An Energy‐Conserving Hair Reflectance Model

We present a reflectance model for dielectric cylinders with rough surfaces such as human hair fibers. Our model is energy conserving and can evaluate arbitrarily many orders of internal reflection. Accounting for compression and contraction of specular cones produces a new longitudinal scattering function which is non‐Gaussian and includes an off‐specular peak. Accounting for roughness in the azimuthal direction leads to an integral across the hair fiber which is efficiently evaluated using a Gaussian quadrature. Solving cubic equations is avoided, caustics are included in the model in a consistent fashion, and more accurate colors are predicted by considering many internal pathways.     

The Dual‐microfacet Model for Capturing Thin Transparent Slabs

We present a new model, called the dual‐microfacet, for those materials such as paper and plastic formed by a thin, transparent slab lying between two surfaces of spatially varying roughness. Light transmission through the slab is represented by a microfacet‐based BTDF which tabulates the microfacet's normal distribution (NDF) as a function of surface location. Though the material is bounded by two surfaces of different roughness, we approximate light transmission through it by a virtual slab determined by a single spatially‐varying NDF. This enables efficient capturing of spatially variant transparent slices. We describe a device for measuring this model over a flat sample by shining light from a CRT behind it and capturing a sequence of images from a single view. Our method captures both angular and spatial variation in the BTDF and provides a good match to measured materials.     

Estimating Specular Roughness and Anisotropy from Second Order Spherical Gradient Illumination

This paper presents a novel method for estimating specular roughness and tangent vectors, per surface point, from polarized second order spherical gradient illumination patterns. We demonstrate that for isotropic BRDFs, only three second order spherical gradients are sufficient to robustly estimate spatially varying specular roughness. For anisotropic BRDFs, an additional two measurements yield specular roughness and tangent vectors per surface point. We verify our approach with different illumination configurations which project both discrete and continuous fields of gradient illumination. Our technique provides a direct estimate of the per-pixel specular roughness and thus does not require off-line numerical optimization that is typical for the measure-and-fit approach to classical BRDF modeling.     

A Physically‐Based BSDF for Modeling the Appearance of Paper

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.     

Abstractive Representation and Exploration of Hierarchically Clustered Diffusion Tensor Fiber Tracts

Diffusion tensor imaging (DTI) has been used to generate fibrous structures in both brain white matter and muscles. Fiber clustering groups the DTI fibers into spatially and anatomically related tracts. As an increasing number of fiber clustering methods have been recently developed, it is important to display, compare, and explore the clustering results efficiently and effectively. In this paper, we present an anatomical visualization technique that reduces the geometric complexity of the fiber tracts and emphasizes the high‐level structures. Beginning with a volumetric diffusion tensor image, we first construct a hierarchical clustering representation of the fiber bundles. These bundles are then reformulated into a 3D multi‐valued volume data. We then build a set of geometric hulls and principal fibers to approximate the shape and orientation of each fiber bundle. By simultaneously visualizing the geometric hulls, individual fibers, and other data sets such as fractional anisotropy, the overall shape of the fiber tracts are highlighted, while preserving the fibrous details. A rater with expert knowledge of white matter structure has evaluated the resulting interactive illustration and confirmed the improvement over straightforward DTI fiber tract visualization.     

Wetting Effects in Hair Simulation

There is considerable recent progress in hair simulations, driven by the high demands in computer animated movies. However, capturing the complex interactions between hair and water is still relatively in its infancy. Such interactions are best modeled as those between water and an anisotropic permeable medium as water can flow into and out of the hair volume biased in hair fiber direction. Modeling the interaction is further challenged when the hair is allowed to move. In this paper, we introduce a simulation model that reproduces interactions between water and hair as a dynamic anisotropic permeable material. We utilize an Eulerian approach for capturing the microscopic porosity of hair and handle the wetting effects using a Cartesian bounding grid. A Lagrangian approach is used to simulate every single hair strand including interactions with each other, yielding fine‐detailed dynamic hair simulation. Our model and simulation generate many interesting effects of interactions between fine‐detailed dynamic hair and water, i.e., water absorption and diffusion, cohesion of wet hair strands, water flow within the hair volume, water dripping from the wet hair strands and morphological shape transformations of wet hair.     

AppFusion: Interactive Appearance Acquisition Using a Kinect Sensor

We present an interactive material acquisition system for average users to capture the spatially varying appearance of daily objects. While an object is being scanned, our system estimates its appearance on‐the‐fly and provides quick visual feedback. We build the system entirely on low‐end, off‐the‐shelf components: a Kinect sensor, a mirror ball and printed markers. We exploit the Kinect infra‐red emitter/receiver, originally designed for depth computation, as an active hand‐held reflectometer, to segment the object into clusters of similar specular materials and estimate the roughness parameters of BRDFs simultaneously. Next, the diffuse albedo and specular intensity of the spatially varying materials are rapidly computed in an inverse rendering framework, using data from the Kinect RGB camera. We demonstrate captured results of a range of materials, and physically validate our system.     

Feature based terrain generation using diffusion equation

This paper presents a diffusion method for generating terrains from a set of parameterized curves that characterize the landform features such as ridge lines, riverbeds or cliffs. Our approach provides the user with an intuitive vector‐based feature‐oriented control over the terrain. Different types of constraints (such as elevation, slope angle and roughness) can be attached to the curves so as to define the shape of the terrain. The terrain is generated from the curve representation by using an efficient multigrid diffusion algorithm. The algorithm can be efficiently implemented on the GPU, which allows the user to interactively create a vast variety of landscapes.     

Uniformization and Density Adaptation for Point Cloud Data Via Graph Laplacian

Point cloud data is one of the most common types of input for geometric processing applications. In this paper, we study the point cloud density adaptation problem that underlies many pre‐processing tasks of points data. Specifically, given a (sparse) set of points Q sampling an unknown surface and a target density function, the goal is to adapt Q to match the target distribution. We propose a simple and robust framework that is effective at achieving both local uniformity and precise global density distribution control. Our approach relies on the Gaussian‐weighted graph Laplacian and works purely in the points setting. While it is well known that graph Laplacian is related to mean‐curvature flow and thus has denoising ability, our algorithm uses certain information encoded in the graph Laplacian that is orthogonal to the mean‐curvature flow. Furthermore, by leveraging the natural scale parameter contained in the Gaussian kernel and combining it with a simulated annealing idea, our algorithm moves points in a multi‐scale manner. The resulting algorithm relies much less on the input points to have a good initial distribution (neither uniform nor close to the target density distribution) than many previous refinement‐based methods. We demonstrate the simplicity and effectiveness of our algorithm with point clouds sampled from different underlying surfaces with various geometric and topological properties.     

Scales and Scale‐like Structures

We present a method for generating scales and scale‐like structures on a polygonal mesh through surface replacement. As input, we require a triangular mesh that will be covered with scales and one or more proxy‐models to be used as the scale's shape. A user begins scale generation by drawing a lateral line on the model to control the distribution and orientation of scales on the surface. We then create a vector field over the surface to control an anisotropic Voronoi tessellation, which represents the region occupied by each scale. Next we replace these regions by cutting the proxy model to match the boundary of the Voronoi region and deform the cut model onto the surface. The result is a fully connected 2‐manifold that is suitable for subsequent post‐processing applications like surface subdivision.     

Rendering Trees with Indirect Lighting in Real Time

High quality lighting is one of the challenges for interactive tree rendering. To this end, this paper presents a lighting model allowing real‐time rendering of trees with convincing indirect lighting. Rather than defining an empirical model to mimic lighting of real trees, we work at a lower level by modeling the spatial distribution of leaves and by assigning them probabilistic properties. We focus mainly on precise low‐frequency lighting that our eyes are more sensitive to and we add high‐frequency details afterwards. The resulting model is efficient and simple to implement on a GPU.     

Dynamic Multi‐View Exploration of Shape Spaces

Statistical shape modeling is a widely used technique for the representation and analysis of the shapes and shape variations present in a population. A statistical shape model models the distribution in a high dimensional shape space, where each shape is represented by a single point. We present a design study on the intuitive exploration and visualization of shape spaces and shape models. Our approach focuses on the dual‐space nature of these spaces. The high‐dimensional shape space represents the population, whereas object space represents the shape of the 3D object associated with a point in shape space. A 3D object view provides local details for a single shape. The high dimensional points in shape space are visualized using a 2D scatter plot projection, the axes of which can be manipulated interactively. This results in a dynamic scatter plot, with the further extension that each point is visualized as a small version of the object shape that it represents. We further enhance the population‐object duality with a new type of view aimed at shape comparison. This new “shape evolution view” visualizes shape variability along a single trajectory in shape space, and serves as a link between the two spaces described above. Our three‐view exploration concept strongly emphasizes linked interaction between all spaces. Moving the cursor over the scatter plot or evolution views, shapes are dynamically interpolated and shown in the object view. Conversely, camera manipulation in the object view affects the object visualizations in the other views. We present a GPU‐accelerated implementation, and show the effectiveness of the three‐view approach using a number of real‐world cases. In these, we demonstrate how this multi‐view approach can be used to visually explore important aspects of a statistical shape model, including specificity, compactness and reconstruction error.     

Realistic Ultrasound Simulation of Complex Surface Models Using Interactive Monte‐Carlo Path Tracing

Ray‐based simulations have been shown to generate impressively realistic ultrasound images in interactive frame rates. Recent efforts used GPU‐based surface raytracing to simulate complex ultrasound interactions such as multiple reflections and refractions. These methods are restricted to perfectly specular reflections (i.e. following only a single reflective/refractive ray), whereas real tissue exhibits roughness of varying degree at tissue interfaces, causing partly diffuse reflections and refractions. Such surface interactions are significantly more complex and can in general not be handled by conventional deterministic raytracing approaches. However, these can be efficiently computed by Monte‐Carlo sampling techniques, where many ray paths are generated with respect to a probability distribution. In this paper, we introduce Monte‐Carlo raytracing for ultrasound simulation. This enables the realistic simulation of ultrasound‐tissue interactions such as soft shadows and fuzzy reflections. We discuss how to properly weight the contribution of each ray path in order to simulate the behaviour of a beamformed ultrasound signal. Tracing many individual rays per transducer element is easily parallelizable on modern GPUs, as opposed to previous approaches based on recursive binary raytracing. We further propose a significant performance optimization based on adaptive sampling.     

Estimation and Modeling of Actual Numerical Errors in Volume Rendering

In this paper we study the comprehensive effects on volume rendered images due to numerical errors caused by the use of finite precision for data representation and processing. To estimate actual error behavior we conduct a thorough study using a volume renderer implemented with arbitrary floating‐point precision. Based on the experimental data we then model the impact of floating‐point pipeline precision, sampling frequency and fixed‐point input data quantization on the fidelity of rendered images. We introduce three models, an average model, which does not adapt to different data nor varying transfer functions, as well as two adaptive models that take the intricacies of a new data set and transfer function into account by adapting themselves given a few different images rendered. We also test and validate our models based on new data that was not used during our model building.     

Visualizing Underwater Ocean Optics

Simulating the in‐water ocean light field is a daunting task. Ocean waters are one of the richest participating media, where light interacts not only with water molecules, but with suspended particles and organic matter as well. The concentration of each constituent greatly affects these interactions, resulting in very different hues. Inelastic scattering events such as fluorescence or Raman scattering imply energy transfers that are usually neglected in the simulations. Our contributions in this paper are a bio‐optical model of ocean waters suitable for computer graphics simulations, along with an improved method to obtain an accurate solution of the in‐water light field based on radiative transfer theory. The method provides a link between the inherent optical properties that define the medium and its apparent optical properties, which describe how it looks. The bio‐optical model of the ocean uses published data from oceanography studies. For inelastic scattering we compute all frequency changes at higher and lower energy values, based on the spectral quantum efficiency function of the medium. The results shown prove the usability of the system as a predictive rendering algorithm. Areas of application for this research span from underwater imagery to remote sensing; the resolution method is general enough to be usable in any type of participating medium simulation.     

Sample Based Visibility for Soft Shadows using Alias‐free Shadow Maps

This paper introduces an accurate real‐time soft shadow algorithm that uses sample based visibility. Initially, we present a GPU‐based alias‐free hard shadow map algorithm that typically requires only a single render pass from the light, in contrast to using depth peeling and one pass per layer. For closed objects, we also suppress the need for a bias. The method is extended to soft shadow sampling for an arbitrarily shaped area‐/volumetric light source using 128‐1024 light samples per screen pixel. The alias‐free shadow map guarantees that the visibility is accurately sampled per screen‐space pixel, even for arbitrarily shaped (e.g. non‐planar) surfaces or solid objects. Another contribution is a smooth coherent shading model to avoid common light leakage near shadow borders due to normal interpolation.     

A General BRDF Representation Based on Tensor Decomposition

Generating photo‐realistic images through Monte Carlo rendering requires efficient representation of light–surface interaction and techniques for importance sampling. Various models with good representation abilities have been developed but only a few of them have their importance sampling procedure. In this paper, we propose a method which provides a good bidirectional reflectance distribution function (BRDF) representation and efficient importance sampling procedure. Our method is based on representing BRDF as a function of tensor products. Four‐dimensional measured BRDF tensor data are factorized using Tucker decomposition. A large data set is used for comparing the proposed BRDF model with a number of well‐known BRDF models. It is shown that the underlying model provides good approximation to BRDFs.     

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.     

Modeling and Estimation of Energy‐Based Hyperelastic Objects

In this paper, we present a method to model hyperelasticity that is well suited for representing the nonlinearity of real‐world objects, as well as for estimating it from deformation examples. Previous approaches suffer several limitations, such as lack of integrability of elastic forces, failure to enforce energy convexity, lack of robustness of parameter estimation, or difficulty to model cross‐modal effects. Our method avoids these problems by relying on a general energy‐based definition of elastic properties. The accuracy of the resulting elastic model is maximized by defining an additive model of separable energy terms, which allow progressive parameter estimation. In addition, our method supports efficient modeling of extreme nonlinearities thanks to energy‐limiting constraints. We combine our energy‐based model with an optimization method to estimate model parameters from force‐deformation examples, and we show successful modeling of diverse deformable objects, including cloth, human finger skin, and internal human anatomy in a medical imaging application.     

Fast Estimation and Rendering of Indirect Highlights

This paper proposes a method for efficiently rendering indirect highlights. Indirect highlights are caused by the primary light source reflecting off two or more glossy surfaces. Accurately simulating such highlights is important to convey the realistic appearance of materials such as chrome and shiny metal. Our method models the glossy BRDF at a surface point as a directional distribution, using a spherical von Mises‐Fisher (vMF) distribution. As our main contribution, we merge multiple vMFs into a combined multimodal distribution. This effectively creates a filtered radiance response function, allowing us to efficiently estimate indirect highlights. We demonstrate our method in a near‐interactive application for rendering scenes with highly glossy objects. Our results produce realistic reflections under both local and environment lighting.