Filtering is critical for representing detail, such as color textures or normal maps, across a variety of scales. While MIP-mapping texture maps is commonplace, accurate normal map filtering remains a challenging problem because of nonlinearities in shading—we cannot simply average nearby surface normals. In this paper, we show analytically that normal map filtering can be formalized as a spherical convolution of the normal distribution function (NDF) and the BRDF, for a large class of common BRDFs such as Lambertian, microfacet and factored measurements. This theoretical result explains many previous filtering techniques as special cases, and leads to a generalization to a broader class of measured and analytic BRDFs. Our practical algorithms leverage a significant body of work that has studied lighting-BRDF convolution. We show how spherical harmonics can be used to filter the NDF for Lambertian and low-frequency specular BRDFs, while spherical von Mises-Fisher distributions can be used for high-frequency materials. 1

We present a technique for interactive relighting in which source radiance, viewing direction, and BRDFs can all be changed on the fly. In handling dynamic BRDFs, our method efficiently accounts for the effects of BRDF modification on the reflectance and incident radiance at a surface point. For reflectance, we develop a BRDF tensor representation that can be factorized into adjustable terms for lighting, viewing, and BRDF parameters. For incident radiance, there exists a non-linear relationship between indirect lighting and BRDFs in a scene, which makes linear light transport frameworks such as PRT unsuitable. To overcome this problem, we introduce precomputed transfer tensors (PTTs) which decompose indirect lighting into precomputable components that are each a function of BRDFs in the scene, and can be rapidly combined at run time to correctly determine incident radiance. We additionally describe a method for efficient handling of high-frequency specular reflections by separating them from the BRDF tensor representation and processing them using precomputed visibility information. With relighting based on PTTs, interactive performance with indirect lighting is demonstrated in applications to BRDF animation and material tuning.

Visual data comprises of multi-scale and inhomogeneous signals. In this paper, we exploit these characteristics and develop an adaptive data approximation technique based on a hierarchical tensor-based transformation. In this technique, an original multi-dimensional image is transformed into a hierarchy of signals to expose its multiscale structures. The signal at each level of the hierarchy is further divided into a number of smaller tensors to expose its spatially inhomogeneous structures. These smaller tensors are further transformed and pruned using a collective tensor approximation technique. Experimental results indicate that our technique can achieve higher compression ratios than existing functional approximation methods, including wavelet transforms, wavelet packet transforms and singlelevel tensor approximation.

Scenes lit with high dynamic range environment maps of real-world environments exhibit all the complex nuances of natural illumination. For applications that need lighting adjustments to the rendered images, editing environment maps directly is still cumbersome. First, designers have to determine which region in the environment map is responsible for the specific lighting feature (e.g. diffuse gradients, highlights and shadows) they desire to edit. Second, determining the parameters of image-editing operations needed to achieve specific changes to the selected lighting feature requires extensive trial-and-error. This paper presents envyLight, an interactive interface for editing natural illumination that combines an algorithm to select environment map regions, by sketching strokes on lighting features in the rendered image, with a small set of editing operations to quickly adjust the selected feature. The envyLight selection algorithm works well for indoor and outdoor lighting corresponding to rendered images where lighting features vary widely in number, size, contrast and edge blur. Furthermore, envyLight selection is general with respect to material type, from matte to sharp glossy, and the complexity of scenes ’ shapes. envyLight editing operations allow designers to quickly alter the position, contrast and edge blur of the selected lighting feature and can be keyframed to support animation.

Abstract — This paper presents a novel basis function, called spherical piecewise constant basis function (SPCBF), for precomputed radiance transfer. SPCBFs have several desirable properties: rotatability, ability to represent all-frequency signals, and support for efficient multiple product. By smartly partitioning the illumination sphere into a set of subregions, and associating each subregion with an SPCBF valued 1 inside the region and 0 elsewhere, we precompute the light coefficients using the resulting SPCBFs. Efficient rotation of the light representation in SPCBFs is achieved by rotating the domain of SPCBFs. During run-time rendering, we approximate the BRDF and visibility coefficients using the set of SPCBFs for light, possibly rotated, through fast lookup of summed-area-table (SAT) and visibility distance table (VDT), respectively. SPCBFs enable new effects such as object rotation in all-frequency rendering of dynamic scenes and onthe-fly BRDF editing under rotating environment lighting. With graphics hardware acceleration, our method achieves real-time frame rates.

We present a real-time relighting and shadowing method for dynamic scenes with varying lighting, view and BRDFs. Our approach is based on a compact representation of reflectance data that allows for changing the BRDF at run-time and a data-driven method for accurately synthesizing self-shadows on articulated and deformable geometries. Unlike previous self-shadowing approaches, we do not rely on local blocking heuristics. We do not fit a model to the BRDF-weighted visibility, but rather only to the visibility that changes during animation. In this manner, our model is more compact than previous techniques and requires less computation both during fitting and at run-time. Our reflectance product operators can re-integrate arbitrary low-frequency view-dependent BRDF effects on-the-fly and are compatible with all previous dynamic visibility generation techniques as well as our own data-driven visibility model. We apply our reflectance product operators to three different visibility generation models, and our data-driven model can achieve framerates well over 300Hz.

Much research in recent times has been conducted towards realtime rendering of accurate glossy reflections under direct, natural illumination including correct occlusions. The view dependent nature of these reflections will always cause this computation to be expensive unless heavily approximated. There also remains a question as to whether humans are even capable of noticing the difference in accuracy or whether our perception of the realism of the scene remains unchanged and thus the extra effort expended in rendering accurate reflections is effectively wasted. We conduct a user study to analyse any decline in perceived realism of glossy scenes rendered with a variety of specular occlusion approximations under a multitude of BRDFs, lighting environments and camera orientations. We demonstrate that although no one approximation is always suitable, it is rare to have a scene whose computational complexity cannot be decreased to some degree.

We propose a novel system for designing and manufacturing surfaces that produce desired caustic images when illuminated by a light source. Our system is based on a nonnegative image decomposition using a set of possibly overlapping anisotropic Gaussian kernels. We utilize this decomposition to construct an array of continuous surface patches, each of which focuses light onto one of the Gaussian kernels, either through refraction or reflection. We show how to derive the shape of each continuous patch and arrange them by performing a discrete assignment of patches to kernels in the desired caustic. Our decomposition provides for high fidelity reconstruction of natural images using a small collection of patches. We demonstrate our approach on a wide variety of caustic images by manufacturing physical surfaces with a small number of patches. Categories and Subject Descriptors (according to ACM CCS): Generation—Line and curve generation

Figure 1: Our algorithm achieves interactive hair rendering and appearance editing under environment lighting, including both single and multiple scattering effects. In this example, the user directly paints onto the hair to edit the spatially-varying scattering parameters. This results in a dynamic simulation of hair coloring. From left to right, the hair is dyed with a progressively more vivid color. The environment map is represented by 40 SRBF lights, and our algorithm runs at 8.3 fps on an NVIDIA GTX 580. We present an interactive algorithm for hair rendering and appearance editing under complex environment lighting represented as spherical radial basis functions (SRBFs). Our main contribution is to derive a compact 1D circular Gaussian representation that can accurately model the hair scattering function introduced by [Marschner et al. 2003]. The primary benefit of this representation is that it enables us to evaluate, at run-time, closed-form integrals of the scattering function with each SRBF light, resulting in efficient computation of both single and multiple scatterings. In contrast to previous work, our algorithm computes the rendering

Abstract — Large scale and structurally complex volume datasets from high-resolution 3D imaging devices or computational simulations pose a number of technical challenges for interactive visual analysis. In this paper, we present the first integration of a multiscale volume representation based on tensor approximation within a GPU-accelerated out-of-core multiresolution rendering framework. Specific contributions include (a) a hierarchical brick-tensor decomposition approach for pre-processing large volume data, (b) a GPU accelerated tensor reconstruction implementation exploiting CUDA capabilities, and (c) an effective tensor-specific quantization strategy for reducing data transfer bandwidth and out-of-core memory footprint. Our multiscale representation allows for the extraction, analysis and display of structural features at variable spatial scales, while adaptive level-of-detail rendering methods make it possible to interactively explore large datasets within a constrained memory footprint. The quality and performance of our prototype system is evaluated on large structurally complex datasets, including gigabyte-sized micro-tomographic volumes. Index Terms—GPU / CUDA, multiscale, tensor reconstruction, interactive volume visualization, multiresolution rendering 1