Gradient‐Domain Photon Density Estimation

The most common solutions to the light transport problem rely on either Monte Carlo (MC) integration or density estimation methods, such as uni‐ & bi‐directional path tracing or photon mapping. Recent gradient‐domain extensions of MC approaches show great promise; here, gradients of the final image are estimated numerically (instead of the image intensities themselves) with coherent paths generated from a deterministic shift mapping. We extend gradient‐domain approaches to light transport simulation based on density estimation. As with previous gradient‐domain methods, we detail important considerations that arise when moving from a primal‐ to gradient‐domain estimator. We provide an efficient and straightforward solution to these problems. Our solution supports stochastic progressive density estimation, so it is robust to complex transport effects. We show that gradient‐domain photon density estimation converges faster than its primal‐domain counterpart, as well as being generally more robust than gradient‐domain uni‐ & bi‐directional path tracing for scenes dominated by complex transport.     

Flux‐Limited Diffusion for Multiple Scattering in Participating Media

For the rendering of multiple scattering effects in participating media, methods based on the diffusion approximation are an extremely efficient alternative to Monte Carlo path tracing. However, in sufficiently transparent regions, classical diffusion approximation suffers from non‐physical radiative fluxes which leads to a poor match to correct light transport. In particular, this prevents the application of classical diffusion approximation to heterogeneous media, where opaque material is embedded within transparent regions. To address this limitation, we introduce flux‐limited diffusion, a technique from the astrophysics domain. This method provides a better approximation to light transport than classical diffusion approximation, particularly when applied to heterogeneous media, and hence broadens the applicability of diffusion‐based techniques. We provide an algorithm for flux‐limited diffusion, which is validated using the transport theory for a point light source in an infinite homogeneous medium. We further demonstrate that our implementation of flux‐limited diffusion produces more accurate renderings of multiple scattering in various heterogeneous datasets than classical diffusion approximation, by comparing both methods to ground truth renderings obtained via volumetric path tracing.     

Practical Path Guiding for Efficient Light‐Transport Simulation

We present a robust, unbiased technique for intelligent light‐path construction in path‐tracing algorithms. Inspired by existing path‐guiding algorithms, our method learns an approximate representation of the scene's spatio‐directional radiance field in an unbiased and iterative manner. To that end, we propose an adaptive spatio‐directional hybrid data structure, referred to as SD‐tree, for storing and sampling incident radiance. The SD‐tree consists of an upper part—a binary tree that partitions the 3D spatial domain of the light field—and a lower part—a quadtree that partitions the 2D directional domain. We further present a principled way to automatically budget training and rendering computations to minimize the variance of the final image. Our method does not require tuning hyperparameters, although we allow limiting the memory footprint of the SD‐tree. The aforementioned properties, its ease of implementation, and its stable performance make our method compatible with production environments. We demonstrate the merits of our method on scenes with difficult visibility, detailed geometry, and complex specular‐glossy light transport, achieving better performance than previous state‐of‐the‐art algorithms.     

Replica Exchange Light Transport

We solve the light transport problem by introducing a novel unbiased Monte Carlo algorithm called replica exchange light transport, inspired by the replica exchange Monte Carlo method in the fields of computational physics and statistical information processing. The replica exchange Monte Carlo method is a sampling technique whose operation resembles simulated annealing in optimization algorithms using a set of sampling distributions. We apply it to the solution of light transport integration by extending the probability density function of an integrand of the integration to a set of distributions. That set of distributions is composed of combinations of the path densities of different path generation types: uniform distributions in the integral domain, explicit and implicit paths in light (particle/photon) tracing, indirect paths in bidirectional path tracing, explicit and implicit paths in path tracing, and implicit caustics paths seen through specular surfaces including the delta function in path tracing. The replica‐exchange light transport algorithm generates a sequence of path samples from each distribution and samples the simultaneous distribution of those distributions as a stationary distribution by using the Markov chain Monte Carlo method. Then the algorithm combines the obtained path samples from each distribution using multiple importance sampling. We compare the images generated with our algorithm to those generated with bidirectional path tracing and Metropolis light transport based on the primary sample space. Our proposing algorithm has better convergence property than bidirectional path tracing and the Metropolis light transport, and it is easy to implement by extending the Metropolis light transport.     

Spectral Mollification for Bidirectional Fluorescence

Fluorescent materials can shift energy between wavelengths, thereby creating bright and saturated colors both in natural and artificial materials. However, rendering fluorescence for continuous wavelengths or combined with wavelength dependent path configurations so far has only been feasible using spectral unidirectional methods. We present a regularization-based approach for supporting fluorescence in a spectral bidirectional path tracer. Our algorithm samples camera and light sub-paths with independent wavelengths, and when connecting them mollifies the BSDF at one of the connecting vertices such that it reradiates light across multiple wavelengths. We discuss arising issues such as color bias in early iterations, consistency of the method and MIS weights in the presence of spectral mollification. We demonstrate our method in scenes combining fluorescence and transport phenomena that are difficult to render with unidirectional or spectrally discrete methods.     

Monte Carlo Methods for Volumetric Light Transport Simulation

The wide adoption of path‐tracing algorithms in high‐end realistic rendering has stimulated many diverse research initiatives. In this paper we present a coherent survey of methods that utilize Monte Carlo integration for estimating light transport in scenes containing participating media. Our work complements the volume‐rendering state‐of‐the‐art report by Cerezo et al. [ CPP*05 ]; we review publications accumulated since its publication over a decade ago, and include earlier methods that are key for building light transport paths in a stochastic manner. We begin by describing analog and non‐analog procedures for free‐path sampling and discuss various expected‐value, collision, and track‐length estimators for computing transmittance. We then review the various rendering algorithms that employ these as building blocks for path sampling. Special attention is devoted to null‐collision methods that utilize fictitious matter to handle spatially varying densities; we import two “next‐flight” estimators originally developed in nuclear sciences. Whenever possible, we draw connections between image‐synthesis techniques and methods from particle physics and neutron transport to provide the reader with a broader context.     

Approximate Bias Compensation for Rendering Scenes with Heterogeneous Participating Media

In this paper we present a novel method for high‐quality rendering of scenes with participating media. Our technique is based on instant radiosity, which is used to approximate indirect illumination between surfaces by gathering light from a set of virtual point lights (VPLs). It has been shown that this principle can be applied to participating media as well, so that the combined single scattering contribution of VPLs within the medium yields full multiple scattering. As in the surface case, VPL methods for participating media are prone to singularities, which appear as bright “splotches” in the image. These artifacts are usually countered by clamping the VPLs' contribution, but this leads to energy loss within the short‐distance light transport. Bias compensation recovers the missing energy, but previous approaches are prohibitively costly. We investigate VPL‐based methods for rendering scenes with participating media, and propose a novel and efficient approximate bias compensation technique. We evaluate our technique using various test scenes, showing it to be visually indistinguishable from ground truth.     

CHC+RT: Coherent Hierarchical Culling for Ray Tracing

We propose a new technique for in‐core and out‐of‐core GPU ray tracing using a generalization of hierarchical occlusion culling in the style of the CHC++ method. Our method exploits the rasterization pipeline and hardware occlusion queries in order to create coherent batches of work for localized shader‐based ray tracing kernels. By combining hierarchies in both ray space and object space, the method is able to share intermediate traversal results among multiple rays. We exploit temporal coherence among similar ray sets between frames and also within the given frame. A suitable management of the current visibility state makes it possible to benefit from occlusion culling for less coherent ray types like diffuse reflections. Since large scenes are still a challenge for modern GPU ray tracers, our method is most useful for scenes with medium to high complexity, especially since our method inherently supports ray tracing highly complex scenes that do not fit in GPU memory. For in‐core scenes our method is comparable to CUDA ray tracing and performs up to 5.94 × better than pure shader‐based ray tracing.     

Skeleton based Vertex Connection Resampling for Bidirectional Path Tracing

Bidirectional path tracing is known to perform poorly for the rendering of highly occluded scenes. Indeed, the connection strategy between light and eye subpaths does not take into account the visibility factor, presenting no contribution for many sampled paths. To improve the efficiency of bidirectional path tracing, we propose a new method for adaptive resampling of connections between light and eye subpaths. Aiming for this objective, we build discrete probability distributions of light subpaths based on a skeleton of the empty space of the scene. In order to demonstrate the efficiency of our algorithm, we compare our method to both standard bidirectional path tracing and a recent important caching method.     

Out-of-core Data Management for Path Tracing on Hybrid Resources

We present a software system that enables path-traced rendering of complex scenes. The system consists of two primary components: an application layer that implements the basic rendering algorithm, and an out-of-core scheduling and data-management layer designed to assist the application layer in exploiting hybrid computational resources (e.g., CPUs and GPUs) simultaneously. We describe the basic system architecture, discuss design decisions of the system's data-management layer, and outline an efficient implementation of a path tracer application, where GPUs perform functions such as ray tracing, shadow tracing, importance-driven light sampling, and surface shading. The use of GPUs speeds up the runtime of these components by factors ranging from two to twenty, resulting in a substantial overall increase in rendering speed. The path tracer scales well with respect to CPUs, GPUs and memory per node as well as scaling with the number of nodes. The result is a system that can render large complex scenes with strong performance and scalability.     

均匀参与介质的渲染方法研究

参与介质在现实世界中广泛存在,光线在参与介质中的传播过程比在表面上的传播过程更加复杂,比如在高度散射参与介质中会发生成千上万次反射、在低散射参与介质中由于表面聚集出现体焦散效果,从而使得光线的模拟过程非常耗时。目前常用的方法包括点、光束和路径统一模型法（unifying points,beams and paths,UPBP）以及流型探索梅特罗波利斯光线传递方法（manifold exploration Metropolis light transport,MEMLT）等,这些方法在一定程度上改进了原有方法,但是在一些特殊情况下仍然需要很长时间才能收敛。本文介绍几种针对均匀参与介质的高效渲染方法。1）基于点的参与介质渲染方法,主要通过在参与介质内分布一些点来分别加速单次、二次和多次散射的计算,在GPU （graphics processing unit）实现的基础上,最终达到可交互的效率,并且支持对任意的均匀参与介质的编辑。2）基于多次反射的预计算模型,预计算出无限参与介质中的多次散射分布,通过分析光照分布的对称性,将该分布的维度从4维减低为3维,并且将该分布应用到多种蒙特卡洛渲染方法中,比如MEMLT、UPBP等,从而提高效率。3）参与介质中的路径指导方法,通过学习光线在参与介质中的分布,该分布用SD-tree （spatial-directional tree）来表示,与相位函数进行重采样来产生出射方向。以上3种方法分别从不同角度加快了参与介质的渲染效率。     

Real‐time Depth of Field Rendering via Dynamic Light Field Generation and Filtering

We present a new algorithm for efficient rendering of high‐quality depth‐of‐field (DoF) effects. We start with a single rasterized view (reference view) of the scene, and sample the light field by warping the reference view to nearby views. We implement the algorithm using NVIDIA's CUDA to achieve parallel processing, and exploit the atomic operations to resolve visibility when multiple pixels warp to the same image location. We then directly synthesize DoF effects from the sampled light field. To reduce aliasing artifacts, we propose an image‐space filtering technique that compensates for spatial undersampling using MIP mapping. The main advantages of our algorithm are its simplicity and generality. We demonstrate interactive rendering of DoF effects in several complex scenes. Compared to existing methods, ours does not require ray tracing and hence scales well with scene complexity.     

Rendering Wave Effects with Augmented Light Field

Ray–based representations can model complex light transport but are limited in modeling diffraction effects that require the simulation of wavefront propagation. This paper provides a new paradigm that has the simplicity of light path tracing and yet provides an accurate characterization of both Fresnel and Fraunhofer diffraction. We introduce the concept of a light field transformer at the interface of transmissive occluders. This generates mathematically sound, virtual, and possibly negative‐valued light sources after the occluder. From a rendering perspective the only simple change is that radiance can be temporarily negative. We demonstrate the correctness of our approach both analytically, as well by comparing values with standard experiments in physics such as the Young's double slit. Our implementation is a shader program in OpenGL that can generate wave effects on arbitrary surfaces.     

Efficient Monte Carlo rendering with realistic lenses

In this paper we present a novel approach to simulate image formation for a wide range of real world lenses in the Monte Carlo ray tracing framework. Our approach sidesteps the overhead of tracing rays through a system of lenses and requires no tabulation. To this end we first improve the precision of polynomial optics to closely match ground‐truth ray tracing. Second, we show how the Jacobian of the optical system enables efficient importance sampling, which is crucial for difficult paths such as sampling the aperture which is hidden behind lenses on both sides. Our results show that this yields converged images significantly faster than previous methods and accurately renders complex lens systems with negligible overhead compared to simple models, e.g. the thin lens model. We demonstrate the practicality of our method by incorporating it into a bidirectional path tracing framework and show how it can provide information needed for sophisticated light transport algorithms.     

A Practical and Controllable Hair and Fur Model for Production Path Tracing

We present an energy‐conserving fiber shading model for hair and fur that is efficient enough for path tracing. Our model adopts a near‐field formulation to avoid the expensive integral across the fiber, accounts for all high order internal reflection events with a single lobe, and proposes a novel, closed‐form distribution for azimuthal roughness based on the logistic distribution. Additionally, we derive, through simulation, a parameterization that relates intuitive user controls such as multiple‐scattering albedo and isotropic cylinder roughness to the underlying physical parameters.     

Multi‐Image Based Photon Tracing for Interactive Global Illumination of Dynamic Scenes

Image space photon mapping has the advantage of simple implementation on GPU without pre‐computation of complex acceleration structures. However, existing approaches use only a single image for tracing caustic photons, so they are limited to computing only a part of the global illumination effects for very simple scenes. In this paper we fully extend the image space approach by using multiple environment maps for photon mapping computation to achieve interactive global illumination of dynamic complex scenes. The two key problems due to the introduction of multiple images are 1) selecting the images to ensure adequate scene coverage; and 2) reliably computing ray‐geometry intersections with multiple images. We present effective solutions to these problems and show that, with multiple environment maps, the image‐space photon mapping approach can achieve interactive global illumination of dynamic complex scenes. The advantages of the method are demonstrated by comparison with other existing interactive global illumination methods.     

Bidirectional Rendering of Vector Light Transport

On the foundations of many rendering algorithms it is the symmetry between the path traversed by light and its adjoint path starting from the camera. However, several effects, including polarization or fluorescence, break that symmetry, and are defined only on the direction of light propagation. This reduces the applicability of bidirectional methods that exploit this symmetry for simulating effectively light transport. In this work, we focus on how to include these non‐symmetric effects within a bidirectional rendering algorithm. We generalize the path integral to support the constraints imposed by non‐symmetric light transport. Based on this theoretical framework, we propose modifications on two bidirectional methods, namely bidirectional path tracing and photon mapping, extending them to support polarization and fluorescence, in both steady and transient state.     

Visualization of Coherent Structures of Light Transport

Inspired by vector field topology, an established tool for the extraction and identification of important features of flows and vector fields, we develop means for the analysis of the structure of light transport. For that, we derive an analogy to vector field topology that defines coherent structures in light transport. We also introduce Finite‐Time Path Deflection (FTPD), a scalar quantity that represents the deflection characteristic of all light transport paths passing through a given point in space. For virtual scenes, the FTPD can be computed directly using path‐space Monte Carlo integration. We visualize the FTPD field for several example scenes and discuss the revealed structures. Lastly, we show that the coherent regions visualized by the FTPD are closely related to the coherent regions in our new topologically‐motivated analysis of light transport. FTPD visualizations are thus also visualizations of the structure of light transport.     

Extending Backward Polygon Beam Tracing to Glossy Scattering Surfaces

Backward polygon beam tracing methods, that is beam tracing from the light source (L), are well suited to gather path coherency from specular (S) scattering surfaces. These methods are useful for modelling and efficiently simulating caustics on diffuse (D) surfaces; an effect due to LS⁺D transport paths. This paper generalizes backward polygon beam tracing to include a glossy (G) scattering surface. To this end the details of a beam tracing lumped model and implementation of L(S | G)D transport paths are presented. Although we limit the discussion to short transport paths, we show that backward beam tracing is faster than photon mapping by an order of magnitude for rendering caustics from glossy and specular surfaces.     

Adaptive Ray‐bundle Tracing with Memory Usage Prediction: Efficient Global Illumination in Large Scenes

This paper proposes an adaptive rendering technique for ray‐bundle tracing. Ray‐bundle tracing can be done by per‐pixel linked‐list construction on a GPU rasterization pipeline. This rasterization based approach offers significant benefits for the efficient generation of light maps (e.g., hardware acceleration, tessellation, and recycling of shaders used in real‐time graphics). However, it is inapplicable to large and complex scenes due to the limited capacity of the GPU memory because it requires a high‐resolution frame buffer and high‐capacity node buffer for the linked‐lists. In addition, memory overflow can potentially occur on the per‐pixel linked‐list since the memory usage of the lists is usually unknown before the rendering process. We introduce an adaptive tiling technique with memory usage prediction. Our method uses an appropriately tiled frame buffer, thus eliminating almost all of the overflow risks thanks to our adaptive tile subdivision scheme. Using this technique, we are able to render high‐quality light maps of large and complex scenes which cannot be computed using previous ray‐bundle based methods.