Gradient Outlier Removal for Gradient‐Domain Path Tracing

We present a new outlier removal technique for a gradient‐domain path tracing (G‐PT) that computes image gradients as well as colors. Our approach rejects gradient outliers whose estimated errors are much higher than those of the other gradients for improving reconstruction quality for the G‐PT. We formulate our outlier removal problem as a least trimmed squares optimization, which employs only a subset of gradients so that a final image can be reconstructed without including the gradient outliers. In addition, we design this outlier removal process so that the chosen subset of gradients maintains connectivity through gradients between pixels, preventing pixels from being isolated. Lastly, the optimal number of inlier gradients is estimated to minimize our reconstruction error. We have demonstrated that our reconstruction with robustly rejecting gradient outliers produces visually and numerically improved results, compared to the previous screened Poisson reconstruction that uses all the gradients.     

Efficient Caustic Rendering with Lightweight Photon Mapping

Robust and efficient rendering of complex lighting effects, such as caustics, remains a challenging task. While algorithms like vertex connection and merging can render such effects robustly, their significant overhead over a simple path tracer is not always justified and – as we show in this paper ‐ also not necessary. In current rendering solutions, caustics often require the user to enable a specialized algorithm, usually a photon mapper, and hand‐tune its parameters. But even with carefully chosen parameters, photon mapping may still trace many photons that the path tracer could sample well enough, or, even worse, that are not visible at all. Our goal is robust, yet lightweight, caustics rendering. To that end, we propose a technique to identify and focus computation on the photon paths that offer significant variance reduction over samples from a path tracer. We apply this technique in a rendering solution combining path tracing and photon mapping. The photon emission is automatically guided towards regions where the photons are useful, i.e., provide substantial variance reduction for the currently rendered image. Our method achieves better photon densities with fewer light paths (and thus photons) than emission guiding approaches based on visual importance. In addition, we automatically determine an appropriate number of photons for a given scene, and the algorithm gracefully degenerates to pure path tracing for scenes that do not benefit from photon mapping.     

Bayesian Collaborative Denoising for Monte Carlo Rendering

The stochastic nature of Monte Carlo rendering algorithms inherently produces noisy images. Essentially, three approaches have been developed to solve this issue: improving the ray‐tracing strategies to reduce pixel variance, providing adaptive sampling by increasing the number of rays in regions needing so, and filtering the noisy image as a post‐process. Although the algorithms from the latter category introduce bias, they remain highly attractive as they quickly improve the visual quality of the images, are compatible with all sorts of rendering effects, have a low computational cost and, for some of them, avoid deep modifications of the rendering engine. In this paper, we build upon recent advances in both non‐local and collaborative filtering methods to propose a new efficient denoising operator for Monte Carlo rendering. Starting from the local statistics which emanate from the pixels sample distribution, we enrich the image with local covariance measures and introduce a nonlocal bayesian filter which is specifically designed to address the noise stemming from Monte Carlo rendering. The resulting algorithm only requires the rendering engine to provide for each pixel a histogram and a covariance matrix of its color samples. Compared to state‐of‐the‐art sample‐based methods, we obtain improved denoising results, especially in dark areas, with a large increase in speed and more robustness with respect to the main parameter of the algorithm. We provide a detailed mathematical exposition of our bayesian approach, discuss extensions to multiscale execution, adaptive sampling and animated scenes, and experimentally validate it on a collection of scenes.     

Handling Fluorescence in a Uni‐directional Spectral Path Tracer

We present two separate improvements to the handling of fluorescence effects in modern uni‐directional spectral rendering systems. The first is the formulation of a new distance tracking scheme for fluorescent volume materials which exhibit a pronounced wavelength asymmetry. Such volumetric materials are an important and not uncommon corner case of wavelength‐shifting media behaviour, and have not been addressed so far in rendering literature. The second one is that we introduce an extension of Hero wavelength sampling which can handle fluorescence events, both on surfaces, and in volumes. Both improvements are useful by themselves, and can be used separately: when used together, they enable the robust inclusion of arbitrary fluorescence effects in modern uni‐directional spectral MIS path tracers. Our extension of Hero wavelength sampling is generally useful, while our proposed technique for distance tracking in strongly asymmetric media is admittedly not very efficient. However, it makes the most of a rather difficult situation, and at least allows the inclusion of such media in uni‐directional path tracers, albeit at comparatively high cost. Which is still an improvement since up to now, their inclusion was not really possible at all, due to the inability of conventional tracking schemes to generate sampling points in such volume materials.     

Time‐Domain Parallelization for Accelerating Cloth Simulation

Cloth simulations, widely used in computer animation and apparel design, can be computationally expensive for real‐time applications. Some parallelization techniques have been proposed for visual simulation of cloth using CPU or GPU clusters and often rely on parallelization using spatial domain decomposition techniques that have a large communication overhead. In this paper, we propose a novel time‐domain parallelization technique that makes use of the two‐level mesh representation to resolve the time‐dependency issue and develop a practical algorithm to smooth the state transition from the corresponding coarse to fine meshes. A load estimation and a load balancing technique used in online partitioning are also proposed to maximize the performance acceleration. Our method achieves a nearly linear performance scaling on manycore clusters and outperforms spatial‐domain parallelization on a diverse set of benchmarks.     

Area‐Preserving Parameterizations for Spherical Ellipses

We present new methods for uniformly sampling the solid angle subtended by a disk. To achieve this, we devise two novel area‐preserving mappings from the unit square [0,1]² to a spherical ellipse (i.e. the projection of the disk onto the unit sphere). These mappings allow for low‐variance stratified sampling of direct illumination from disk‐shaped light sources. We discuss how to efficiently incorporate our methods into a production renderer and demonstrate the quality of our maps, showing significantly lower variance than previous work.     

Glint Rendering based on a Multiple‐Scattering Patch BRDF

Rendering materials such as metallic paints, scratched metals and rough plastics requires glint integrators that can capture all micro‐specular highlights falling into a pixel footprint, faithfully replicating surface appearance. Specular normal maps can be used to represent a wide range of arbitrary micro‐structures. The use of normal maps comes with important drawbacks though: the appearance is dark overall due to back‐facing normals and importance sampling is suboptimal, especially when the micro‐surface is very rough. We propose a new glint integrator relying on a multiple‐scattering patch‐based BRDF addressing these issues. To do so, our method uses a modified version of microfacet‐based normal mapping [SHHD17] designed for glint rendering, leveraging symmetric microfacets. To model multiple‐scattering, we re‐introduce the lost energy caused by a perfectly specular, single‐scattering formulation instead of using expensive random walks. This reflectance model is the basis of our patch‐based BRDF, enabling robust sampling and artifact‐free rendering with a natural appearance. Additional calculation costs amount to about 40% in the worst cases compared to previous methods [YHMR16, CCM18].     

Fiber‐Level On‐the‐Fly Procedural Textiles

Procedural textile models are compact, easy to edit, and can achieve state‐of‐the‐art realism with fiber‐level details. However, these complex models generally need to be fully instantiated (aka. realized ) into 3D volumes or fiber meshes and stored in memory, We introduce a novel realization‐minimizing technique that enables physically based rendering of procedural textiles, without the need of full model realizations. The key ingredients of our technique are new data structures and search algorithms that look up regular and flyaway fibers on the fly, efficiently and consistently. Our technique works with compact fiber‐level procedural yarn models in their exact form with no approximation imposed. In practice, our method can render very large models that are practically unrenderable using existing methods, while using considerably less memory (60–200× less) and achieving good performance.     

Spectral Gradient Sampling for Path Tracing

Spectral Monte‐Carlo methods are currently the most powerful techniques for simulating light transport with wavelength‐dependent phenomena (e.g., dispersion, colored particle scattering, or diffraction gratings). Compared to trichromatic rendering, sampling the spectral domain requires significantly more samples for noise‐free images. Inspired by gradient‐domain rendering, which estimates image gradients, we propose spectral gradient sampling to estimate the gradients of the spectral distribution inside a pixel. These gradients can be sampled with a significantly lower variance by carefully correlating the path samples of a pixel in the spectral domain, and we introduce a mapping function that shifts paths with wavelength‐dependent interactions. We compute the result of each pixel by integrating the estimated gradients over the spectral domain using a one‐dimensional screened Poisson reconstruction. Our method improves convergence and reduces chromatic noise from spectral sampling, as demonstrated by our implementation within a conventional path tracer.     

Quantifying the Error of Light Transport Algorithms

This paper proposes a new methodology for measuring the error of unbiased physically based rendering algorithms. The current state of the art includes mean squared error (MSE) based metrics and visual comparisons of equal‐time renderings of competing algorithms. Neither is satisfying as MSE does not describe behavior and can exhibit significant variance, and visual comparisons are inherently subjective. Our contribution is two‐fold: First, we propose to compute many short renderings instead of a single long run and use the short renderings to estimate MSE expectation and variance as well as per‐pixel standard deviation. An algorithm that achieves good results in most runs, but with occasional outliers is essentially unreliable, which we wish to quantify numerically. We use per‐pixel standard deviation to identify problematic lighting effects of rendering algorithms. The second contribution is the error spectrum ensemble (ESE), a tool for measuring the distribution of error over frequencies. The ESE serves two purposes: It reveals correlation between pixels and can be used to detect outliers, which offset the amount of error substantially.     

Sequences with Low‐Discrepancy Blue‐Noise 2‐D Projections

Distributions of samples play a very important role in rendering, affecting variance, bias and aliasing in Monte‐Carlo and Quasi‐Monte Carlo evaluation of the rendering equation. In this paper, we propose an original sampler which inherits many important features of classical low‐discrepancy sequences (LDS): a high degree of uniformity of the achieved distribution of samples, computational efficiency and progressive sampling capability. At the same time, we purposely tailor our sampler in order to improve its spectral characteristics, which in turn play a crucial role in variance reduction, anti‐aliasing and improving visual appearance of rendering. Our sampler can efficiently generate sequences of multidimensional points, whose power spectra approach so‐called Blue‐Noise (BN) spectral property while preserving low discrepancy (LD) in certain 2‐D projections. In our tile‐based approach, we perform permutations on subsets of the original Sobol LDS. In a large space of all possible permutations, we select those which better approach the target BN property, using pair‐correlation statistics. We pre‐calculate such “good” permutations for each possible Sobol pattern, and store them in a lookup table efficiently accessible in runtime. We provide a complete and rigorous proof that such permutations preserve dyadic partitioning and thus the LDS properties of the point set in 2‐D projections. Our construction is computationally efficient, has a relatively low memory footprint and supports adaptive sampling. We validate our method by performing spectral/discrepancy/aliasing analysis of the achieved distributions, and provide variance analysis for several target integrands of theoretical and practical interest.     

Real‐time Locomotion Controller using an Inverted‐Pendulum‐based Abstract Model

In this paper, we propose a novel motion controller for the online generation of natural character locomotion that adapts to new situations such as changing user control or applying external forces. This controller continuously estimates the next footstep while walking and running, and automatically switches the stepping strategy based on situational changes. To develop the controller, we devise a new physical model called an inverted‐pendulum‐based abstract model (IPAM). The proposed abstract model represents high‐dimensional character motions, inheriting the naturalness of captured motions by estimating the appropriate footstep location, speed and switching time at every frame. The estimation is achieved by a deep learning based regressor that extracts important features in captured motions. To validate the proposed controller, we train the model using captured motions of a human stopping, walking, and running in a limited space. Then, the motion controller generates human‐like locomotion with continuously varying speeds, transitions between walking and running, and collision response strategies in a cluttered space in real time.     

A Geometrically Consistent Viscous Fluid Solver with Two‐Way Fluid‐Solid Coupling

We present a grid‐based fluid solver for simulating viscous materials and their interactions with solid objects. Our method formulates the implicit viscosity integration as a minimization problem with consistently estimated volume fractions to account for the sub‐grid details of free surfaces and solid boundaries. To handle the interplay between fluids and solid objects with viscosity forces, we also formulate the two‐way fluid‐solid coupling as a unified minimization problem based on the variational principle, which naturally enforces the boundary conditions. Our formulation leads to a symmetric positive definite linear system with a sparse matrix regardless of the monolithically coupled solid objects. Additionally, we present a position‐correction method using density constraints to enforce the uniform distributions of fluid particles and thus prevent the loss of fluid volumes. We demonstrate the effectiveness of our method in a wide range of viscous fluid scenarios.     

A Color‐Pair Based Approach for Accurate Color Harmony Estimation

Harmonious color combinations can stimulate positive user emotional responses. However, a widely open research question is: how can we establish a robust and accurate color harmony measure for the public and professional designers to identify the harmony level of a color theme or color set. Building upon the key discovery that color pairs play an important role in harmony estimation, in this paper we present a novel color‐pair based estimation model to accurately measure the color harmony. It first takes a two‐layer maximum likelihood estimation (MLE) based method to compute an initial prediction of color harmony by statistically modeling the pair‐wise color preferences from existing datasets. Then, the initial scores are refined through a back‐propagation neural network (BPNN) with a variety of color features extracted in different color spaces, so that an accurate harmony estimation can be obtained at the end. Our extensive experiments, including performance comparisons of harmony estimation applications, show the advantages of our method in comparison with the state of the art methods.     

Distortion‐Free Displacement Mapping

Displacement mapping is routinely used to add geometric details in a fast and easy‐to‐control way, both in offline rendering as well as recently in interactive applications such as games. However, it went largely unnoticed (with the exception of McGuire and Whitson [MW08]) that, when applying displacement mapping to a surface with a low‐distortion parametrization, this parametrization is distorted as the geometry was changed by the displacement mapping. Typical resulting artifacts are “rubber band”‐like distortion patterns in areas of strong displacement change where a small isotropic area in texture space is mapped to a large anisotropic area in world space. We describe a fast, fully GPU‐based two‐step procedure to resolve this problem. First, a correction deformation is computed from the displacement map. Second, two variants to apply this correction when computing displacement mapping are proposed. The first variant is backward‐compatible and can resolve the artifact in any rendering pipeline without modifying it and without requiring additional computation at render time, but only works for bijective parametrizations. The second variant works for more general parametrizations, but requires to modify the rendering code and incurs a very small computational overhead.     

On‐Site Example‐Based Material Appearance Acquisition

We present a novel example‐based material appearance modeling method suitable for rapid digital content creation. Our method only requires a single HDR photograph of a homogeneous isotropic dielectric exemplar object under known natural illumination. While conventional methods for appearance modeling require prior knowledge on the object shape, our method does not, nor does it recover the shape explicitly, greatly simplifying on‐site appearance acquisition to a lightweight photography process suited for non‐expert users. As our central contribution, we propose a shape‐agnostic BRDF estimation procedure based on binary RGB profile matching. We also model the appearance of materials exhibiting a regular or stationary texture‐like appearance, by synthesizing appropriate mesostructure from the same input HDR photograph and a mesostructure exemplar with (roughly) similar features. We believe our lightweight method for on‐site shape‐agnostic appearance acquisition presents a suitable alternative for a variety of applications that require plausible “rapid‐appearance‐modeling”.