We present a generative model for isotropic bidirectional reflectance distribution functions (BRDFs) based on acquired reflectance data. Instead of using analytical reflectance models, we represent each BRDF as a dense set of measurements. This allows us to interpolate and extrapolate in the space of acquired BRDFs to create new BRDFs. We treat each acquired BRDF as a single high-dimensional vector taken from a space of all possible BRDFs. We apply both linear (subspace) and non-linear (manifold) dimensionality reduction tools in an effort to discover a lowerdimensional representation that characterizes our measurements. We let users define perceptually meaningful parametrization directions to navigate in the reduced-dimension BRDF space. On the low-dimensional manifold, movement along these directions produces novel but valid BRDFs.

We compress storage and accelerate performance of precomputed radiance transfer (PRT), which captures the way an object shadows, scatters, and reflects light. PRT records over many surface points a transfer matrix. At run-time, this matrix transforms a vector of spherical harmonic coefficients representing distant, low-frequency source lighting into exiting radiance. Per-point transfer matrices form a high-dimensional surface signal that we compress using clustered principal component analysis (CPCA), which partitions many samples into fewer clusters each approximating the signal as an affine subspace. CPCA thus reduces the high-dimensional transfer signal to a low-dimensional set of perpoint weights on a per-cluster set of representative matrices. Rather than computing a weighted sum of representatives and applying this result to the lighting, we apply the representatives to the lighting per-cluster (on the CPU) and weight these results perpoint (on the GPU). Since the output of the matrix is lowerdimensional than the matrix itself, this reduces computation. We also increase the accuracy of encoded radiance functions with a new least-squares optimal projection of spherical harmonics onto the hemisphere. We describe an implementation on graphics hardware that performs real-time rendering of glossy objects with dynamic self-shadowing and interreflection without fixing the view or light as in previous work. Our approach also allows significantly increased lighting frequency when rendering diffuse objects and includes subsurface scattering.

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We present a signal-processing framework for light transport. We study the frequency content of radiance and how it is altered by phenomena such as shading, occlusion, and transport. This extends previous work that considered either spatial or angular dimensions, and it offers a comprehensive treatment of both space and angle. We show that occlusion, a multiplication in the primal, amounts in the Fourier domain to a convolution by the spectrum of the blocker. Propagation corresponds to a shear in the space-angle frequency domain, while reflection on curved objects performs a different shear along the angular frequency axis. As shown by previous work, reflection is a convolution in the primal and therefore a multiplication in the Fourier domain. Our work shows how the spatial components of lighting are affected by this angular convolution. Our framework predicts the characteristics of interactions such as caustics and the disappearance of the shadows of small features. Predictions on the frequency content can then be used to control sampling rates for rendering. Other potential applications include precomputed radiance transfer and inverse rendering.

Figure 1: Photograph compared to a face rendered using our skin reflectance model. The rendered image was composited on top of the photograph. Right: Changing the albedo and BRDF using statistics of measured model parameters from a sample population. We have measured 3D face geometry, skin reflectance, and subsurface scattering using custom-built devices for 149 subjects of varying age, gender, and race. We developed a novel skin reflectance model whose parameters can be estimated from measurements. The model decomposes the large amount of measured skin data into a spatially-varying analytic BRDF, a diffuse albedo map, and diffuse subsurface scattering. Our model is intuitive, physically plausible, and – since we do not use the original measured data – easy to edit as well. High-quality renderings come close to reproducing real photographs. The analysis of the model parameters for our sample population reveals variations according to subject age, gender, skin type, and external factors (e.g., sweat, cold, or makeup). Using our statistics, a user can edit the overall appearance of a face (e.g., changing skin type and age) or change small-scale features using texture synthesis (e.g., adding moles and freckles). We are making the collected statistics publicly available to the research community for applications in face synthesis and analysis.

This paper presents a technique for estimating the spatially-varying reflectance properties of a surface based on its appearance during a single pass of a linear light source. By using a linear light rather than a point light source as the illuminant, we are able to reliably observe and estimate the diffuse color, specular color, and specular roughness of each point of the surface. The reflectometry apparatus we use is simple and inexpensive to build, requiring a single direction of motion for the light source and a fixed camera viewpoint. Our model fitting technique first renders a reflectance table of how diffuse and specular reflectance lobes would appear under moving linear light source illumination. Then, for each pixel we compare its series of intensity values to the tabulated reflectance lobes to determine which reflectance model parameters most closely produce the observed reflectance values. Using two passes of the linear light source at different angles, we can also estimate per-pixel surface normals as well as the reflectance parameters. Additionally our system records a per-pixel height map for the object and estimates its per-pixel translucency. We produce real-time renderings of the captured objects using a custom hardware shading algorithm. We apply the technique to a test object exhibiting a variety of materials as well as to an illuminated manuscript with gold lettering. To demonstrate the technique's accuracy, we compare renderings of the captured models to real photographs of the original objects.

One of the main challenges in computer graphics is still the realistic rendering of complex materials such as fabric or skin. The difficulty arises from the complex meso structure and reflectance behavior defining the unique look-and-feel of a material. A wide class of such realistic materials can be described as 2D-texture under varying light- and view direction namely the Bidirectional Texture Function (BTF). Since an easy and general method for modeling BTFs is not available, current research concentrates on image-based methods which rely on measured BTFs (acquired real-world data) in combination with appropriate synthesis methods. Recent results have shown that this approach greatly improves the visual quality of rendered surfaces and therefore the quality of applications such as virtual prototyping. This STAR will present in detail the state-of-the-art techniques for the main tasks involved in producing photo-realistic renderings using measured BTFs

Results overview: First, a volumetric scalar data set of size 256 3 requiring 16 MB is shown. Second, the hierarchically encoded data set (0.78 MB) is directly rendered using programmable graphics hardware. Third, one time step (256 3) of a 1.4 GB shock wave simulation is shown. Fourth, the same time step is directly rendered out of a compressed sequence of 70 MB. Rendering the data sets to a 512 2 viewport runs at 11 and 24 fps, respectively, on an ATI 9700. A survey of graphics developers on the issue of texture mapping hardware for volume rendering would most likely find that the vast majority of them view limited texture memory as one of the most serious drawbacks of an otherwise fine technology. In this paper, we propose a compression scheme for static and time-varying volumetric data sets based on vector quantization that allows us to circumvent this limitation. We describe a hierarchical quantization scheme that is based on a multiresolution covariance analysis of the original field. This allows for the efficient encoding of large-scale data sets, yet providing a mechanism to exploit temporal coherence in non-stationary fields. We show, that decoding and rendering the compressed data stream can be done on the graphics chip using programmable hardware. In this way, data transfer between the CPU and the graphics processing unit (GPU) can be minimized thus enabling flexible and memory efficient real-time rendering options. We demonstrate the effectiveness of our approach by demonstrating interactive renditions of Gigabyte data sets at reasonable fidelity on commodity graphics hardware.

In this paper we present two novel reflectance measurement procedures that require fewer total measurements than standard uniform sampling approaches. First, we acquire densely sampled reflectance data for a large collection of different materials. Using these densely sampled measurements we analyze the general surface reflectance function to determine the local signal variation at each point in the function’s domain. We then use wavelet analysis to derive a common basis for all of the acquired reflectance functions as well as a corresponding non-uniform sampling pattern that corresponds to all non-zero wavelet coefficients. Second, we show that the reflectance of an arbitrary material can be represented as a linear combination of the surface reflectance functions. Furthermore, our analysis provides a reduced set of sampling points that permits us to robustly estimate the coefficients of this linear combination. These procedures dramatically shorten the acquisition time for isotropic reflectance measurements. We present a detailed description and analysis of our measurement approaches and sampling strategies.