Differentiable path tracing offers a principled route to recovering physical material and lighting parameters, but the combination of high variance and poor numerical conditioning often makes it too brittle to use in practice. This is especially the case when lighting is altogether unknown, or when the scene contains complex light transport effects. Prior work recently showed that the variance reduction provided by a radiance cache can alleviate these challenges. We revisit the combination of inverse rendering and radiance caching with a twist, by introducing a spatial blending field that locally interpolates between the cache and standard unbiased estimators. Recursive application of this idea yields a rich design space of evaluation strategies and inter-estimator consistency losses; we map this space and identify effective components. A surprising property of the resulting algorithm is that it can accurately recover material parameters even when the lighting is not uniquely identifiable from the observations. Our experiments demonstrate significant improvements in speed and robustness over prior work, making a strong case for including radiance caching as a standard component of future physically based inverse rendering systems.

We present GroomLight, a novel method for relightable hair appearance modeling from multi-view images. Existing hair capture methods struggle to balance photorealistic rendering with relighting capabilities. Analytical material models, while physically grounded, often fail to fully capture appearance details. Conversely, neural rendering approaches excel at view synthesis but generalize poorly to novel lighting conditions. GroomLight addresses this challenge by combining the strengths of both paradigms. It employs an extended hair BSDF model to capture primary light transport and a light-aware residual model to reconstruct the remaining details. We further propose a hybrid inverse rendering pipeline to optimize both components, enabling high-fidelity relighting, view synthesis, and material editing. Extensive evaluations on real-world hair data demonstrate state-of-the-art performance of our method. Our project website is at: https://syntec-research.github.io/GroomLight.

3D Gaussian splatting (3DGS) is a popular radiance field method, with many application-specific extensions. Most variants rely on the same core algorithm: depth-sorting of Gaussian splats then rasterizing in primitive order. This ensures correct alpha compositing, but can cause rendering artifacts due to built-in approximations. Moreover, for a fixed representation, sorted rendering offers little control over render cost and visual fidelity. For example, and counter-intuitively, rendering a lower-resolution image is not necessarily faster. In this work, we address the above limitations by combining 3D Gaussian splatting with stochastic rasterization. Concretely, we leverage an unbiased Monte Carlo estimator of the volume rendering equation. This removes the need for sorting, and allows for accurate 3D blending of overlapping Gaussians. The number of Monte Carlo samples further imbues 3DGS with a way to trade off computation time and quality. We implement our method using OpenGL shaders, enabling efficient rendering on modern GPU hardware. At a reasonable visual quality, our method renders more than four times faster than sorted rasterization.

We introduce a method that automatically and jointly updates both continuous and discrete parameters of a compound lens design, to improve its performance in terms of sharpness, speed, or both. Previous methods for compound lens design use gradient-based optimization to update continuous parameters (e.g., curvature of individual lens elements) of a given lens topology, requiring extensive expert intervention to realize topology changes. By contrast, our method can additionally optimize discrete parameters such as number and type (e.g., singlet or doublet) of lens elements. Our method achieves this capability by combining gradient-based optimization with a tailored Markov chain Monte Carlo sampling algorithm, using transdimensional mutation and paraxial projection operations for efficient global exploration. We show experimentally on a variety of lens design tasks that our method effectively explores an expanded design space of compound lenses, producing better designs than previous methods and pushing the envelope of speed-sharpness tradeoffs achievable by automated lens design.

Variance reduction techniques are widely used for reducing the noise of Monte Carlo integration. However, these techniques are typically designed with the assumption that the integrand is scalar-valued. Recognizing that rendering and inverse rendering broadly involve vector-valued integrands, we identify the limitations of classical variance reduction methods in this context. To address this, we introduce ratio control variates, an estimator that leverages a ratio-based approach instead of the conventional difference-based control variates. Our analysis and experiments demonstrate that ratio control variables can significantly reduce the mean squared error of vector-valued integration compared to existing methods and are broadly applicable to various rendering and inverse rendering tasks.

Inverse rendering has emerged as a standard tool to reconstruct the parameters of appearance models from images (e.g., textured BSDFs). In this work, we present several novel contributions motivated by the practical challenges of recovering high-resolution surface appearance textures, including spatially-varying subsurface scattering parameters. First, we propose Laplacian mipmapping , which combines differentiable mipmapping and a Laplacian pyramid representation into an effective preconditioner. This seemingly simple technique significantly improves the quality of recovered surface textures on a set of challenging inverse rendering problems. Our method automatically adapts to the render and texture resolutions, only incurs moderate computational cost and achieves better quality than prior work while using fewer hyperparameters. Second, we introduce a specialized gradient computation algorithm for textured, path-traced subsurface scattering, which facilitates faithful reconstruction of translucent materials. By using path tracing, we enable the recovery of complex appearance while avoiding the approximations of the previously used diffusion dipole methods. Third, we demonstrate the application of both these techniques to reconstructing the textured appearance of human faces from sparse captures. Our method recovers high-quality relightable appearance parameters that are compatible with current production renderers.

Partial differential equations can model diverse physical phenomena including heat diffusion, incompressible flows, and electrostatic potentials. Given a description of an object's boundary and interior, traditional methods solve such PDEs by densely meshing the interior and then solving a large and sparse linear system derived from this mesh. Recent grid-free solvers take an alternative approach and avoid this complexity in exchange for randomness: they compute stochastic solution estimates and generally bear a striking resemblance to physically-based rendering algorithms. In this article, we develop algorithms targeting the inverse form of this problem: given an already existing solution of a PDE, we infer parameters characterizing the boundary and interior. In the grid-free setting, there are again significant connections to rendering, and we show how insights from both fields can be combined to compute unbiased derivative estimates that enable gradient-based optimization. In this process, we encounter new challenges that must be addressed to obtain practical solutions. We introduce acceleration and variance reduction strategies and show how to differentiate branching random walks in reverse mode. We finally demonstrate our approach on both simulated data and a real-world electrical impedance tomography experiment, where we reconstruct the position of a conducting object from voltage measurements taken in a saline-filled tank.

High-fidelity, photorealistic 3D capture of a human face is a long-standing problem in computer graphics – the complex material of skin, intricate geometry of hair, and fine scale textural details make it challenging. Traditional techniques rely on very large and expensive capture rigs to reconstruct explicit mesh geometry and appearance maps, and are limited by the accuracy of hand-crafted reflectance models. More recent volumetric methods (e.g., NeRFs) have enabled view-synthesis and sometimes relighting by learning an implicit representation of the density and reflectance basis, but suffer from artifacts and blurriness due to the inherent ambiguities in volumetric modeling. These problems are further exacerbated when capturing with few cameras and light sources. We present a novel technique for high-quality capture of a human face for 3D view synthesis and relighting using a sparse, compact capture rig consisting of 15 cameras and 15 lights. Our method combines a neural volumetric representation with traditional mesh reconstruction from multiview stereo. The proxy geometry allows us to anchor the 3D density field to prevent artifacts and guide the disentanglement of intrinsic radiance components of the face appearance such as diffuse and specular reflectance, and incident radiance (shadowing) fields. Our hybrid representation significantly improves the state-of-the-art quality for arbitrarily dense renders of a face from desired camera viewpoint as well as environmental, directional, and near-field lighting.

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.

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.

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.

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.

Abstract We present a novel algorithm to denoise deep Monte Carlo renderings, in which pixels contain multiple colour values, each for a different range of depths. Deep images are a more expressive representation of the scene than conventional flat images. However, since each depth bin receives only a fraction of the flat pixel's samples, denoising the bins is harder due to the less accurate mean and variance estimates. Furthermore, deep images lack a regular structure in depth—the number of depth bins and their depth ranges vary across pixels. This prevents a straightforward application of patch‐based distance metrics frequently used to improve the robustness of existing denoising filters. We address these constraints by combining a flat image‐space non‐local means filter operating on pixel colours with a deep cross‐bilateral filter operating on auxiliary features (albedo, normal, etc.). Our approach significantly reduces noise in deep images while preserving their structure. To our best knowledge, our algorithm is the first to enable efficient deep‐compositing workflows with denoised Monte Carlo renderings. We demonstrate the performance of our filter on a range of scenes highlighting the challenges and advantages of denoising deep images.

Modern rendering systems are confronted with a dauntingly large and growing set of requirements: in their pursuit of realism, physically based techniques must increasingly account for intricate properties of light, such as its spectral composition or polarization. To reduce prohibitive rendering times, vectorized renderers exploit coherence via instruction-level parallelism on CPUs and GPUs. Differentiable rendering algorithms propagate derivatives through a simulation to optimize an objective function, e.g., to reconstruct a scene from reference images. Catering to such diverse use cases is challenging and has led to numerous purpose-built systems---partly, because retrofitting features of this complexity onto an existing renderer involves an error-prone and infeasibly intrusive transformation of elementary data structures, interfaces between components, and their implementations (in other words, everything). We propose Mitsuba 2, a versatile renderer that is intrinsically retargetable to various applications including the ones listed above. Mitsuba 2 is implemented in modern C++ and leverages template metaprogramming to replace types and instrument the control flow of components such as BSDFs, volumes, emitters, and rendering algorithms. At compile time, it automatically transforms arithmetic, data structures, and function dispatch, turning generic algorithms into a variety of efficient implementations without the tedium of manual redesign. Possible transformations include changing the representation of color, generating a "wide" renderer that operates on bundles of light paths, just-in-time compilation to create computational kernels that run on the GPU, and forward/reverse-mode automatic differentiation. Transformations can be chained, which further enriches the space of algorithms derived from a single generic implementation. We demonstrate the effectiveness and simplicity of our approach on several applications that would be very challenging to create without assistance: a rendering algorithm based on coherent MCMC exploration, a caustic design method for gradient-index optics, and a technique for reconstructing heterogeneous media in the presence of multiple scattering.

Subsurface scattering, in which light refracts into a translucent material to interact with its interior, is the dominant mode of light transport in many types of organic materials. Accounting for this phenomenon is thus crucial for visual realism, but explicit simulation of the complex internal scattering process is often too costly. BSSRDF models based on analytic transport solutions are significantly more efficient but impose severe assumptions that are almost always violated, e.g. planar geometry, isotropy, low absorption, and spatio-directional separability. The resulting discrepancies between model and usage lead to objectionable errors in renderings, particularly near geometric features that violate planarity. This article introduces a new shape-adaptive BSSRDF model that retains the efficiency of prior analytic methods while greatly improving overall accuracy. Our approach is based on a conditional variational autoencoder, which learns to sample from a reference distribution produced by a brute-force volumetric path tracer. In contrast to the path tracer, our autoencoder directly samples outgoing locations on the object surface, bypassing a potentially lengthy internal scattering process. The distribution is conditional on both material properties and a set of features characterizing geometric variation in a neighborhood of the incident location. We use a low-order polynomial to model the local geometry as an implicitly defined surface, capturing curvature, thickness, corners, as well as cylindrical and toroidal regions. We present several examples of objects with challenging medium parameters and complex geometry and compare to ground truth simulations and prior work.

Abstract We present a novel algorithm to reconstruct high‐quality images from sampled pixels and gradients in gradient‐domain Rendering. Our approach extends screened Poisson reconstruction by adding additional regularization constraints. Our key idea is to exploit local patches in feature images, which contain per‐pixels normals, textures, position, etc., to formulate these constraints. We describe a GPU implementation of our approach that runs on the order of seconds on megapixel images. We demonstrate a significant improvement in image quality over screened Poisson reconstruction under the L1 norm. Because we adapt the regularization constraints to the noise level in the input, our algorithm is consistent and converges to the ground truth.