Abstract We present a kernel‐predicting neural denoising method for path‐traced deep‐Z images that facilitates their usage in animation and visual effects production. Deep‐Z images provide enhanced flexibility during compositing as they contain color, opacity, and other rendered data at multiple depth‐resolved bins within each pixel. However, they are subject to noise, and rendering until convergence is prohibitively expensive. The current state of the art in deep‐Z denoising yields objectionable artifacts, and current neural denoising methods are incapable of handling the variable number of depth bins in deep‐Z images. Our method extends kernel‐predicting convolutional neural networks to address the challenges stemming from denoising deep‐Z images. We propose a hybrid reconstruction architecture that combines the depth‐resolved reconstruction at each bin with the flattened reconstruction at the pixel level. Moreover, we propose depth‐aware neighbor indexing of the depth‐resolved inputs to the convolution and denoising kernel application operators, which reduces artifacts caused by depth misalignment present in deep‐Z images. We evaluate our method on a production‐quality deep‐Z dataset, demonstrating significant improvements in denoising quality and performance compared to the current state‐of‐the‐art deep‐Z denoiser. By addressing the significant challenge of the cost associated with rendering path‐traced deep‐Z images, we believe that our approach will pave the way for broader adoption of deep‐Z workflows in future productions.

Simulating the light transport of volumetric effects poses significant challenges and costs, especially in the presence of heterogeneous volumes. Generating stochastic paths for volume rendering involves multiple decisions, and previous works mainly focused on directional and distance sampling, where the volume scattering probability (VSP), i.e., the probability of scattering inside a volume, is indirectly determined as a byproduct of distance sampling. We demonstrate that direct control over the VSP can significantly improve efficiency and present an unbiased volume rendering algorithm based on an existing resampling framework for precise control over the VSP. Compared to previous state-of-the-art, which can only increase the VSP without guaranteeing to reach the desired value, our method also supports decreasing the VSP. We further present a data-driven guiding framework to efficiently learn and query an approximation of the optimal VSP everywhere in the scene without the need for user control. Our approach can easily be combined with existing path-guiding methods for directional sampling at minimal overhead and shows significant improvements over the state-of-the-art in various complex volumetric lighting scenarios.

Abstract We investigate the use of neural fields for modelling diverse mesoscale structures, such as fur, fabric and grass. Instead of using classical graphics primitives to model the structure, we propose to employ a versatile volumetric primitive represented by a neural reflectance field (NeRF‐Tex), which jointly models the geometry of the material and its response to lighting. The NeRF‐Tex primitive can be instantiated over a base mesh to ‘texture’ it with the desired meso and microscale appearance. We condition the reflectance field on user‐defined parameters that control the appearance. A single NeRF texture thus captures an entire space of reflectance fields rather than one specific structure. This increases the gamut of appearances that can be modelled and provides a solution for combating repetitive texturing artifacts. We also demonstrate that NeRF textures naturally facilitate continuous level‐of‐detail rendering. Our approach unites the versatility and modelling power of neural networks with the artistic control needed for precise modelling of virtual scenes. While all our training data are currently synthetic, our work provides a recipe that can be further extended to extract complex, hard‐to‐model appearances from real images.

Abstract We propose a learning‐based method for light‐path construction in path tracing algorithms, which iteratively optimizes and samples from what we refer to as spatio‐directional Gaussian mixture models (SDMMs). In particular, we approximate incident radiance as an online‐trained 5D mixture that is accelerated by a D‐tree. Using the same framework, we approximate BSDFs as pre‐trained D mixtures, where is the number of BSDF parameters. Such an approach addresses two major challenges in path‐guiding models. First, the 5D radiance representation naturally captures correlation between the spatial and directional dimensions. Such correlations are present in, for example parallax and caustics. Second, by using a tangent‐space parameterization of Gaussians, our spatio‐directional mixtures can perform approximate product sampling with arbitrarily oriented BSDFs. Existing models are only able to do this by either foregoing anisotropy of the mixture components or by representing the radiance field in local (normal aligned) coordinates, which both make the radiance field more difficult to learn. An additional benefit of the tangent‐space parameterization is that each individual Gaussian is mapped to the solid sphere with low distortion near its centre of mass. Our method performs especially well on scenes with small, localized luminaires that induce high spatio‐directional correlation in the incident radiance.

Abstract We propose a method for constructing feature sets that significantly improve the quality of neural denoisers for Monte Carlo renderings with volumetric content. Starting from a large set of hand‐crafted features, we propose a feature selection process to identify significantly pruned near‐optimal subsets. While a naive approach would require training and testing a separate denoiser for every possible feature combination, our selection process requires training of only a single probe denoiser for the selection task. Moreover, our approximate solution has an asymptotic complexity that is quadratic to the number of features compared to the exponential complexity of the naive approach, while also producing near‐optimal solutions. We demonstrate the usefulness of our approach on various state‐of‐the‐art denoising methods for volumetric content. We observe improvements in denoising quality when using our automatically selected feature sets over the hand‐crafted sets proposed by the original methods.

We propose an adaptive sampling and reconstruction method for offline Monte Carlo rendering. Our method produces sampling maps constrained by a user-defined budget that minimize the expected future denoising error. Compared to other state-of-the-art methods, which produce the necessary training data on the fly by composing pre-rendered images, our method samples from analytic noise distributions instead. These distributions are compact and closely approximate the pixel value distributions stemming from Monte Carlo rendering. Our method can efficiently sample training data by leveraging only a few per-pixel statistics of the target distribution, which provides several benefits over the current state of the art. Most notably, our analytic distributions' modeling accuracy and sampling efficiency increase with sample count, essential for high-quality offline rendering. Although our distributions are approximate, our method supports joint end-to-end training of the sampling and denoising networks. Finally, we propose the addition of a global summary module to our architecture that accumulates valuable information from image regions outside of the network's receptive field. This information discourages sub-optimal decisions based on local information. Our evaluation against other state-of-the-art neural sampling methods demonstrates denoising quality and data efficiency improvements.

Abstract We propose a deep‐learning method for automatically decomposing noisy Monte Carlo renderings into components that kernel‐predicting denoisers can denoise more effectively. In our model, a neural decomposition module learns to predict noisy components and corresponding feature maps, which are consecutively reconstructed by a denoising module. The components are predicted based on statistics aggregated at the pixel level by the renderer. Denoising these components individually allows the use of per‐component kernels that adapt to each component's noisy signal characteristics. Experimentally, we show that the proposed decomposition module consistently improves the denoising quality of current state‐of‐the‐art kernel‐predicting denoisers on large‐scale academic and production datasets.

We present a technique for adaptively partitioning neural scene representations. Our method disentangles lighting, material, and geometric information yielding a scene representation that preserves the orthogonality of these components, improves interpretability of the model, and allows compositing new scenes by mixing components of existing ones. The proposed adaptive partitioning respects the uneven entropy of individual components and permits compressing the scene representation to lower its memory footprint and potentially reduce the evaluation cost of the model. Furthermore, the partitioned representation enables an in-depth analysis of existing image generators. We compare the flow of information through individual partitions, and by contrasting it to the impact of additional inputs (G-buffer), we are able to identify the roots of undesired visual artifacts, and propose one possible solution to remedy the poor performance. We also demonstrate the benefits of complementing traditional forward renderers by neural representations and synthesis, e.g. to infer expensive shading effects, and show how these could improve production rendering in the future if developed further.

Recreating the appearance of humans in virtual environments for the purpose of movie, video game, or other types of production involves the acquisition of a geometric representation of the human body and its scattering parameters which express the interaction between the geometry and light propagated throughout the scene. Teeth appearance is defined not only by the light and surface interaction, but also by its internal geometry and the intra-oral environment, posing its own unique set of challenges. Therefore, we present a system specifically designed for capturing the optical properties of live human teeth such that they can be realistically re-rendered in computer graphics. We acquire our data in vivo in a conventional multiple camera and light source setup and use exact geometry segmented from intra-oral scans. To simulate the complex interaction of light in the oral cavity during inverse rendering we employ a novel pipeline based on derivative path tracing with respect to both optical properties and geometry of the inner dentin surface. The resulting estimates of the global derivatives are used to extract parameters in a joint numerical optimization. The final appearance faithfully recreates the acquired data and can be directly used in conventional path tracing frameworks for rendering virtual humans.

We address the challenge of efficiently rendering massive assemblies of grains within a forward path-tracing framework. Previous approaches exist for accelerating high-order scattering for a limited, and static, set of granular materials, often requiring scene-dependent precomputation. We significantly expand the admissible regime of granular materials by considering heterogeneous and dynamic granular mixtures with spatially varying grain concentrations, pack rates, and sizes. Our method supports both procedurally generated grain assemblies and dynamic assemblies authored in off-the-shelf particle simulation tools. The key to our speedup lies in two complementary aggregate scattering approximations which we introduced to jointly accelerate construction of short and long light paths. For low-order scattering, we accelerate path construction using novel grain scattering distribution functions (GSDF) which aggregate intra-grain light transport while retaining important grain-level structure. For high-order scattering, we extend prior work on shell transport functions (STF) to support dynamic, heterogeneous mixtures of grains with varying sizes. We do this without a scene-dependent precomputation and show how this can also be used to accelerate light transport in arbitrary continuous heterogeneous media. Our multi-scale rendering automatically minimizes the usage of explicit path tracing to only the first grain along a light path, or can avoid it completely, when appropriate, by switching to our aggregate transport approximations. We demonstrate our technique on animated scenes containing heterogeneous mixtures of various types of grains that could not previously be rendered efficiently. We also compare to previous work on a simpler class of granular assemblies, reporting significant computation savings, often yielding higher accuracy results.

Abstract Facial appearance capture is now firmly established within academic research and used extensively across various application domains, perhaps most prominently in the entertainment industry through the design of virtual characters in video games and films. While significant progress has occurred over the last two decades, no single survey currently exists that discusses the similarities, differences, and practical considerations of the available appearance capture techniques as applied to human faces. A central difficulty of facial appearance capture is the way light interacts with skin—which has a complex multi‐layered structure—and the interactions that occur below the skin surface can, by definition, only be observed indirectly. In this report, we distinguish between two broad strategies for dealing with this complexity. “Image‐based methods” try to exhaustively capture the exact face appearance under different lighting and viewing conditions, and then render the face through weighted image combinations. “Parametric methods” instead fit the captured reflectance data to some parametric appearance model used during rendering, allowing for a more lightweight and flexible representation but at the cost of potentially increased rendering complexity or inexact reproduction. The goal of this report is to provide an overview that can guide practitioners and researchers in assessing the tradeoffs between current approaches and identifying directions for future advances in facial appearance capture.

We address the problem of modeling and rendering granular materials---such as large structures made of sand, snow, or sugar---where an aggregate object is composed of many randomly oriented, but discernible grains. These materials pose a particular challenge as the complex scattering properties of individual grains, and their packing arrangement, can have a dramatic effect on the large-scale appearance of the aggregate object. We propose a multi-scale modeling and rendering framework that adapts to the structure of scattered light at different scales. We rely on path tracing the individual grains only at the finest scale, and---by decoupling individual grains from their arrangement---we develop a modular approach for simulating longer-scale light transport. We model light interactions within and across grains as separate processes and leverage this decomposition to derive parameters for classical radiative transport, including standard volumetric path tracing and a diffusion method that can quickly summarize the large scale transport due to many grain interactions. We require only a one-time precomputation per exemplar grain, which we can then reuse for arbitrary aggregate shapes and a continuum of different packing rates and scales of grains. We demonstrate our method on scenes containing mixtures of tens of millions of individual, complex, specular grains that would be otherwise infeasible to render with standard techniques.

Abstract We present a novel appearance model for paper. Based on our appearance measurements for matte and glossy paper, we find that paper exhibits a combination of subsurface scattering, specular reflection, retroreflection, and surface sheen. Classic microfacet and simple diffuse reflection models cannot simulate the double‐sided appearance of a thin layer. Our novel BSDF model matches our measurements for paper and accounts for both reflection and transmission properties. At the core of the BSDF model is a method for converting a multi‐layer subsurface scattering model (BSSRDF) into a BSDF, which allows us to retain physically‐based absorption and scattering parameters obtained from the measurements. We also introduce a method for computing the amount of light available for subsurface scattering due to transmission through a rough dielectric surface. Our final model accounts for multiple scattering, single scattering, and surface reflection and is capable of rendering paper with varying levels of roughness and glossiness on both sides.

We present a method for practical physical reproduction and design of homogeneous materials with desired subsurface scattering. Our process uses a collection of different pigments that can be suspended in a clear base material. Our goal is to determine pigment concentrations that best reproduce the appearance and subsurface scattering of a given target material. In order to achieve this task we first fabricate a collection of material samples composed of known mixtures of the available pigments with the base material. We then acquire their reflectance profiles using a custom-built measurement device. We use the same device to measure the reflectance profile of a target material. Based on the database of mappings from pigment concentrations to reflectance profiles, we use an optimization process to compute the concentration of pigments to best replicate the target material appearance. We demonstrate the practicality of our method by reproducing a variety of different translucent materials. We also present a tool that allows the user to explore the range of achievable appearances for a given set of pigments.

We present an automatic approach to design and manufacture passive display devices based on optical hidden image decoding. Motivated by classical steganography techniques we construct Magic Lenses , composed of refractive lenslet arrays, to reveal hidden images when placed over potentially unstructured printed or displayed source images. We determine the refractive geometry of these surfaces by formulating and efficiently solving an inverse light transport problem, taking into account additional constraints imposed by the physical manufacturing processes. We fabricate several variants on the basic magic lens idea including using a single source image to encode several hidden images which are only revealed when the lens is placed at prescribed orientations on the source image or viewed from different angles. We also present an important special case, the universal lens , that forms an injection mapping from the lens surface to the source image grid, allowing it to be used with arbitrary source images. We use this type of lens to generate hidden animation sequences. We validate our simulation results with many real-world manufactured magic lenses, and experiment with two separate manufacturing processes.

Abstract We propose a novel system for designing and manufacturing surfaces that produce desired caustic images when illuminated by a light source. Our system is based on a nonnegative image decomposition using a set of possibly overlapping anisotropic Gaussian kernels. We utilize this decomposition to construct an array of continuous surface patches, each of which focuses light onto one of the Gaussian kernels, either through refraction or reflection. We show how to derive the shape of each continuous patch and arrange them by performing a discrete assignment of patches to kernels in the desired caustic. Our decomposition provides for high fidelity reconstruction of natural images using a small collection of patches. We demonstrate our approach on a wide variety of caustic images by manufacturing physical surfaces with a small number of patches.