Physically Based Rendering

Physically based rendering (PBR) is a computer graphics approach that seeks to render images in a way that models the flow of light in the real world. Many PBR pipelines aim to achieve photorealism. Feasible and quick approximations of the bidirectional reflectance distribution function and rendering equation are of mathematical importance in this field. Photogrammetry may be used to help discover and encode accurate optical properties of materials. Shaders may be used to implement PBR principles.

Shape, Light, and Material Decomposition from Images using Monte Carlo Rendering and Denoising

Jon Hasselgren, Nikolai Hofmann, Jacob Munkberg

NVIDIA

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Recent advances in differentiable rendering have enabled high-quality reconstruction of 3D scenes from multi-view images. Most methods rely on simple rendering algorithms: pre-filtered direct lighting or learned representations of irradiance. We show that a more realistic shading model, incorporating ray tracing and Monte Carlo integration, substantially improves decomposition into shape, materials & lighting. Unfortunately, Monte Carlo integration provides estimates with significant noise, even at large sample counts, which makes gradient-based inverse rendering very challenging. To address this, we incorporate multiple importance sampling and denoising in a novel inverse rendering pipeline. This substantially improves convergence and enables gradient-based optimization at low sample counts. We present an efficient method to jointly reconstruct geometry (explicit triangle meshes), materials, and lighting, which substantially improves material and light separation compared to previous work. We argue that denoising can become an integral part of high quality inverse rendering pipelines.

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Neural methods for multi-view reconstruction; BRDF and lighting estimation; Image denoisers

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nvdiffrec, NeRFactor

Path-Space Differentiable Rendering

Cheng Zhang, Bailey Miller, Kai Yan, Ioannis Gkioulekas, Shuang Zhao

University of California, Irvine; Carnegie Mellon University

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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.

Related Works

Path-space rendering; Derivatives for rendering; Physics-based differentiable rendering; Derivatives for vision; Automatic differentiation

Inverse Path Tracing for Joint Material and Lighting Estimation

Dejan Azinovi?, Tzu-Mao Li, Anton Kaplanyan, Matthias Nie

Technical University of Munich; MIT CSAIL; Facebook Reality Labs

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Modern computer vision algorithms have brought significant advancement to 3D geometry reconstruction. However, illumination and material reconstruction remain less studied, with current approaches assuming very simplified models for materials and illumination. We introduce Inverse Path Tracing, a novel approach to jointly estimate the material properties of objects and light sources in indoor scenes by using an invertible light transport simulation. We assume a coarse geometry scan, along with corresponding images and camera poses. The key contribution of this work is an accurate and simultaneous retrieval of light sources and physically based material properties (e.g., diffuse reflectance, specular reflectance, roughness, etc.) for the purpose of editing and re-rendering the scene under new conditions. To this end, we introduce a novel optimization method using a differentiable Monte Carlo renderer that computes derivatives with respect to the estimated unknown illumination and material properties. This enables joint optimization for physically correct light transport and material models using a tailored stochastic gradient descent.

The Rendering Equation

James T. Kajiya

California Institute of Technology

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We present an integral equation which generalizes a variety of known rendering algorithms. In the course of discussing a monte carlo solution we also present a new form of variance reduction, called Hierarchical sampling and give a number of elaborations shows that it may be an efficient new technique for a wide variety of monte carlo procedures. The resulting rendering algorithm extends the range of optical phenomena which can be effectively simulated.

Differentiable Signed Distance Function Rendering

Delio Vicini, S

École Polytechnique Fédérale de Lausanne (EPFL)

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Physically-based differentiable rendering has recently emerged as an attractive new technique for solving inverse problems that recover complete 3D scene representations from images. The inversion of shape parameters is of particular interest but also poses severe challenges: shapes are intertwined with visibility, whose discontinuous nature introduces severe bias in computed derivatives unless costly precautions are taken. Shape representations like triangle meshes suffer from additional difficulties, since the continuous optimization of mesh parameters cannot introduce topological changes. One common solution to these difficulties entails representing shapes using signed distance functions (SDFs) and gradually adapting their zero level set during optimization. Previous differentiable rendering of SDFs did not fully account for visibility gradients and required the use of mask or silhouette supervision, or discretization into a triangle mesh. In this article, we show how to extend the commonly used sphere tracing algorithm so that it additionally outputs a reparameterization that provides the means to compute accurate shape parameter derivatives. At a high level, this resembles techniques for differentiable mesh rendering, though we show that the SDF representation admits a particularly efficient reparameterization that outperforms prior work. Our experiments demonstrate the reconstruction of (synthetic) objects without complex regularization or priors, using only a per-pixel RGB loss.

NRTF: Neural Radiance Transfer Fields for Relightable Novel-view Synthesis with Global Illumination

Linjie Lyu, Ayush Tewari, Thomas Leimkuehler, Marc Habermann, Christian Theobalt

Max Planck Institute for Informatics, Saarland Informatics Campus; MIT

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Given a set of images of a scene, the re-rendering of this scene from novel views and lighting conditions is an important and challenging problem in Computer Vision and Graphics. On the one hand, most existing works in Computer Vision usually impose many assumptions regarding the image formation process, e.g. direct illumination and predefined materials, to make scene parameter estimation tractable. On the other hand, mature Computer Graphics tools allow modeling of complex photo-realistic light transport given all the scene parameters. Combining these approaches, we propose a method for scene relighting under novel views by learning a neural precomputed radiance transfer function, which implicitly handles global illumination effects using novel environment maps. Our method can be solely supervised on a set of real images of the scene under a single unknown lighting condition. To disambiguate the task during training, we tightly integrate a differentiable path tracer in the training process and propose a combination of a synthesized OLAT and a real image loss. Results show that the recovered disentanglement of scene parameters improves significantly over the current state of the art and, thus, also our re-rendering results are more realistic and accurate.

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Precomputed Radiance Transfer; Inverse Rendering and Relighting

NeILF: Neural Incident Light Field for Physically-based Material Estimation

Yao Yao, Jingyang Zhang, Jingbo Liu, Yihang Qu, Tian Fang, David McKinnon, Yanghai Tsin, Long Quan

Apple; HKUST

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We present a differentiable rendering framework for material and lighting estimation from multi-view images and a reconstructed geometry. In the framework, we represent scene lightings as the Neural Incident Light Field (NeILF) and material properties as the surface BRDF modelled by multi-layer perceptrons. Compared with recent approaches that approximate scene lightings as the 2D environment map, NeILF is a fully 5D light field that is capable of modelling illuminations of any static scenes. In addition, occlusions and indirect lights can be handled naturally by the NeILF representation without requiring multiple bounces of ray tracing, making it possible to estimate material properties even for scenes with complex lightings and geometries. We also propose a smoothness regularization and a Lambertian assumption to reduce the material-lighting ambiguity during the optimization. Our method strictly follows the physically-based rendering equation, and jointly optimizes material and lighting through the differentiable rendering process. We have intensively evaluated the proposed method on our in-house synthetic dataset, the DTU MVS dataset, and real-world BlendedMVS scenes. Our method is able to outperform previous methods by a significant margin in terms of novel view rendering quality, setting a new state-of-the-art for image-based material and lighting estimation.

Related Works

The Rendering Equation; Differentiable Rendering; Material and Lighting Estimation

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PhySG, SG-ENV, NeRFactor, NeRF

Physically Based Rendering: From Theory To Implementation, Third Edition

Matt Pharr, Wenzel Jakob, and Greg Humphreys

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Photorealistic computer graphics is ubiquitous today, with applications that include entertainment—notably, movies and video games; product design; and architecture. Over the past decade, physically-based approaches to rendering have become widely used, where an accurate modeling of the physics of light scattering is at the heart of image synthesis. These approaches offer both visual realism and predictability. Physically Based Rendering describes both the mathematical theory behind a modern photorealistic rendering system as well as its practical implementation. A method known as “literate programming” combines human-readable documentation and source code into a single reference that is specifically designed to aid comprehension. The ideas and software in this book show the reader how to design and employ a full-featured rendering system capable of creating stunning imagery.

Rendering Synthetic Objects into Real Scenes: Bridging Traditional and Image-based Graphics with Global Illumination and High Dynamic Range Photography

Paul Debevec

University of California at Berkeley

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We present a method that uses measured scene radiance and global illumination in order to add new objects to light-based models with correct lighting. The method uses a high dynamic range image-based model of the scene, rather than synthetic light sources, to illuminate the new objects. To compute the illumination, the scene is considered as three components: the distant scene, the local scene, and the synthetic objects. The distant scene is assumed to be photometrically unaffected by the objects, obviating the need for reflectance model information. The local scene is endowed with estimated reflectance model information so that it can catch shadows and receive reflected light from the new objects. Renderings are created with a standard global illumination method by simulating the interaction of light amongst the three components. A differential rendering technique allows for good results to be obtained when only an estimate of the local scene reflectance properties is known. We apply the general method to the problem of rendering synthetic objects into real scenes. The light-based model is constructed from an approximate geometric model of the scene and by using a light probe to measure the incident illumination at the location of the synthetic objects. The global illumination solution is then composited into a photograph of the scene using the differential rendering technique. We conclude by discussing the relevance of the technique to recovering surface reflectance properties in uncontrolled lighting situations. Applications of the method include visual effects, interior design, and architectural visualization.

Related Works

Optical Film Compositing; Global Illumination; Compositing Objects into Photography

BRDF: Geometrical Considerations and Nomenclature for Reflectance

F.E. Nicodemus, J.C. Richmond, J.J. Hsia, I.W. Ginsberg, T. Limperis

NATIONAL BUREAU OF STANDARDS

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A unified approach to the specification of reflectance, in terms of both incident- and reflected beam geometry, is presented. Nomenclature to facilitate this approach is proposed. Under specified conditions-including uniform irradiance, a uniform, isotropic, plane surface, and allowance for edge effects due to sub-surface scattering-the geometrical reflecting properties of a reflecting surface are readily characterized or specified in terms of the bidirectional reflectancedistribution function (BRDF). The BRDF is a derivative, a distribution function, relating the irradiance incident from one given direction to its contribution to the reflected radiance in another direction. Nomenclature (concepts, terms, symbols, and units) for categorizing and specifying reflectance quantities for a variety of different beam configurations (both incident and reflected beams) is described, and all are defined and interrelated in terms of the BRDF. The conditions under which the formalism can be applied, including situations involving considerable sub-surface scattering, are carefully established. The entire treatment is limited to the domain of classical geometrical-optics radiometry and does not take into account interference and diffraction phenomena, such as are frequently encountered with highly coherent radiant flux. The other radiation parameters such as wavelength, (temporal) modulation, and polarization and the effects of fluorescence (or phosphorescence) are discussed briefly.

Category: Physically Based Rendering

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