 2022 . Reconstructing translucent objects using differentiable rendering // Proceedings of 2022 ACM SIGGRAPH Conference Proceedings . Vancouver， Canada ： ACM： 1 - 10 ［ DOI： 10.1145/3528233.3530714 http://dx.doi.org/10.1145/3528233.3530714 ］

Fischer M and Ritschel T . 2023 . Plateau-reduced differentiable path tracing // Proceedings of 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition （CVPR） . Vancouver， Canada ： IEEE： 4285 - 4294 ［ DOI： 10.1109/CVPR52729.2023.00417 http://dx.doi.org/10.1109/CVPR52729.2023.00417 ］

Gao F Z ， Zhang L H ， Wang L ， Cheng J M and Zhang J W . 2023 . Transparent object reconstruction via implicit differentiable refraction rendering // Proceedings of 2023 SIGGRAPH Asia Conference Papers . Sydney， Australia ： ACM： 1 - 11 ［ DOI： 10.1145/3610548.3618236 http://dx.doi.org/10.1145/3610548.3618236 ］

Gkioulekas I ， Levin A and Zickler T . 2016 . An evaluation of computational imaging techniques for heterogeneous inverse scattering // Proceedings of the 14th European Conference ， Computer Vision ——ECCV 2016. Amsterdam， the Netherlands ： Springer International Publishing： 685 - 701 ［ DOI： 10.1007/978-3-319-46487-9_42 http://dx.doi.org/10.1007/978-3-319-46487-9_42 ］

Gkioulekas I ， Zhao S ， Bala K ， Zickler T and Levin A . 2013 . Inverse volume rendering with material dictionaries . ACM Transactions on Graphics ， 32 （ 6 ）： # 162 ［ DOI： 10.1145/2508363.2508377 http://dx.doi.org/10.1145/2508363.2508377 ］

Goel P ， Cohen L ， Guesman J ， Thamizharasan V ， Tompkin J and Ritchie D . 2020 . Shape from tracing： towards reconstructing 3D object geometry and SVBRDF material from images via differentiable path tracing // Proceedings of 2020 International Conference on 3D Vision （3DV） . Fukuoka， Japan ： IEEE Computer Society： 1186 - 1195 ［ DOI： 10.1109/3DV50981.2020.00129 http://dx.doi.org/10.1109/3DV50981.2020.00129 ］

Hasselgren J ， Hofmann N and Munkberg J . 2022 . Shape ， light， and material decomposition from images using Monte Carlo rendering and denoising// Proceedings of the 36th International Conference on Neural Information Processing Systems . New Orleans， USA ： Curran Associates Inc. ， 35 ： 22856 - 22869

Jakob W ， Speierer S ， Roussel N and Vicini D . 2022 . DR.JIT： a just-in-time compiler for differentiable rendering . ACM Transactions on Graphics ， 41 （ 4 ）： # 124 ［ DOI： 10.1145/3528223.3530099 http://dx.doi.org/10.1145/3528223.3530099 ］

Kajiya J T . 1986 . The rendering equation // Proceedings of the 13th Annual Conference on Computer Graphics and Interactive Techniques . New York， USA ： Association for Computing Machinery： 143 - 150 ［ DOI： 10.1145/15922.15902 http://dx.doi.org/10.1145/15922.15902 ］

Khungurn P ， Schroeder D ， Zhao S ， Bala K and Marschner S . 2015 . Matching real fabrics with micro-appearance models . ACM Transactions on Graphics ， 35 （ 1 ）： # 1 ［ DOI： 10.1145/2818648 http://dx.doi.org/10.1145/2818648 ］

Leal L G . 2007 . Advanced Transport Phenomena： Fluid Mechanics and Convective Transport Processes. Cambridge Series in Chemical Engineering . Cambridge ： Cambridge University Press . ［ DOI： 10.1017/CBO9780511800245 http://dx.doi.org/10.1017/CBO9780511800245 ］

Levis A ， Schechner Y Y ， Aides A and Davis A B . 2015 . Airborne three-dimensional cloud tomography // Proceedings of 2015 IEEE International Conference on Computer Vision （ICCV） . Santiago， Chile ： IEEE： 3379 - 3387 ［ DOI： 10.1109/ICCV.2015.386 http://dx.doi.org/10.1109/ICCV.2015.386 ］

Li T M ， Aittala M ， Durand F and Lehtinen J . 2018 . Differentiable Monte Carlo ray tracing through edge sampling . ACM Transactions on Graphics ， 37 （ 6 ）： # 222 ［ DOI： 10.1145/3272127.3275109 http://dx.doi.org/10.1145/3272127.3275109 ］

Loubet G ， Holzschuch N and Jakob W . 2019 . Reparameterizing discontinuous integrands for differentiable rendering . ACM Transactions on Graphics ， 38 （ 6 ）： # 228 ［ DOI： 10.1145/3355089.3356510 http://dx.doi.org/10.1145/3355089.3356510 ］

Luan F J ， Zhao S ， Bala K and Dong Z . 2021 . Unified shape and SVBRDF recovery using differentiable Monte Carlo rendering . Computer Graphics Forum ， 40 （ 4 ）： 101 - 113 ［ DOI： 10.1111/cgf.14344 http://dx.doi.org/10.1111/cgf.14344 ］

Lyu J H ， Wu B J ， Lischinski D ， Cohen-Or D and Huang H . 2020 . Differentiable refraction-tracing for mesh reconstruction of transparent objects . ACM Transactions on Graphics ， 39 （ 6 ）： # 195 ［ DOI： 10.1145/3414685.3417815 http://dx.doi.org/10.1145/3414685.3417815 ］

Lyu L J ， Tewari A ， Habermann M ， Saito S ， Zollhöfer M ， Leimkühler T and Theobalt C . 2023 . Diffusion posterior illumination for ambiguity-aware inverse rendering . ACM Transactions on Graphics ， 42 （ 6 ）： # 233 ［ DOI： 10.1145/3618357 http://dx.doi.org/10.1145/3618357 ］

Müller T ， Rousselle F ， Nov􀅡k J and Keller A . 2021 . Real-time neural radiance caching for path tracing . ACM Transactions on Graphics ， 40 （ 4 ）： # 36 ［ DOI： 10.1145/3450626.3459812 http://dx.doi.org/10.1145/3450626.3459812 ］

Nicolet B ， Jacobson A and Jakob W . 2021 . Large steps in inverse rendering of geometry . ACM Transactions on Graphics ， 40 （ 6 ）： # 248 ［ DOI： 10.1145/3478513.3480501 http://dx.doi.org/10.1145/3478513.3480501 ］

Nicolet B ， Rousselle F ， Novak J ， Keller A ， Jakob W and Müller T . 2023 . Recursive control variates for inverse rendering . ACM Transactions on Graphics ， 42 （ 4 ）： # 62 ［ DOI： 10.1145/3592139 http://dx.doi.org/10.1145/3592139 ］

Nimier-David M ， Dong Z ， Jakob W and Kaplanyan A . 2021 . Material and lighting reconstruction for complex indoor scenes with texture-space differentiable rendering // Proceedings of 2021 Eurographics Symposium on Rendering （DL-only Track） . The Eurographics Association ［ DOI： 10.2312/sr.20211292 http://dx.doi.org/10.2312/sr.20211292 ］

Nimier-David M ， Müller T ， Keller A and Jakob W . 2022 . Unbiased inverse volume rendering with differential trackers . ACM Transactions on Graphics ， 41 （ 4 ）： # 44 ［ DOI： 10.1145/3528223.3530073 http://dx.doi.org/10.1145/3528223.3530073 ］

Nimier-David M ， Speierer S ， Ruiz B and Jakob W . 2020 . Radiative backpropagation： an adjoint method for lightning-fast differentiable rendering . ACM Transactions on Graphics ， 39 （ 4 ）： # 146 ［ DOI： 10.1145/3386569.3392406 http://dx.doi.org/10.1145/3386569.3392406 ］

Nimier-David M ， Vicini D ， Zeltner T and Jakob W . 2019 . Mitsuba 2： a retargetable forward and inverse renderer . ACM Transactions on Graphics ， 38 （ 6 ）： # 203 ［ DOI： 10.1145/3355089.3356498 http://dx.doi.org/10.1145/3355089.3356498 ］

Nindel T K ， Iser T ， Rittig T ， Wilkie A and Křiv􀅡nek J . 2021 . A gradient-based framework for 3D print appearance optimization . ACM Transactions on Graphics ， 40 （ 4 ）： # 178 ［ DOI： 10.1145/3450626.3459844 http://dx.doi.org/10.1145/3450626.3459844 ］

Palfinger W . 2022 . Continuous remeshing for inverse rendering . Computer Animation and Virtual Worlds ， 33 （ 5 ）： #e 2101 ［ DOI： 10.1002/cav.2101 http://dx.doi.org/10.1002/cav.2101 ］

Shem-Tov K ， Bangaru S P ， Levin A and Gkioulekas I . 2020 . Towards reflectometry from interreflections // Proceedings of 2020 IEEE International Conference on Computational Photography （ICCP） . Saint Louis， USA ： IEEE： 1 - 12 ［ DOI： 10.1109/ICCP48838.2020.9105251 http://dx.doi.org/10.1109/ICCP48838.2020.9105251 ］

Shen T C ， Gao J ， Yin K X ， Liu M Y and Fidler S . 2021 . Deep marching Tetrahedra： a hybrid representation for high-resolution 3D shape synthesis //Proceedings of the 35th Conference on Neural Information Processing Systems. ［s.l.］： Curran Associates Inc .： 6087 - 6101

Teh A ， O’Toole M and Gkioulekas I . 2022 . Adjoint nonlinear ray tracing . ACM Transactions on Graphics ， 41 （ 4 ）： # 126 ［ DOI： 10.1145/3528223.3530077 http://dx.doi.org/10.1145/3528223.3530077 ］

Tong X C ， Liu H T D ， Gingold Y and Jacobson A . 2023 . Differentiable heightfield path tracing with accelerated discontinuities // Proceedings of 2023 ACM SIGGRAPH Conference Proceedings . New York， USA ： Association for Computing Machinery： 1 - 9 ［ DOI： 10.1145/3588432.3591530 http://dx.doi.org/10.1145/3588432.3591530 ］

Velinov Z ， Papas M ， Bradley D ， Gotardo P ， Mirdehghan P ， Marschner S ， Nov􀅡k J and Beeler T . 2018 . Appearance capture and modeling of human teeth . ACM Transactions on Graphics ， 37 （ 6 ）： # 207 ［ DOI： 10.1145/3272127.3275098 http://dx.doi.org/10.1145/3272127.3275098 ］

Vicini D ， Speierer S and Jakob W . 2021 . Path replay backpropagation： differentiating light paths using constant memory and linear time . ACM Transactions on Graphics ， 40 （ 4 ）： # 108 ［ DOI： 10.1145/3450626.3459804 http://dx.doi.org/10.1145/3450626.3459804 ］

Vicini D ， Speierer S and Jakob W . 2022 . Differentiable signed distance function rendering . ACM Transactions on Graphics ， 41 （ 4 ）： # 125 ［ DOI： 10.1145/3528223.3530139 http://dx.doi.org/10.1145/3528223.3530139 ］

Wang Y C ， Wyman C ， Wu L F and Zhao S . 2023 . Amortizing samples in physics-based inverse rendering using ReSTIR . ACM Transactions on Graphics ， 42 （ 6 ）： # 214 ［ DOI： 10.1145/3618331 http://dx.doi.org/10.1145/3618331 ］

Worchel M and Alexa M . 2023 . Differentiable rendering of parametric geometry . ACM Transactions on Graphics ， 42 （ 6 ）： # 232 ［ DOI： 10.1145/3618387 http://dx.doi.org/10.1145/3618387 ］

Wu J X ， Lin Y and Lu D H . 2023 . DR-Occluder： generating Occluders using differentiable rendering . ACM Transactions on Graphics ， 42 （ 6 ）： # 231 ［ DOI： 10.1145/3618346 http://dx.doi.org/10.1145/3618346 ］

Wu L F ， Cai G Y ， Ramamoorthi R and Zhao S . 2021 . Differentiable time-gated rendering . ACM Transactions on Graphics ， 40 （ 6 ）： # 287 ［ DOI： 10.1145/3478513.3480489 http://dx.doi.org/10.1145/3478513.3480489 ］

Xing J K ， Hu X J ， Luan F J ， Yan L Q and Xu K . 2023 . Extended path space manifolds for physically based differentiable rendering // Proceedings of 2023 SIGGRAPH Asia Conference Papers . Sydney， Australia ： ACM： 1 - 11 ［ DOI： 10.1145/3610548.3618195 http://dx.doi.org/10.1145/3610548.3618195 ］

Xing J K ， Luan F J ， Yan L Q ， Hu X J ， Qian H D and Xu K . 2022 . Differentiable rendering using RGBXY derivatives and optimal transport . ACM Transactions on Graphics ， 41 （ 6 ）： # 189 ［ DOI： 10.1145/3550454.3555479 http://dx.doi.org/10.1145/3550454.3555479 ］

Xu P Y ， Bangaru S ， Li T M and Zhao S . 2023 . Warped-area Reparameterization of differential path integrals . ACM Transactions on Graphics ， 42 （ 6 ）： # 213 ［ DOI： 10.1145/3618330 http://dx.doi.org/10.1145/3618330 ］

Xu W W ， Zhou Y ， Wu H Z and Guo J . 2021 . Differential rendering： a survey . Journal of Image and Graphics ， 26 （ 6 ）： 1521 - 1535 .

许威威，周漾，吴鸿智，过洁 . 2021 . 可微绘制技术研究进展 . 中国图象图形学报， 26 （ 6 ）： 1521 - 1535 ［ DOI： 10.11834/jig.200853 http://dx.doi.org/10.11834/jig.200853 ］

Yan K ， Lassner C ， Budge B ， Dong Z and Zhao S . 2022 . Efficient estimation of boundary integrals for path-space differentiable rendering . ACM Transactions on Graphics ， 41 （ 4 ）： # 123 ［ DOI： 10.1145/3528223.3530080 http://dx.doi.org/10.1145/3528223.3530080 ］

Yan K ， Luan F J ， Hašan M ， Groueix T ， Deschaintre V and Zhao S . 2023 . PSDR-Room： single photo to scene using differentiable rendering // Proceedings of 2023 SIGGRAPH Asia Conference Papers . Sydney， Australia ： ACM： 1 - 11 ［ DOI： 10.1145/3610548.3618165 http://dx.doi.org/10.1145/3610548.3618165 ］

Yang Y T ， Barnes C ， Adams A and Finkelstein A . 2022 . A δ ： autodiff for discontinuous programs-applied to shaders . ACM Transactions on Graphics ， 41 （ 4 ）： # 135 ［ DOI： 10.1145/3528223.3530125 http://dx.doi.org/10.1145/3528223.3530125 ］

Ye Z P ， Xia W Y ， Sun Z Y ， Yi R ， Yu M J and Liu Y J . 2021 . From traditional rendering to differentiable rendering： theories， methods and applications . Scientia Sinica Informationis ， 51 （ 7 ）： 1043 - 1067

叶子鹏，夏雯宇，孙志尧，易冉，余旻婧，刘永进 . 2021 . 从传统渲染到可微渲染：基本原理、方法和应用 . 中国科学：信息科学）， 51 （ 7 ）： 1043 - 1067 ［ DOI： 10.1360/SSI-2020-0272 http://dx.doi.org/10.1360/SSI-2020-0272 ］

Yi S ， Kim D ， Choi K ， Jarabo A ， Gutierrez D and Kim M H . 2021 . Differentiable transient rendering . ACM Transactions on Graphics ， 40 （ 6 ）： # 286 ［ DOI： 10.1145/3478513.3480498 http://dx.doi.org/10.1145/3478513.3480498 ］

Yu Z H ， Zhang C ， Maury O ， Hery C ， Dong Z and Zhao S . 2023 . Efficient path-space differentiable volume rendering with respect to shapes . Computer Graphics Forum ， 42 （ 4 ）： #e 14884 ［ DOI： 10.1111/cgf.14884 http://dx.doi.org/10.1111/cgf.14884 ］

Yu Z H ， Zhang C ， Nowrouzezahrai D ， Dong Z and Zhao S . 2022 . Efficient differentiation of pixel reconstruction filters for path-space differentiable rendering . ACM Transactions on Graphics ， 41 （ 6 ）： # 191 ［ DOI： 10.1145/3550454.3555500 http://dx.doi.org/10.1145/3550454.3555500 ］

Zeltner T ， Speierer S ， Georgiev I and Jakob W . 2021 . Monte Carlo estimators for differential light transport . ACM Transactions on Graphics ， 40 （ 4 ）： # 78 ［ DOI： 10.1145/3450626.3459807 http://dx.doi.org/10.1145/3450626.3459807 ］

Zhang C ， Dong Z ， Doggett M and Zhao S . 2021a . Antithetic sampling for Monte Carlo differentiable rendering . ACM Transactions on Graphics ， 40 （ 4 ）： # 77 ［ DOI： 10.1145/3450626.3459783 http://dx.doi.org/10.1145/3450626.3459783 ］

Zhang C ， Miller B ， Yan K ， Gkioulekas I and Zhao S . 2020 . Path-space differentiable rendering . ACM Transactions on Graphics ， 39 （ 4 ）： # 143 ［ DOI： 10.1145/3386569.3392383 http://dx.doi.org/10.1145/3386569.3392383 ］

Zhang C ， Wu L F ， Zheng C X ， Gkioulekas I ， Ramamoorthi R and Zhao S . 2019 . A differential theory of radiative transfer . ACM Transactions on Graphics ， 38 （ 6 ）： # 227 ［ DOI： 10.1145/3355089.3356522 http://dx.doi.org/10.1145/3355089.3356522 ］

Zhang C ， Yu Z H and Zhao S . 2021b . Path-space differentiable rendering of participating media . ACM Transactions on Graphics ， 40 （ 4 ）： # 76 ［ DOI： 10.1145/3450626.3459782 http://dx.doi.org/10.1145/3450626.3459782 ］

Zhang Z Y ， Roussel N and Jakob W . 2023 . Projective sampling for differentiable rendering of geometry . ACM Transactions on Graphics ， 42 （ 6 ）： # 212 ［ DOI： 10.1145/3618385 http://dx.doi.org/10.1145/3618385 ］

Zhao S ， Wu L F ， Durand F and Ramamoorthi R . 2016 . Downsampling scattering parameters for rendering anisotropic media . ACM Transactions on Graphics ， 35 （ 6 ）： # 166 ［ DOI： 10.1145/2980179.2980228 http://dx.doi.org/10.1145/2980179.2980228 ］

Zheng S K ， Zhou Z Q ， Chen X ， Yan D F ， Zhang C Y ， Geng Y F ， Gu Y and Xu K . 2022 . LuisaRender： a high-performance rendering framework with layered and unified interfaces on stream architectures . ACM Transactions on Graphics ， 41 （ 6 ）： # 232 ［ DOI： 10.1145/3550454.3555463 http://dx.doi.org/10.1145/3550454.3555463 ］

Zhou Y ， Wu L F ， Ramamoorthi R and Yan L Q . 2021 . Vectorization for fast， analytic， and differentiable visibility . ACM Transactions on Graphics ， 40 （ 3 ）： # 27 ［ DOI： 10.1145/3452097 http://dx.doi.org/10.1145/3452097 ］