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We propose a set of techniques to efficiently importance sample the derivatives of a wide range of Bidirectional Reflectance Distribution Function (BRDF) models. In differentiable rendering, BRDFs are replaced by their differential BRDF counterparts, which are real-valued and can have negative values. This leads to a new source of variance arising from their change in sign. Real-valued functions cannot be perfectly importance sampled by a positive-valued PDF, and the direct application of BRDF sampling leads to high variance. Previous attempts at antithetic sampling only addressed the derivative with the roughness parameter of isotropic microfacet BRDFs. Our work generalizes BRDF derivative sampling to anisotropic microfacet models, mixture BRDFs, Oren-Nayar, Hanrahan-Krueger, among other analytic BRDFs.

Our method first decomposes the real-valued differential BRDF into a sum of single-signed functions, eliminating variance from a change in sign. Next, we importance sample each of the resulting single-signed functions separately. The first decomposition, positivization, partitions the real-valued function based on its sign, and is effective at variance reduction when applicable. However, it requires analytic knowledge of the roots of the differential BRDF, and for it to be analytically integrable too. Our key insight is that the single-signed functions can have overlapping support, which significantly broadens the ways we can decompose a real-valued function. Our product and mixture decompositions exploit this property, and they allow us to support several BRDF derivatives that positivization could not handle. For a wide variety of BRDF derivatives, our method significantly reduces the variance (up to 58× in some cases) at equal computation cost and enables better recovery of spatially varying textures through gradient-descent-based inverse rendering.

 

Neural image representations offer the possibility of high fidelity, compact storage, and resolution-independent accuracy, providing an attractive alternative to traditional pixel- and grid-based representations. However, coordinate neural networks fail to capture discontinuities present in the image and tend to blur across them; we aim to address this challenge. In many cases, such as rendered images, vector graphics, diffusion curves, or solutions to partial differential equations, the locations of the discontinuities are known. We take those locations as input, represented as linear, quadratic, or cubic Bézier curves, and construct a feature field that is discontinuous across these locations and smooth everywhere else. Finally, we use a shallow multi-layer perceptron to decode the features into the signal value. To construct the feature field, we develop a new data structure based on a curved triangular mesh, with features stored on the vertices and on a subset of the edges that are marked as discontinuous. We show that our method can be used to compress a 100, 000²-pixel rendered image into a 25MB file; can be used as a new diffusion-curve solver by combining with Monte-Carlo-based methods or directly supervised by the diffusion-curve energy; or can be used for compressing 2D physics simulation data.

 

Precomputed Radiance Transfer (PRT) remains an attractive solution for real‐time rendering of complex light transport effects such as glossy global illumination. After precomputation, we can relight the scene with new environment maps while changing viewpoint in real‐time. However, practical PRT methods are usually limited to low‐frequency spherical harmonic lighting. All‐frequency techniques using wavelets are promising but have so far had little practical impact. The curse of dimensionality and much higher data requirements have typically limited them to relighting with fixed view or only direct lighting with triple product integrals. In this paper, we demonstrate a hybrid neural‐wavelet PRT solution to high‐frequency indirect illumination, including glossy reflection, for relighting with changing view. Specifically, we seek to represent the light transport function in the Haar wavelet basis. For global illumination, we learn the wavelet transport using a small multi‐layer perceptron (MLP) applied to a feature field as a function of spatial location and wavelet index, with reflected direction and material parameters being other MLP inputs. We optimize/learn the feature field (compactly represented by a tensor decomposition) and MLP parameters from multiple images of the scene under different lighting and viewing conditions. We demonstrate real‐time (512 x 512 at 24 FPS, 800 x 600 at 13 FPS) precomputed rendering of challenging scenes involving view‐dependent reflections and even caustics.

 

Neural material reflectance representations address some limitations of traditional analytic BRDFs with parameter textures; they can theoretically represent any material data, whether a complex synthetic microgeometry with displacements, shadows and interreflections, or real measured reflectance. However, they still approximate the material on an infinite plane, which prevents them from correctly handling silhouette and parallax effects for viewing directions close to grazing. The goal of this paper is to design a neural material representation capable of correctly handling such silhouette effects. We extend the neural network query to take surface curvature information as input, while the query output is extended to return a transparency value in addition to reflectance. We train the new neural representation on synthetic data that contains queries spanning a variety of surface curvatures. We show an ability to accurately represent complex silhouette behavior that would traditionally require more expensive and less flexible techniques, such as on-the-fly geometry displacement or ray marching. 

The continued advancements of time-of-flight imaging devices have enabled new imaging pipelines with numerous applications. Consequently, several forward rendering techniques capable of accurately and efficiently simulating these devices have been introduced. However, general-purpose differentiable rendering techniques that estimate derivatives of time-of-flight images are still lacking. In this paper, we introduce a new theory of differentiable time-gated rendering that enjoys the generality of differentiating with respect to arbitrary scene parameters. Our theory also allows the design of advanced Monte Carlo estimators capable of handling cameras with near-delta or discontinuous time gates. We validate our theory by comparing derivatives generated with our technique and finite differences. Further, we demonstrate the usefulness of our technique using a few proof-of-concept inverse-rendering examples that simulate several time-of-flight imaging scenarios. 

Path guiding is a promising technique to reduce the variance of path tracing. Although existing online path guiding algorithms can eventually learn good sampling distributions given a large amount of time and samples, the speed of learning becomes a major bottleneck. In this paper, we accelerate the learning of sampling distributions by training a light-weight neural network offline to reconstruct from sparse samples. Uniquely, we design our neural network to directly operate convolutions on a sparse quadtree, which regresses a high-quality hierarchical sampling distribution. Our approach can reconstruct reasonably accurate sampling distributions faster, allowing for efficient path guiding and rendering. In contrast to the recent offline neural path guiding techniques that reconstruct low-resolution 2D images for sampling, our novel hierarchical framework enables more fine-grained directional sampling with less memory usage, effectively advancing the practicality and efficiency of neural path guiding. In addition, we take advantage of hybrid bidirectional samples including both path samples and photons, as we have found this more robust to different light transport scenarios compared to using only one type of sample as in previous work. Experiments on diverse testing scenes demonstrate that our approach often improves rendering results with better visual quality and lower errors. Our framework can also provide the proper balance of speed, memory cost, and robustness.