A Sparse Parametric Mixture Model for BTF Compression,Editing and Rendering

Bidirectional texture functions (BTFs) represent the appearance of complex materials. Three major shortcomings with BTFs are the bulky storage, the difficulty in editing and the lack of efficient rendering methods. To reduce storage, many compression techniques have been applied to BTFs, but the results are difficult to edit. To facilitate editing, analytical models have been fit, but at the cost of accuracy of representation for many materials. It becomes even more challenging if efficient rendering is also needed. We introduce a high‐quality general representation that is, at once, compact, easily editable, and can be efficiently rendered. The representation is computed by adopting the stagewise Lasso algorithm to search for a sparse set of analytical functions, whose weighted sum approximates the input appearance data. We achieve compression rates comparable to a state‐of‐the‐art BTF compression method. We also demonstrate results in BTF editing and rendering.     

Depth of Field Effects for Interactive Direct Volume Rendering

In this paper, a method for interactive direct volume rendering is proposed for computing depth of field effects, which previously were shown to aid observers in depth and size perception of synthetically generated images. The presented technique extends those benefits to volume rendering visualizations of 3D scalar fields from CT/MRI scanners or numerical simulations. It is based on incremental filtering and as such does not depend on any pre‐computation, thus allowing interactive explorations of volumetric data sets via on‐the‐fly editing of the shading model parameters or (multi‐dimensional) transfer functions.     

Real‐time Shading with Filtered Importance Sampling

We propose an analysis of numerical integration based on sampling theory, whereby the integration error caused by aliasing is suppressed by pre‐filtering. We derive a pre‐filter for evaluating the illumination integral yielding filtered importance sampling, a simple GPU‐based rendering algorithm for image‐based lighting. Furthermore, we extend the algorithm with real‐time visibility computation. Free from any pre‐computation, the algorithm supports fully dynamic scenes and, above all, is simple to implement.     

Estimating Color and Texture Parameters for Vector Graphics

Diffusion curves are a powerful vector graphic representation that stores an image as a set of 2D Bezier curves with colors defined on either side. These colors are diffused over the image plane, resulting in smooth color regions as well as sharp boundaries. In this paper, we introduce a new automatic diffusion curve coloring algorithm. We start by defining a geometric heuristic for the maximum density of color control points along the image curves. Following this, we present a new algorithm to set the colors of these points so that the resulting diffused image is as close as possible to a source image in a least squares sense. We compare our coloring solution to the existing one which fails for textured regions, small features, and inaccurately placed curves. The second contribution of the paper is to extend the diffusion curve representation to include texture details based on Gabor noise. Like the curves themselves, the defined texture is resolution independent, and represented compactly. We define methods to automatically make an initial guess for the noise texure, and we provide intuitive manual controls to edit the parameters of the Gabor noise. Finally, we show that the diffusion curve representation itself extends to storing any number of attributes in an image, and we demonstrate this functionality with image stippling an hatching applications.     

Lazy Solid Texture Synthesis

Existing solid texture synthesis algorithms generate a full volume of color content from a set of 2D example images. We introduce a new algorithm with the unique ability to restrict synthesis to a subset of the voxels, while enforcing spatial determinism. This is especially useful when texturing objects, since only a thick layer around the surface needs to be synthesized. A major difficulty lies in reducing the dependency chain of neighborhood matching, so that each voxel only depends on a small number of other voxels. Our key idea is to synthesize a volume from a set of pre‐computed 3D candidates, each being a triple of interleaved 2D neighborhoods. We present an efficient algorithm to carefully select in a pre‐process only those candidates forming consistent triples. This significantly reduces the search space during subsequent synthesis. The result is a new parallel, spatially deterministic solid texture synthesis algorithm which runs efficiently on the GPU. Our approach generates high resolution solid textures on surfaces within seconds. Memory usage and synthesis time only depend on the output textured surface area. The GPU implementation of our method rapidly synthesizes new textures for the surfaces appearing when interactively breaking or cutting objects.     

Textures on Rank‐1 Lattices

Storing textures on orthogonal tensor product lattices is predominant in computer graphics, although it is known that their sampling efficiency is not optimal. In two dimensions, the hexagonal lattice provides the maximum sampling efficiency. However, handling these lattices is difficult, because they are not able to tile an arbitrary rectangular region and have an irrational basis. By storing textures on rank‐1 lattices, we resolve both problems: Rank‐1 lattices can closely approximate hexagonal lattices, while all coordinates of the lattice points remain integer. At identical memory footprint texture quality is improved as compared to traditional orthogonal tensor product lattices due to the higher sampling efficiency. We introduce the basic theory of rank‐1 lattice textures and present an algorithmic framework which easily can be integrated into existing off‐line and real‐time rendering systems.     

A Multidirectional Occlusion Shading Model for Direct Volume Rendering

In this paper, we present a novel technique which simulates directional light scattering for more realistic interactive visualization of volume data. Our method extends the recent directional occlusion shading model by enabling light source positioning with practically no performance penalty. Light transport is approximated using a tilted cone‐shaped function which leaves elliptic footprints in the opacity buffer during slice‐based volume rendering. We perform an incremental blurring operation on the opacity buffer for each slice in front‐to‐back order. This buffer is then used to define the degree of occlusion for the subsequent slice. Our method is capable of generating high‐quality soft shadowing effects, allows interactive modification of all illumination and rendering parameters, and requires no pre‐computation.     

Computer‐Suggested Facial Makeup

Finding the best makeup for a given human face is an art in its own right. Experienced makeup artists train for years to be skilled enough to propose a best‐fit makeup for an individual. In this work we propose a system that automates this task. We acquired the appearance of 56 human faces, both without and with professional makeup. To this end, we use a controlled‐light setup, which allows to capture detailed facial appearance information, such as diffuse reflectance, normals, subsurface‐scattering, specularity, or glossiness. A 3D morphable face model is used to obtain 3D positional information and to register all faces into a common parameterization. We then define makeup to be the change of facial appearance and use the acquired database to find a mapping from the space of human facial appearance to makeup. Our main application is to use this mapping to suggest the best‐fit makeup for novel faces that are not in the database. Further applications are makeup transfer, automatic rating of makeup, makeup‐training, or makeup‐exaggeration. As our makeup representation captures a change in reflectance and scattering, it allows us to synthesize faces with makeup in novel 3D views and novel lighting with high realism. The effectiveness of our approach is further validated in a user‐study.     

Characteristic Point Maps

Extremely dense spatial sampling is often needed to prevent aliasing when rendering objects with high frequency variations in geometry and reflectance. To accelerate the rendering process, we introduce characteristic point maps (CPMs), a hierarchy of view-independent points, which are chosen to preserve the appearance of the original model across different scales. In preprocessing, randomized matrix column sampling is used to reduce an initial dense sampling to a minimum number of characteristic points with associated weights. In rendering, the reflected radiance is computed using a weighted average of reflectances from characteristic points. Unlike existing techniques, our approach requires no restrictions on the original geometry or reflectance functions.     

An Analytical Solution to Single Scattering in Homogeneous Participating Media

Despite their numerous applications, efficiently rendering participating media remains a challenging task due to the intricacy of the radiative transport equation. As they provide a generic means of solving a wide variety of problems, numerical methods are most often used to solve the air-light integral even under simplifying assumptions. In this paper, we present a novel analytical approach to single scattering from isotropic point light sources in homogeneous media. We derive the first closed-form solution to the air-light integral in isotropic media and extend this formulation to anisotropic phase functions. The technique relies neither on pre-computation nor on storage, and we provide a practical implementation allowing for an explicit control on the accuracy of the solutions. Finally, we demonstrate its quantitative and qualitative benefits over both previous numerical and analytical approaches.     

Illuminated 3D Scatterplots

In contrast to 2D scatterplots, the existing 3D variants have the advantage of showing one additional data dimension, but suffer from inadequate spatial and shape perception and therefore are not well suited to display structures of the underlying data. We improve shape perception by applying a new illumination technique to the pointcloud representation of 3D scatterplots. Points are classified as locally linear, planar, and volumetric structures—according to the eigenvalues of the inverse distance-weighted covariance matrix at each data element. Based on this classification, different lighting models are applied: codimension-2 illumination, surface illumination, and emissive volumetric illumination. Our technique lends itself to efficient GPU point rendering and can be combined with existing methods like semi-transparent rendering, halos, and depth or attribute based color coding. The user can interactively navigate in the dataset and manipulate the classification and other visualization parameters. We demonstrate our visualization technique by showing examples of multi-dimensional data and of generic pointcloud data.     

BTF Compression via Sparse Tensor Decomposition

In this paper, we present a novel compression technique for Bidirectional Texture Functions based on a sparse tensor decomposition. We apply the K-SVD algorithm along two different modes of a tensor to decompose it into a small dictionary and two sparse tensors. This representation is very compact, allowing for considerably better compression ratios at the same RMS error than possible with current compression techniques like PCA, N-mode SVD and Per Cluster Factorization. In contrast to other tensor decomposition based techniques, the use of a sparse representation achieves a rendering performance that is at high compression ratios similar to PCA based methods.     

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.     

Precomputed Atmospheric Scattering

We present a new and accurate method to render the atmosphere in real time from any viewpoint from ground level to outer space, while taking Rayleigh and Mie multiple scattering into account. Our method reproduces many effects of the scattering of light, such as the daylight and twilight sky color and aerial perspective for all view and light directions, or the Earth and mountain shadows (light shafts) inside the atmosphere. Our method is based on a formulation of the light transport equation that is precomputable for all view points, view directions and sun directions. We show how to store this data compactly and propose a GPU compliant algorithm to precompute it in a few seconds. This precomputed data allows us to evaluate at runtime the light transport equation in constant time, without any sampling, while taking into account the ground for shadows and light shafts.     

An Analysis of the In‐Out BRDF Factorization for View‐Dependent Relighting

Interactive rendering with dynamic natural lighting and changing view is a long‐standing goal in computer graphics. Recently, precomputation‐based methods for all‐frequency relighting have made substantial progress in this direction. Many of the most successful algorithms are based on a factorization of the BRDF into incident and outgoing directions, enabling each term to be precomputed independent of viewing direction, and re‐combined at run‐time. However, there has so far been no theoretical understanding of the accuracy of this factorization, nor the number of terms needed. In this paper, we conduct a theoretical and empirical analysis of the BRDF in‐out factorization. For Phong BRDFs, we obtain analytic results, showing that the number of terms needed grows linearly with the Phong exponent, while the factors correspond closely to spherical harmonic basis functions. More generally, the number of terms is quadratic in the frequency content of the BRDF along the reflected or half‐angle direction. This analysis gives clear practical guidance on the number of factors needed for a given material. Different objects in a scene can each be represented with the correct number of terms needed for that particular BRDF, enabling both accuracy and interactivity.