The Realist Graphic Computer Laboratory

Laboratory

Differentiable Physically Based Rendering: Algorithms, Systems and Applications

Physically based rendering methods can create photorealistic images by simulating the propagation and interaction of light in a virtual scene. Given a scene description including the shape of objects, participating media, material properties, etc., the simulation computes an image representing the radiance reaching the sensor.This thesis, however, pursues the corresponding inverse problem: given observations such as pictures of a scene, we want to recover a plausible description of its components. Unfortunately, the rendering process is typically far too complex to invert analytically. We therefore turn to iterative gradient-based approximations of the inverse, that require efficiently estimating gradients of an objective function with respect to the scene parameters of interest.The first part of this thesis is dedicated to algorithms for gradient estimation. We consider the usage of automatic differentiation and examine the associated tradeoffs. Next, we introduce radiative backpropagation, an adjoint method that casts the gradient estimation problem into a modified light transport problem, unlocking vastly more efficient implementations. For the case of participating media, we propose differential ratio tracking, a sampling technique that addresses the bias and high variance found in existing gradient estimators.In the second part, we focus on the design of systems to support effective differentiable rendering research, including the efficient implementation of the algorithms above. We describe the architecture and features of Mitsuba 2, an open-source retargetable physically based renderer. Mitsuba 2 supports different representations of colors (RGB, spectral, polarized), computing platforms (scalar, CPU vectorized, GPU), and numerical precision, within a single codebase. Importantly, automatic differentiation can be applied throughout the system. Then, we extend this design by applying an automatic conversion from wavefront-style rendering to a megakernel-based approach, leveraging just-in-time compilation. We obtain a fast, flexible and memory-efficient framework for primal and differentiable physically based rendering.Finally, the third part showcases three applications of differentiable physically based rendering: caustic design, inverse volume rendering, and material & lighting estimation in real indoor scenes. In all cases, special care is taken to avoid sub-optimal local minima due to the ambiguous and non-convex nature of the reconstruction problems.

EPFL2022

Dr.Jit: A Just-In-Time Compiler for Differentiable Rendering

Wenzel Alban Jakob, Nicolas Julien Roussel, Sébastien Nicolas Speierer, Delio Aleardo Vicini

Dr.Jit is a new just-in-time compiler for physically based rendering and its derivative. Dr.Jit expedites research on these topics in two ways: first, it traces high-level simulation code (e.g., written in Python) and aggressively simplifies and specializes the resulting program representation, producing data-parallel kernels with state-of-the-art performance on CPUs and GPUs. Second, it simplifies the development of differentiable rendering algorithms. Efficient methods in this area turn the derivative of a simulation into a simulation of the derivative. Dr.Jit provides fine-grained control over the process of automatic differentiation to help with this transformation. Specialization is particularly helpful in the context of differentiation, since large parts of the simulation ultimately do not influence the computed gradients. Dr.Jit tracks data dependencies globally to find and remove redundant computation.

ASSOC COMPUTING MACHINERY2022

Differentiable Signed Distance Function Rendering

Wenzel Alban Jakob, Sébastien Nicolas Speierer, Delio Aleardo Vicini

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.

ASSOC COMPUTING MACHINERY2022

Large Steps in Inverse Rendering of Geometry

Wenzel Alban Jakob, Baptiste Alexandre Marie Philippe Claude Nicolet

Inverse reconstruction from images is a central problem in many scientific and engineering disciplines. Recent progress on differentiable rendering has led to methods that can efficiently differentiate the full process of image formation with respect to millions of parameters to solve such problems via gradient-based optimization. At the same time, the availability of cheap derivatives does not necessarily make an inverse problem easy to solve. Mesh-based representations remain a particular source of irritation: an adverse gradient step involving vertex positions could turn parts of the mesh inside-out, introduce numerous local self-intersections, or lead to inadequate usage of the vertex budget due to distortion. These types of issues are often irrecoverable in the sense that subsequent optimization steps will further exacerbate them. In other words, the optimization lacks robustness due to an objective function with substantial non-convexity. Such robustness issues are commonly mitigated by imposing additional regularization, typically in the form of Laplacian energies that quantify and improve the smoothness of the current iterate. However, regularization introduces its own set of problems: solutions must now compromise between solving the problem and being smooth. Furthermore, gradient steps involving a Laplacian energy resemble Jacobi's iterative method for solving linear equations that is known for its exceptionally slow convergence. We propose a simple and practical alternative that casts differentiable rendering into the framework of preconditioned gradient descent. Our preconditioner biases gradient steps towards smooth solutions without requiring the final solution to be smooth. In contrast to Jacobi-style iteration, each gradient step propagates information among all variables, enabling convergence using fewer and larger steps. Our method is not restricted to meshes and can also accelerate the reconstruction of other representations, where smooth solutions are generally expected. We demonstrate its superior performance in the context of geometric optimization and texture reconstruction.

ASSOC COMPUTING MACHINERY2021

Differentiable inverse rendering based on radiative backpropagation

Wenzel Alban Jakob, Merlin Eléazar Nimier-David

A computer-implemented inverse rendering method is provided. The method comprises: computing an adjoint image by differentiating an objective function that evaluates the quality of a rendered image, image elements of the adjoint image encoding the sensitivity of spatially corresponding image elements of the rendered image with respect to the objective function; sampling the adjoint image at a respective sample position to determine a respective adjoint radiance value associated with the respective sample position; emitting the respective adjoint radiance value into a scene model characterised by scene parameters; determining an interaction location of a respective incident adjoint radiance value with a surface and/or volume of the scene model; determining a respective incident radiance value or an approximation thereof at the interaction location, the respective incident radiance value expressing the amount of incident radiance that travels from the surrounding environment towards the interaction location; and updating a scene parameter gradient by using at least the interaction location and the respective incident adjoint radiance value and the respective incident radiance value or its approximation at the interaction location.

2021

Light Path Gradients for Forward and Inverse Rendering

Tizian Lucien Zeltner

Physically based rendering is a process for photorealistic digital image synthesis and one of the core problems in computer graphics. It involves simulating the light transport, i.e. the emission, propagation, and scattering of light through a virtual scene that is defined by a detailed description of object geometry and appearance. Research over the last decades has led to sophisticated rendering techniques and recently, the inversion of this process, i.e. recovering scene parameters from image observations, has also received significant attention. In this thesis, we investigate methods in both physically based forward and inverse rendering that exploit light path gradients.The first part is concerned with scattering from specular surfaces, which produces complex optical effects that are frequently encountered in realistic scenes: intricate caustics due to focused reflection, multiple refractions, and high-frequency glints from specular microstructure. Yet, despite their importance and considerable research to this end, sampling of light paths that cause these effects remains a formidable challenge of forward rendering.We propose a surprisingly simple and general path sampling strategy that targets the examples above. Valid light path configurations need to fulfill the physical laws of reflection and refraction, and we find these using a numerical root-finding process that is driven by geometric light path gradients. In contrast to prior work, our method supports high-frequency normal- or displacement-mapped geometry, samples specular-diffuse-specular (SDS) paths, and is compatible with standard Monte Carlo methods including unidirectional path tracing. We demonstrate our method on a range of challenging scenes and evaluate it against state-of-the-art methods for rendering caustics and glints.In the second part, we consider differentiable rendering algorithms. These propagate derivatives through the full light transport simulation to solve inverse rendering problems via gradient-based optimization. Recent progress has led to methods that can simultaneously compute derivatives with respect to millions of scene parameters. At the same time, elementary properties of these methods remain poorly understood.Current algorithms for differentiable rendering are constructed by mechanically differentiating a given primal algorithm. As differentiation fundamentally changes the underlying problem, this is often suboptimal and instead, primal and differential algorithms should be decoupled so that the latter can suitably adapt. This is surprisingly complex. Even the most basic Monte Carlo path tracer already involves several design choices concerning the techniques for sampling materials and emitters, and their combination, e.g. via multiple importance sampling (MIS). Differentiation causes a veritable explosion of this decision tree: should we differentiate only the estimator, or also the sampling technique? Should MIS be applied before or after differentiation? Are specialized derivative sampling strategies of any use? How should visibility-related discontinuities be handled when millions of parameters are differentiated simultaneously? We provide a taxonomy and analysis of different estimators for differential light transport to provide intuition about these and related questions.

EPFL2021

A Non-Exponential Transmittance Model for Volumetric Scene Representations

Wenzel Alban Jakob, Delio Aleardo Vicini

We introduce a novel transmittance model to improve the volumetric representation of 3D scenes. The model can represent opaque surfaces in the volumetric light transport framework. Volumetric representations are useful for complex scenes, and become increasingly popular for level of detail and scene reconstruction. The traditional exponential transmittance model found in volumetric light transport cannot capture correlations in visibility across volume elements. When representing opaque surfaces as volumetric density, this leads to both bloating of silhouettes and light leaking artifacts. By introducing a parametric non-exponential transmittance model, we are able to approximate these correlation effects and significantly improve the accuracy of volumetric appearance representation of opaque scenes. Our parametric transmittance model can represent a continuum between the linear transmittance that opaque surfaces exhibit and the traditional exponential transmittance encountered in participating media and unstructured geometries. This covers a large part of the spectrum of geometric structures encountered in complex scenes. In order to handle the spatially varying transmittance correlation effects, we further extend the theory of non-exponential participating media to a heterogeneous transmittance model. Our model is compact in storage and computationally efficient both for evaluation and for reverse-mode gradient computation. Applying our model to optimization algorithms yields significant improvements in volumetric scene appearance quality. We further show improvements for relevant applications, such as scene appearance prefiltering, image-based scene reconstruction using differentiable rendering, neural representations, and compare it to a conventional exponential model.

ASSOC COMPUTING MACHINERY2021

Path Replay Backpropagation: Differentiating Light Paths using Constant Memory and Linear Time

Wenzel Alban Jakob, Sébastien Nicolas Speierer, Delio Aleardo Vicini

Differentiable physically-based rendering has become an indispensable tool for solving inverse problems involving light. Most applications in this area jointly optimize a large set of scene parameters to minimize an objective function, in which case reverse-mode differentiation is the method of choice for obtaining parameter gradients. However, existing techniques that perform the necessary differentiation step suffer from either statistical bias or a prohibitive cost in terms of memory and computation time. For example, standard techniques for automatic differentiation based on program transformation or Wengert tapes lead to impracticably large memory usage when applied to physically-based rendering algorithms. A recently proposed adjoint method by Nimier-David et al. [2020] reduces this to a constant memory footprint, but the computation time for unbiased gradient estimates then becomes quadratic in the number of scattering events along a light path. This is problematic when the scene contains highly scattering materials like participating media. In this paper, we propose a new unbiased backpropagation algorithm for rendering that only requires constant memory, and whose computation time is linear in the number of scattering events (i.e., just like path tracing). Our approach builds on the invertibility of the local Jacobian at scattering interactions to recover the various quantities needed for reverse-mode differentiation. Our method also extends to specular materials such as smooth dielectrics and conductors that cannot be handled by prior work.

ASSOC COMPUTING MACHINERY2021

Slope-Space Integrals for Specular Next Event Estimation

Wenzel Alban Jakob, Guillaume Rémi Bruno Loubet, Tizian Lucien Zeltner

Monte Carlo light transport simulations often lack robustness in scenes containing specular or near-specular materials. Widely used uni- and bidirectional sampling strategies tend to find light paths involving such materials with insufficient probability, producing unusable images that are contaminated by significant variance. This article addresses the problem of sampling a light path connecting two given scene points via a single specular reflection or refraction, extending the range of scenes that can be robustly handled by unbiased path sampling techniques. Our technique enables efficient rendering of challenging transport phenomena caused by such paths, such as underwater caustics or caustics involving glossy metallic objects. We derive analytic expressions that predict the total radiance due to a single reflective or refractive triangle with a microfacet BSDF and we show that this reduces to the well known Lambert boundary integral for irradiance. We subsequently show how this can be leveraged to efficiently sample connections on meshes comprised of vast numbers of triangles. Our derivation builds on the theory of off-center microfacets and involves integrals in the space of surface slopes. Our approach straightforwardly applies to the related problem of rendering glints with high-resolution normal maps describing specular microstructure. Our formulation alleviates problems raised by singularities in filtering integrals and enables a generalization of previous work to perfectly specular materials. We also extend previous work to the case of GGX distributions and introduce new techniques to improve accuracy and performance.

ASSOC COMPUTING MACHINERY2020