Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
research-article

Path-space differentiable rendering

Published: 12 August 2020 Publication History
  • Get Citation Alerts
  • Abstract

    Physics-based differentiable rendering, the estimation of derivatives of radiometric measures with respect to arbitrary scene parameters, has a diverse array of applications from solving analysis-by-synthesis problems to training machine learning pipelines incorporating forward rendering processes. Unfortunately, general-purpose differentiable rendering remains challenging due to the lack of efficient estimators as well as the need to identify and handle complex discontinuities such as visibility boundaries.
    In this paper, we show how path integrals can be differentiated with respect to arbitrary differentiable changes of a scene. We provide a detailed theoretical analysis of this process and establish new differentiable rendering formulations based on the resulting differential path integrals. Our path-space differentiable rendering formulation allows the design of new Monte Carlo estimators that offer significantly better efficiency than state-of-the-art methods in handling complex geometric discontinuities and light transport phenomena such as caustics.
    We validate our method by comparing our derivative estimates to those generated using the finite-difference method. To demonstrate the effectiveness of our technique, we compare inverse-rendering performance with a few state-of-the-art differentiable rendering methods.

    Supplementary Material

    VTT File (3386569.3392383.vtt)
    ZIP File (a143-zhang.zip)
    Supplemental files.
    MP4 File (3386569.3392383.mp4)
    Presentation video

    References

    [1]
    Luke Anderson, Tzu-Mao Li, Jaakko Lehtinen, and Frédo Durand. 2017. Aether: an embedded domain specific sampling language for Monte Carlo rendering. ACM
    [2]
    Trans. Graph. 36, 4 (2017), 99:1--99:16.
    [3]
    James Arvo. 1994. The Irradiance Jacobian for partially occluded polyhedral sources. In SIGGRAPH '94. 343--350.
    [4]
    Dejan Azinovic, Tzu-Mao Li, Anton Kaplanyan, and Matthias Niessner. 2019. Inverse Path Tracing for Joint Material and Lighting Estimation. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR).
    [5]
    Paolo Cermelli, Eliot Fried, and Morton E Gurtin. 2005. Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces. Journal of Fluid Mechanics 544 (2005), 339--351.
    [6]
    Subrahmanyan Chandrasekhar. 1960. Radiative Transfer. Courier Corporation.
    [7]
    Chengqian Che, Fujun Luan, Shuang Zhao, Kavita Bala, and Ioannis Gkioulekas. 2018. Inverse transport networks. arXiv preprint arXiv:1809.10820 (2018).
    [8]
    Min Chen and James Arvo. 2000. Theory and application of specular path perturbation. ACM Trans. Graph. 19, 4 (2000), 246--278.
    [9]
    Ioannis Gkioulekas, Anat Levin, and Todd Zickler. 2016. An Evaluation of Computational Imaging Techniques for Heterogeneous Inverse Scattering. In Computer Vision - ECCV 2016. Springer International Publishing, 685--701.
    [10]
    Ioannis Gkioulekas, Shuang Zhao, Kavita Bala, Todd Zickler, and Anat Levin. 2013. Inverse volume rendering with material dictionaries. ACM Trans. Graph. 32, 6 (2013), 162:1--162:13.
    [11]
    Andreas Griewank and Andrea Walther. 2008. Evaluating derivatives: principles and techniques of algorithmic differentiation. Vol. 105. Siam.
    [12]
    Pavel Grinfeld. 2013. Introduction to tensor analysis and the calculus of moving surfaces. Springer.
    [13]
    Morton E Gurtin. 1981. An introduction to continuum mechanics. Academic press.
    [14]
    Milovš Hašan and Ravi Ramamoorthi. 2013. Interactive albedo editing in path-traced volumetric materials. ACM Trans. Graph. 32, 2 (2013), 11:1--11:11.
    [15]
    Homan Igehy. 1999. Tracing ray differentials. In SIGGRAPH '99. 179--186.
    [16]
    Wenzel Jakob and Steve Marschner. 2012. Manifold Exploration: A Markov Chain Monte Carlo Technique for Rendering Scenes with Difficult Specular Transport. ACM Trans. Graph. 31, 4 (2012), 58:1--58:13.
    [17]
    Henrik Wann Jensen. 1995. Importance driven path tracing using the photon map. In Rendering Techniques' 95. Springer, 326--335.
    [18]
    James T. Kajiya. 1986. The Rendering Equation. SIGGRAPH Comput. Graph. 20, 4 (1986), 143--150.
    [19]
    Hiroharu Kato, Yoshitaka Ushiku, and Tatsuya Harada. 2018. Neural 3D mesh renderer. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 3907--3916.
    [20]
    Csaba Kelemen, László Szirmay-Kalos, György Antal, and Ferenc Csonka. 2002. A simple and robust mutation strategy for the Metropolis light transport algorithm. In Computer Graphics Forum, Vol. 21. Wiley Online Library, 531--540.
    [21]
    Pramook Khungurn, Daniel Schroeder, Shuang Zhao, Kavita Bala, and Steve Marschner. 2015. Matching real fabrics with micro-appearance models. ACM Trans. Graph. 35, 1 (2015), 1:1--1:26.
    [22]
    Diederik P Kingma and Jimmy Ba. 2014. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014).
    [23]
    Tzu-Mao Li, Miika Aittala, Frédo Durand, and Jaakko Lehtinen. 2018a. Differentiable Monte Carlo ray tracing through edge sampling. ACM Trans. Graph. 37, 6 (2018), 222:1--222:11.
    [24]
    Tzu-Mao Li, Jaakko Lehtinen, Ravi Ramamoorthi, Wenzel Jakob, and Frédo Durand. 2015. Anisotropic Gaussian mutations for Metropolis light transport through Hessian-Hamiltonian dynamics. ACM Trans. Graph. 34, 6 (2015), 209:1--209:13.
    [25]
    Zhengqin Li, Zexiang Xu, Ravi Ramamoorthi, Kalyan Sunkavalli, and Manmohan Chandraker. 2018b. Learning to reconstruct shape and spatially-varying reflectance from a single image. ACM Trans. Graph. 37, 6 (2018), 269:1--269:11.
    [26]
    Matthew M Loper and Michael J Black. 2014. OpenDR: an approximate differentiable renderer. In European Conference on Computer Vision. Springer, 154--169.
    [27]
    Guillaume Loubet, Nicolas Holzschuch, and Wenzel Jakob. 2019. Reparameterizing discontinuous integrands for differentiable rendering. ACM Trans. Graph. 38, 6 (2019).
    [28]
    James L McClelland, David E Rumelhart, PDP Research Group, et al. 1986. Parallel distributed processing. Explorations in the microstructure of cognition 2 (1986), 216--271.
    [29]
    Abhimitra Meka, Maxim Maximov, Michael Zollhoefer, Avishek Chatterjee, Hans-Peter Seidel, Christian Richardt, and Christian Theobalt. 2018. Lime: Live intrinsic material estimation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 6315--6324.
    [30]
    Merlin Nimier-David, Delio Vicini, Tizian Zeltner, and Wenzel Jakob. 2019. Mitsuba 2: a retargetable forward and inverse renderer. ACM Transactions on Graphics (TOG) 38, 6 (2019), 203.
    [31]
    Mark Pauly, Thomas Kollig, and Alexander Keller. 2000. Metropolis light transport for participating media. In Rendering Techniques 2000. Springer, 11--22.
    [32]
    Ravi Ramamoorthi, Dhruv Mahajan, and Peter Belhumeur. 2007. A first-order analysis of lighting, shading, and shadows. ACM Trans. Graph. 26, 1 (2007), 2:1--2:21.
    [33]
    Osborne Reynolds. 1903. Papers on mechanical and physical subjects: the sub-mechanics of the universe. Vol. 3. The University Press.
    [34]
    Soumyadip Sengupta, Angjoo Kanazawa, Carlos D Castillo, and David W Jacobs. 2018. SfSNet: Learning shape, reflectance and illuminance of faces in the wild'. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 6296--6305.
    [35]
    Denis Sumin, Tobias Rittig, Vahid Babaei, Thomas Nindel, Alexander Wilkie, Piotr Didyk, Bernd Bickel, Jaroslav Křivánek, Karol Myszkowski, and Tim Weyrich. 2019. Geometry-aware scattering compensation for 3D printing. ACM Trans. Graph. 38, 4 (2019), 111:1--111:14.
    [36]
    Chia-Yin Tsai, Aswin C. Sankaranarayanan, and Ioannis Gkioulekas. 2019. Beyond volumetric albedo---a surface optimization framework for non-line-of-sight imaging. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR).
    [37]
    Eric Veach. 1997. Robust Monte Carlo methods for light transport simulation. Vol. 1610. Stanford University PhD thesis.
    [38]
    Eric Veach and Leonidas Guibas. 1995. Bidirectional estimators for light transport. In Photorealistic Rendering Techniques. Springer, 145--167.
    [39]
    Eric Veach and Leonidas J. Guibas. 1997. Metropolis Light Transport. In Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '97). ACM Press/Addison-Wesley Publishing Co., 65--76.
    [40]
    Zdravko Velinov, Marios Papas, Derek Bradley, Paulo Gotardo, Parsa Mirdehghan, Steve Marschner, Jan Novák, and Thabo Beeler. 2018. Appearance Capture and Modeling of Human Teeth. ACM Trans. Graph. 37, 6 (2018), 207:1--207:13.
    [41]
    Robert Edwin Wengert. 1964. A simple automatic derivative evaluation program. Commun. ACM 7, 8 (1964), 463--464.
    [42]
    Andrew P. Witkin and Paul S. Heckbert. 1994. Using particles to sample and control implicit surfaces. In Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '94). ACM, 269--277.
    [43]
    Jiajun Wu, Joshua B Tenenbaum, and Pushmeet Kohli. 2017. Neural scene de-rendering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 699--707.
    [44]
    Cheng Zhang, Lifan Wu, Changxi Zheng, Ioannis Gkioulekas, Ravi Ramamoorthi, and Shaung Zhao. 2019. A differential theory of radiative transfer. ACM Trans. Graph. 38, 6 (2019), 227:1--227:16.
    [45]
    Shuang Zhao, Lifan Wu, Frédo Durand, and Ravi Ramamoorthi. 2016. Downsampling scattering parameters for rendering anisotropic media. ACM Trans. Graph. 35, 6 (2016), 166:1--166:11.
    [46]
    Changxi Zheng and Doug L. James. 2012. Energy-based self-collision culling for arbitrary mesh deformations. ACM Trans. Graph. 31, 4 (2012), 98:1--98:12.

    Cited By

    View all
    • (2024)DEMO: Real-Time Simulation of Wireless Signal Propagation for Dynamic Environment Through GPU-Based Ray TracingProceedings of the ACM SIGCOMM 2024 Conference: Posters and Demos10.1145/3672202.3673725(98-100)Online publication date: 4-Aug-2024
    • (2024)View-Independent Adjoint Light Tracing for Lighting Design OptimizationACM Transactions on Graphics10.1145/366218043:3(1-16)Online publication date: 3-May-2024
    • (2024)Target-Aware Image Denoising for Inverse Monte Carlo RenderingACM Transactions on Graphics10.1145/365818243:4(1-11)Online publication date: 19-Jul-2024
    • Show More Cited By

    Index Terms

    1. Path-space differentiable rendering

      Recommendations

      Comments

      Information & Contributors

      Information

      Published In

      cover image ACM Transactions on Graphics
      ACM Transactions on Graphics  Volume 39, Issue 4
      August 2020
      1732 pages
      ISSN:0730-0301
      EISSN:1557-7368
      DOI:10.1145/3386569
      Issue’s Table of Contents
      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      Published: 12 August 2020
      Published in TOG Volume 39, Issue 4

      Permissions

      Request permissions for this article.

      Check for updates

      Author Tags

      1. Monte Carlo rendering
      2. differentiable rendering
      3. path integral

      Qualifiers

      • Research-article

      Contributors

      Other Metrics

      Bibliometrics & Citations

      Bibliometrics

      Article Metrics

      • Downloads (Last 12 months)70
      • Downloads (Last 6 weeks)11
      Reflects downloads up to 10 Aug 2024

      Other Metrics

      Citations

      Cited By

      View all
      • (2024)DEMO: Real-Time Simulation of Wireless Signal Propagation for Dynamic Environment Through GPU-Based Ray TracingProceedings of the ACM SIGCOMM 2024 Conference: Posters and Demos10.1145/3672202.3673725(98-100)Online publication date: 4-Aug-2024
      • (2024)View-Independent Adjoint Light Tracing for Lighting Design OptimizationACM Transactions on Graphics10.1145/366218043:3(1-16)Online publication date: 3-May-2024
      • (2024)Target-Aware Image Denoising for Inverse Monte Carlo RenderingACM Transactions on Graphics10.1145/365818243:4(1-11)Online publication date: 19-Jul-2024
      • (2024)Conditional Mixture Path Guiding for Differentiable RenderingACM Transactions on Graphics10.1145/365813343:4(1-11)Online publication date: 19-Jul-2024
      • (2024)Transforming a Non-Differentiable Rasterizer into a Differentiable One with Stochastic Gradient EstimationProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/36512987:1(1-16)Online publication date: 13-May-2024
      • (2024)Importance Sampling BRDF DerivativesACM Transactions on Graphics10.1145/364861143:3(1-21)Online publication date: 9-Apr-2024
      • (2024)Path-Space Differentiable Rendering of Implicit SurfacesACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657473(1-11)Online publication date: 13-Jul-2024
      • (2024)NeRF as a Non-Distant Environment Emitter in Physics-based Inverse RenderingACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657404(1-12)Online publication date: 13-Jul-2024
      • (2024)Aperture-Aware Lens DesignACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657398(1-10)Online publication date: 13-Jul-2024
      • (2024)Residual path integrals for re‐renderingComputer Graphics Forum10.1111/cgf.1515243:4Online publication date: 24-Jul-2024
      • Show More Cited By

      View Options

      Get Access

      Login options

      Full Access

      View options

      PDF

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader

      Media

      Figures

      Other

      Tables

      Share

      Share

      Share this Publication link

      Share on social media