Photon Beam Diffusion: A Hybrid Monte Carlo Method for Subsurface Scattering

We present photon beam diffusion, an efficient numerical method for accurately rendering translucent materials. Our approach interprets incident light as a continuous beam of photons inside the material. Numerically integrating diffusion from such extended sources has long been assumed computationally prohibitive, leading to the ubiquitous single‐depth dipole approximation and the recent analytic sum‐of‐Gaussians approach employed by Quantized Diffusion. In this paper, we show that numerical integration of the extended beam is not only feasible, but provides increased speed, flexibility, numerical stability, and ease of implementation, while retaining the benefits of previous approaches. We leverage the improved diffusion model, but propose an efficient and numerically stable Monte Carlo integration scheme that gives equivalent results using only 3–5 samples instead of 20–60 Gaussians as in previous work. Our method can account for finite and multi‐layer materials, and additionally supports directional incident effects at surfaces. We also propose a novel diffuse exact single‐scattering term which can be integrated in tandem with the multi‐scattering approximation. Our numerical approach furthermore allows us to easily correct inaccuracies of the diffusion model and even combine it with more general Monte Carlo rendering algorithms. We provide practical details necessary for efficient implementation, and demonstrate the versatility of our technique by incorporating it on top of several rendering algorithms in both research and production rendering systems.     

On the Effective Dimension of Light Transport

Light transport is often characterized within a high‐dimensional space although practitioners have long known that it commonly behaves as a much lower‐dimensional phenomenon. We study the effective dimension of light transport over a neighborhood on the scene manifold and show that under plausible assumptions the dimensionality is characterized by the spectrum of the spatio‐spectral concentration problem. This allows us to improve existing estimates for the dimension in computer graphics using a more insightful derivation and for the first time we obtain optimal representations. The relevance of our results for existing rendering applications is discussed.     

Spatial Adjacency Maps for Translucency Simulation under General Illumination

Rendering translucent materials in real time is usually done by using surface diffusion and/or (translucent) shadow maps. The downsides of these approaches are, that surface diffusion cannot handle translucency effects that show up when rendering thin objects, and that translucent shadow maps are only available for point light sources. Furthermore, translucent shadow maps introduce limitations to shadow mapping techniques exploiting the same maps. In this paper we present a novel approach for rendering translucent materials at interactive frame rates. Our approach allows for an efficient calculation of translucency with native support for general illumination conditions, especially area and environment lighting, at high accuracy. The proposed technique's only parameter is the used diffusion profile, and thus it works out of the box without any parameter tuning. Furthermore, it can be used in combination with any existing surface diffusion techniques to add translucency effects. Our approach introduces Spatial Adjacency Maps that depend on precalculations to be done for fixed meshes. We show that these maps can be updated in real time to also handle deforming meshes and that our results are of superior quality as compared to other well known real‐time techniques for rendering translucency.     

Single-pass Scalable Subsurface Rendering with Lightcuts

This paper presents a new, scalable, single pass algorithm for computing subsurface scattering using the diffusion approximation. Instead of pre‐computing a globally conservative estimate of the surface irradiance like previous two pass methods, the algorithm simultaneously refines hierarchical and adaptive estimates of both the surface irradiance and the subsurface transport. By using an adaptive, top‐down refinement method, the algorithm directs computational effort only to simulating those eye‐surface‐light paths that make significant contributions to the final image. Because the algorithm is driven by image importance, it scales more efficiently than previous methods that have a linear dependence on translucent surface area. We demonstrate that in scenes with many translucent objects and in complex lighting environments, our new algorithm has a significant performance advantage.     

Accurate Translucent Material Rendering under Spherical Gaussian Lights

In this paper we present a new algorithm for accurate rendering of translucent materials under Spherical Gaussian (SG) lights. Our algorithm builds upon the quantized‐diffusion BSSRDF model recently introduced in [ [dI11] ]. Our main contribution is an efficient algorithm for computing the integral of the BSSRDF with an SG light. We incorporate both single and multiple scattering components. Our model improves upon previous work by accounting for the incident angle of each individual SG light. This leads to more accurate rendering results, notably elliptical profiles from oblique illumination. In contrast, most existing models only consider the total irradiance received from all lights, hence can only generate circular profiles. Experimental results show that our method is suitable for rendering of translucent materials under finite‐area lights or environment lights that can be approximated by a small number of SGs.     

Heat Walk: Robust Salient Segmentation of Non‐rigid Shapes

Segmenting three dimensional objects using properties of heat diffusion on meshes aim to produce salient results. The few existing algorithms based on heat diffusion do not use the full knowledge that can be gained from heat diffusion and are sensitive to varying kinds of perturbations. Our simple algorithm, Heat Walk, converts the implicit information in the heat kernel to explicit knowledge about the pathways for maximum heat flow capacity. We develop a two stage strategy for segmentation. In the first stage we quickly identify regions which are dominated by heat accumulators by employing a greedy algorithm. The second stage partitions out dissipative regions from the previously discovered accumulative regions by using a KL‐divergence based criterion. The resulting algorithm is both independent of human intervention and fast because of the globally aware directed walk along the maximal heat flow capacity. Extensive experimental evidence shows the method is robust to a variety of noise factors including topological short circuits, surface holes, pose variations, variations in tessellation, missing features, scaling, as well as normal and shot noise. Comparison with the Princeton Segmentation Benchmark (PSB) shows that our method is comparable with state of the art segmentation methods and has additional advantages of being robust and self contained. Based upon theoretical insight the convergence and stability of the Heat Walk is shown.     

Example‐Based Fractured Appearance

A common weathering effect is the appearance of cracks due to material fractures. Previous exemplar‐based aging and weathering methods have either reused images or sought to replicate observed patterns exactly. We introduce a new approach to exemplar‐based modeling that creates weathered patterns on synthetic objects by matching the statistics of fracture patterns in a photograph. We present a user study to determine which statistics are correlated to visual similarity and how they are perceived by the user. We then describe a revised physically‐based fracture model capable of producing a wide range of crack patterns at interactive rates. We demonstrate how a Bayesian optimization method can determine the parameters of this model so it can produce a pattern with the same key statistics as an exemplar. Finally, we present results using our approach and various exemplars to produce a variety of fracture effects in synthetic renderings of complex environments. The speed of the fracture simulation allows interactive previews of the fractured results and its application on large scale environments.     

Path‐space Motion Estimation and Decomposition for Robust Animation Filtering

Renderings of animation sequences with physics‐based Monte Carlo light transport simulations are exceedingly costly to generate frame‐by‐frame, yet much of this computation is highly redundant due to the strong coherence in space, time and among samples. A promising approach pursued in prior work entails subsampling the sequence in space, time, and number of samples, followed by image‐based spatio‐temporal upsampling and denoising. These methods can provide significant performance gains, though major issues remain: firstly, in a multiple scattering simulation, the final pixel color is the composite of many different light transport phenomena, and this conflicting information causes artifacts in image‐based methods. Secondly, motion vectors are needed to establish correspondence between the pixels in different frames, but it is unclear how to obtain them for most kinds of light paths (e.g. an object seen through a curved glass panel). To reduce these ambiguities, we propose a general decomposition framework, where the final pixel color is separated into components corresponding to disjoint subsets of the space of light paths. Each component is accompanied by motion vectors and other auxiliary features such as reflectance and surface normals. The motion vectors of specular paths are computed using a temporal extension of manifold exploration and the remaining components use a specialized variant of optical flow. Our experiments show that this decomposition leads to significant improvements in three image‐based applications: denoising, spatial upsampling, and temporal interpolation.     

Real-time homogenous translucent material editing

This paper presents a novel method for real-time homogenous translucent material editing under fixed illumination. We consider the complete analytic BSSRDF model proposed by Jensen et al. [ [JMLH01] ], including both multiple scattering and single scattering. Our method allows the user to adjust the analytic parameters of BSSRDF and provides high-quality, real-time rendering feedback. Inspired by recently developed Precomputed Radiance Transfer (PRT) techniques, we approximate both the multiple scattering diffuse reflectance function and the single scattering exponential attenuation function in the analytic model using basis functions, so that re-computing the outgoing radiance at each vertex as parameters change reduces to simple dot products. In addition, using a non-uniform piecewise polynomial basis, we are able to achieve smaller approximation error than using bases adopted in previous PRT-based works, such as spherical harmonics and wavelets. Using hardware acceleration, we demonstrate that our system generates images comparable to [ [JMLH01] ]at real-time frame-rates.     

Adaptive Space Deformations Based on Rigid Cells

We propose a new adaptive space deformation method for interactive shape modeling. A novel energy formulation based on elastically coupled volumetric cells yields intuitive detail preservation even under large deformations. By enforcing rigidity of the cells, we obtain an extremely robust numerical solver for the resulting nonlinear optimization problem. Scalability is achieved using an adaptive spatial discretization that is decoupled from the resolution of the embedded object. Our approach is versatile and easy to implement, supports thin-shell and solid deformations of 2D and 3D objects, and is applicable to arbitrary sample-based representations, such as meshes, triangle soups, or point clouds.     

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.     

Progressive Virtual Beam Lights

A recent technique that forms virtual ray lights (VRLs) from path segments in media, reduces the artifacts common to VPL approaches in participating media, however, distracting singularities still remain. We present Virtual Beam Lights (VBLs), a progressive many‐lights algorithm for rendering complex indirect transport paths in, from, and to media. VBLs are efficient and can handle heterogeneous media, anisotropic scattering, and moderately glossy surfaces, while provably converging to ground truth. We inflate ray lights into beam lights with finite thicknesses to eliminate the remaining singularities. Furthermore, we devise several practical schemes for importance sampling the various transport contributions between camera rays, light rays, and surface points. VBLs produce artifact‐free images faster than VRLs, especially when glossy surfaces and/or anisotropic phase functions are present. Lastly, we employ a progressive thickness reduction scheme for VBLs in order to render results that converge to ground truth.     

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.     

BendyLights: Artistic Control of Direct Illumination by Curving Light Rays

In computer cinematography, artists routinely use non‐physical lighting models to achieve desired appearances. This paper presents BendyLights, a non‐physical lighting model where light travels nonlinearly along splines, allowing artists to control light direction and shadow position at different points in the scene independently. Since the light deformation is smoothly defined at all world‐space positions, the resulting non‐physical lighting effects remain spatially consistent, avoiding the frequent incongruences of many non‐physical models. BendyLights are controlled simply by reshaping splines, using familiar interfaces, and require very few parameters. BendyLight control points can be keyframed to support animated lighting effects. We demonstrate BendyLights both in a realtime rendering system for editing and a production renderer for final rendering, where we show that BendyLights can also be used with global illumination.     

Shape-aware Volume Illustration

We introduce a novel volume illustration technique for regularly sampled volume datasets. The fundamental difference between previous volume illustration algorithms and ours is that our results are shape-aware, as they depend not only on the rendering styles, but also the shape styles. We propose a new data structure that is derived from the input volume and consists of a distance volume and a segmentation volume. The distance volume is used to reconstruct a continuous field around the object boundary, facilitating smooth illustrations of boundaries and silhouettes. The segmentation volume allows us to abstract or remove distracting details and noise, and apply different rendering styles to different objects and components. We also demonstrate how to modify the shape of illustrated objects using a new 2D curve analogy technique. This provides an interactive method for learning shape variations from 2D hand-painted illustrations by drawing several lines. Our experiments on several volume datasets demonstrate that the proposed approach can achieve visually appealing and shape-aware illustrations. The feedback from medical illustrators is quite encouraging.     

ISHair: Importance Sampling for Hair Scattering

We present an importance sampling method for the bidirectional scattering distribution function (bsdf) of hair. Our method is based on the multi‐lobe hair scattering model presented by Sadeghi et al. [ [SPJT10] ]. We reduce noise by drawing samples from a distribution that approximates the bsdf well. Our algorithm is efficient and easy to implement, since the sampling process requires only the evaluation of a few analytic functions, with no significant memory overhead or need for precomputation. We tested our method in a research raytracer and a production renderer based on micropolygon rasterization. We show significant improvements for rendering direct illumination using multiple importance sampling and for rendering indirect illumination using path tracing.     

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.     

Scalable Height Field Self‐Shadowing

We present a new method suitable for general purpose graphics processing units to render self‐shadows on dynamic height fields under dynamic light environments in real‐time. Visibility for each point in the height field is determined as the exact horizon for a set of azimuthal directions in time linear in height field size and the number of directions. The surface is shaded using the horizon information and a high‐resolution light environment extracted on‐line from a high dynamic range cube map, allowing for detailed extended shadows. The desired accuracy for any geometric content and lighting complexity can be matched by choosing a suitable number of azimuthal directions. Our method is able to represent arbitrary features of both high‐ and low‐frequency, unifying hard and soft shadowing. We achieve 23 fps on 1024×1024 height fields with 64 azimuthal directions under a 256×64 environment lighting on an Nvidia GTX 280 GPU.     

A Significance Cache for Accelerating Global Illumination

Rendering using physically based methods requires substantial computational resources. Most methods that are physically based use straightforward techniques that may excessively compute certain types of light transport, while ignoring more important ones. Importance sampling is an effective and commonly used technique to reduce variance in such methods. Most current approaches for physically based rendering based on Monte Carlo methods sample the BRDF and cosine term, but are unable to sample the indirect illumination as this is the term that is being computed. Knowledge of the incoming illumination can be especially useful in the case of hard to find light paths, such as caustics or scenes which rely primarily on indirect illumination. To facilitate the determination of such paths, we propose a caching scheme which stores important directions, and is analytically sampled to calculate important paths. Results show an improvement over BRDF sampling and similar illumination importance sampling.     

Matting and Compositing for Fresnel Reflection on Wavy Surfaces

This paper introduces a framework that can extract an alpha matte from a single image with Fresnel reflection, and that can composite other objects with the image such that plausible reflections are included. Our method handles reflections in a plane with small undulations, for example, a water surface with waves or a glossy tabletop. During the matting stage, our method first estimates the transmission color, which is assumed to be uniform, and then calculates a reflection image and alpha matte based on user markups. However, accurate extraction of the matte becomes challenging when a plane has small undulations because these create perturbations in the matte. We therefore propose a filter that can refine the matte effectively. In the compositing stage, the reflection of a composited object is synthesized by ray tracing in real time. We demonstrate the effectiveness of our method through comparisons with ground‐truth data and results using natural images as inputs.