Correlated visibility sampling for direct illumination

State-of-the-art importance sampling strategies for direct illumination take into account the importance of the incident illumination, as well as the surface BRDF. Hence, these techniques achieve low variance in unoccluded regions. However, the resulting images still have noise in partially occluded regions as these techniques do not take visibility into account during the sampling process. We introduce the notion of correlated visibility sampling, which considers visibility in partially occluded regions during the sampling process, thereby improving the quality of the shadowed regions. We aim to draw samples in the partially occluded regions according to the triple product of the incident illumination, BRDF and visibility using Monte Carlo sampling followed by Metropolis sampling.     

Practical Product Importance Sampling for Direct Illumination

We present a practical algorithm for sampling the product of environment map lighting and surface reflectance. Our method builds on wavelet‐based importance sampling, but has a number of important advantages over previous methods. Most importantly, we avoid using precomputed reflectance functions by sampling the BRDF on‐the‐fly. Hence, all types of materials can be handled, including anisotropic and spatially varying BRDFs, as well as procedural shaders. This also opens up for using very high resolution, uncompressed, environment maps. Our results show that this gives a significant reduction of variance compared to using lower resolution approximations. In addition, we study the wavelet product, and present a faster algorithm geared for sampling purposes. For our application, the computations are reduced to a simple quadtree‐based multiplication. We build the BRDF approximation and evaluate the product in a single tree traversal, which makes the algorithm both faster and more flexible than previous methods.     

Importance sampling of products from illumination and BRDF using spherical radial basis functions

In this paper, a new approach for the importance sampling of products from a complex high dynamic range (HDR) environment map and measured bidirectional reflectance distribution function (BRDF) data using spherical radial basis functions (SRBFs) is presented. In the pre-process, a complex HDR environment map and measured BRDF data are transformed into a scattered SRBF representation by using a non-uniform and non-negative SRBF fitting algorithm. An initial guess is determined for the fitting operation. In the run-time rendering process, after the product of the two SRBFs is evaluated, this is used to guide the number of samples. The sampling is done by mixing samples from the various “product” SRBFs using multiple importance sampling. Hence, the proposed approach efficiently renders images with multiple HDR environment maps and measured BRDFs.     

Generating Reflected Directions from BRDF Data

Monte-Carlo path tracing algorithms for computer graphics require that given an incident light ray at a surface an outgoing direction can be computed with a distribution given by the magnitude of the bidirectional reflectance distribution function (BRDF). For analytic reflectance functions this can be done using various techniques including inverting the function, or tabulating some representation of the inverse. However, measured BRDF data sets are too large for this to be practical. We present a method to generate reflection rays distributed according to the magnitude of the BRDF. The method relies on a wavelet-based representation of the BRDF. This representation is efficient and compact, allowing large, anisotropic measured BRDF data sets to be represented with a few thousand coefficients. In particular, we exploit the wavelet representation to quickly compute integrals over ranges of the BRDF.     

Spherical piecewise constant basis functions for all-frequency precomputed radiance transfer

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. We run-time 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 on-the-fly BRDF editing under rotating environment lighting. With graphics hardware acceleration, our method achieves real-time frame rates.     

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.     

Modelling dynamic memory management in constraint-based testing

Constraint-based testing (CBT) is the process of generating test cases against a testing objective by using constraint solving techniques. When programs contain dynamic memory allocation and loops, constraint reasoning becomes challenging as new variables and new constraints should be created during the test data generation process. In this paper, we address this problem by proposing a new constraint model of C programs based on operators that model dynamic memory management. These operators apply powerful deduction rules on abstract states of the memory enhancing the constraint reasoning process. This allows to automatically generate test data respecting complex coverage objectives. We illustrate our approach on a well-known difficult example program that contains dynamic memory allocation/deallocation, structures and loops. We describe our implementation and provide preliminary experimental results on this example that show the highly deductive potential of the approach.     

Validation of the MODIS reflectance product under UK conditions

Surface reflectance obtained from remote-sensing data is the main input to almost all remote-sensing applications. The availability and special characteristics of Moderate Resolution Imaging Spectroradiometer (MODIS) products have led to their use worldwide. Validation of the MODIS reflectance product is then crucial to provid information on uncertainty in the reflectance data, and in other MODIS products and in the applied surface–atmosphere models. Compact Airborne Spectrographic Imager (CASI) and Système Pour l'Observation de la Terre (SPOT) data, collected during the Network for Calibration and Validation in Earth Observation (NCAVEO) 2006 Field Campaign, were applied to validate daily MODIS reflectance data over a site in the southern UK. The difference in the view geometry of at-nadir CASI and SPOT data and off-nadir MODIS data was dealt with using a semi-empirical bidirectional reflectance distribution function (BRDF) model. The validation results showed that for our particular study site, the absolute errors in the MODIS reflectance product were too large to allow the albedo data to be used directly in climate models. The errors were mainly related to the uncertainties in the MODIS atmospheric variables, the BRDF model, and undetected clouds and cloud shadows. More generally, the study highlights the extreme difficulty of achieving pixel-level validation of coarse spatial resolution satellite sensor data in an environment in which the atmosphere is constantly changing, and in which the landscape is characterized by high space–time heterogeneity.     

Efficient Reflectance and Visibility Approximations for Environment Map Rendering

We present a technique for approximating isotropic BRDFs and precomputed self-occlusion that enables accurate and efficient prefiltered environment map rendering. Our approach uses a nonlinear approximation of the BRDF as a weighted sum of isotropic Gaussian functions. Our representation requires a minimal amount of storage, can accurately represent BRDFs of arbitrary sharpness, and is above all, efficient to render. We precompute visibility due to self-occlusion and store a low-frequency approximation suitable for glossy reflections. We demonstrate our method by fitting our representation to measured BRDF data, yielding high visual quality at real-time frame rates.     

Bidirectional Importance Sampling for Unstructured Direct Illumination

Recent research in bidirectional importance sampling has focused primarily on structured illumination sources such as distant environment maps, while unstructured illumination has received little attention. In this paper, we present a method for bidirectional importance sampling of unstructured illumination, allowing us to use the same method for sampling both distant as well as local/indirect sources. Building upon recent work in [ WFA*05 ], we model complex illumination as a large set of point lights. The subsequent sampling process draws samples only from this point set. We start by constructing a piecewise constant approximation for the lighting using an illumination cut [ CPWAP08 ]. We show that this cut can be used directly for illumination importance sampling. We then use BRDF importance sampling followed by sample counting to update the cut, resulting in a bidirectional distribution that closely approximates the product of the illumination and BRDF. Drawing visibility samples from this new distribution significantly reduces the sampling variance. As a main advance over previous work, our method allows for unstructured sources, including arbitrary local direct lighting and one-bounce of indirect lighting.     

Algorithm for retrieval of the effective snow grain size and pollution amount from satellite measurements

We present an algorithm for retrieval of the effective Snow Grain Size and Pollution amount (SGSP) from satellite measurements. As well as our previous version (Zege et al., 2008, 1998), the new algorithm is based on the analytical solution for snow reflectance within the asymptotic radiative transfer theory. The SGSP algorithm does not use any assumptions on snow grain shape and allows for the snow pack bidirectional reflectance distribution function (BRDF). The algorithm includes a new atmospheric correction procedure that allows for snow BRDF. This SGSP algorithm has been thoroughly validated with computer simulations. Its sensitivity to the atmosphere model has been investigated. It is shown that the inaccuracy of the snow characteristic retrieval due to the uncertainty in the aerosol and molecular atmosphere model is negligible, as compared to that due to the measurement errors at least for aerosol loads typical for polar regions. The significant advantage of the SGSP over conventional algorithms, which use a priori assumptions about particle shape and (or) not allow for the BRDF of the individual snow pack, is that the developed retrieval still works at low sun elevations, which are typical for polar regions.     

三维物体表面材质实时编辑

艺术家进行设计时,常常需要一种可以交瓦地修改模型表面材质的工具.为了在环境光下对模型表面的材质进行实时编辑,提出一种基于预计算辐射传输的算法:首先预计算环境光相对于模型表面每一个顶点的可见性;然后在绘制时实时计算物体表面的双向反射分布函数(BRDF);最后通过查找环境光相对于模型表面每一个顶点的可见性,快速绘制出物体表面材质.实验结果表明,使用该算法,用户可以通过调节BRDF的参数,实现物体表面材质的实时动态编辑,同时支持动态视点和动态环境光.     

A New Ward BRDF Model with Bounded Albedo

Due to its realistic appearance, computational convenience, and efficient Monte Carlo sampling, Ward's anisotropic BRDF is widely used in computer graphics for modeling specular reflection. Incorporating the criticism that the Ward and the Ward‐Dür model do not meet energy balance at grazing angles, we propose a modified BRDF that is energy conserving and preserves Helmholtz reciprocity. The new BRDF is computationally cheap to evaluate, admits efficient importance sampling, and thus sustains the main benefits of the Ward model. We show that the proposed BRDF is better suited for fitting measured reflectance data of a linoleum floor used in a real‐world building than the Ward and the Ward‐Dür model.     

An assessment of angular variations of red and NIR reflectances in multi-date IRS-1D Wide Field Sensor data

A study has been carried out to assess angular variations in red and near infrared (NIR) reflectance of different features of the Earth's surface in a common overlap area of accumulated four-date Indian Remote Sensing Satellite (IRS-1D) Wide Field Sensor (WiFS) data from the first fortnight of October 2003. An improved dark object subtraction (DOS) method has been used to perform image based atmospheric corrections. Red and NIR reflectance variations of four structurally different classes—dense vegetation (shrub), sparse crop (pearl millet/maize), wasteland and forest with Sun-target-sensor geometry were analysed. A linearly constrained least squares technique was used to estimate red and NIR model coefficients of the linear Ross Thick-Li Sparse (RTLS) semi- empirical Bidirectional Reflectance Distribution Function (BRDF) model and compared with Moderate Resolution Imaging Spectrometer (MODIS) BRDF product coefficients. The relative reflectance difference between two dates as well as anisotropic factors for red and NIR for all classes and dates were also computed. Red and NIR reflectance of the four land cover classes at different locations with different observation geometry were estimated using both WiFS derived and MODIS BRDF product RTLS model coefficients and compared with WiFS observed reflectance. It was found that the mean relative difference in red and NIR reflectances between consecutive dates varied between 4–11% and 6–8%, respectively, while the computed mean anisotropy factors varied between 3–10% in the red and 8–11% in the NIR. A small anisotropy in the Normalized Difference Vegetation Index (NDVI) as a function of the scattering angle was observed for the four land cover classes. This may imply that angular effects in WiFS are relatively small and do not exceed 10–11 % for the land cover classes considered here.     

基于Harr 小波的动态场景全频阴影绘制算法

针对现有的预计算辐射传递算法对三维场景限制严格、适合于低频光照环境等问题,提出了一种动态场景的全频阴影绘制算法.在预处理阶段使用球体对三维物体进行拟合,同时对光照函数和BRDF(bidirectional reflectance distribution function)函数进行Harr小波变换;在运行时阶段利用不同基函数的优势,在像素基空间进行多个球体可见性函数的快速合并,在小波基空间进行光照函数、BRDF函数和可见性函数的三乘积分,得到最终的光照值.使用CUDA(computed unified device architecture)实现了该算法,充分利用了图形硬件的最新功能.实验结果表明,阴影绘制质量有很大的提高,可以基本达到实时绘制.     

Barycentric parameterizations for isotropic BRDFs

A bidirectional reflectance distribution function (BRDF) is often expressed as a function of four real variables: two spherical coordinates in each of the "incoming" and "outgoing" directions. However, many BRDFs reduce to functions of fewer variables. For example, isotropic reflection can be represented by a function of three variables. Some BRDF models can be reduced further. In This work, we introduce new sets of coordinates which we use to reduce the dimensionality of several well-known analytic BRDFs as well as empirically measured BRDF data. The proposed coordinate systems are barycentric with respect to a triangular support with a direct physical interpretation. One coordinate set is based on the BRDF mode) proposed by Lafortune. Another set, based on a model of Ward, is associated with the "halfway" vector common in analytical BRDF formulas. Through these coordinate sets we establish lower bounds on the approximation error inherent in the models on which they are based. We present a third set of coordinates, not based on any analytical model, that performs well in approximating measured data. Finally, our proposed variables suggest novel ways of constructing and visualizing BRDFs.     

Multi-temporal MODIS-Landsat data fusion for relative radiometric normalization, gap filling, and prediction of Landsat data

A semi-physical fusion approach that uses the MODIS BRDF/Albedo land surface characterization product and Landsat ETM+ data to predict ETM+ reflectance on the same, an antecedent, or subsequent date is presented. The method may be used for ETM+ cloud/cloud shadow and SLC-off gap filling and for relative radiometric normalization. It is demonstrated over three study sites, one in Africa and two in the U.S. (Oregon and Idaho) that were selected to encompass a range of land cover land use types and temporal variations in solar illumination, land cover, land use, and phenology. Specifically, the 30 m ETM+ spectral reflectance is predicted for a desired date as the product of observed ETM+ reflectance and the ratio of the 500 m surface reflectance modeled using the MODIS BRDF spectral model parameters and the sun-sensor geometry on the predicted and observed Landsat dates. The difference between the predicted and observed ETM+ reflectance (prediction residual) is compared with the difference between the ETM+ reflectance observed on the two dates (temporal residual) and with respect to the MODIS BRDF model parameter quality. For all three scenes, and all but the shortest wavelength band, the mean prediction residual is smaller than the mean temporal residual, by up to a factor of three. The accuracy is typically higher at ETM+ pixel locations where the MODIS BRDF model parameters are derived using the best quality inversions. The method is most accurate for the ETM+ near-infrared (NIR) band; mean NIR prediction residuals are 9%, 12% and 14% of the mean NIR scene reflectance of the African, Oregon and Idaho sites respectively. The developed fusion approach may be applied to any high spatial resolution satellite data, does not require any tuning parameters and so may be automated, is applied on a per-pixel basis and is unaffected by the presence of missing or contaminated neighboring Landsat pixels, accommodates for temporal variations due to surface changes (e.g., phenological, land cover/land use variations) observable at the 500 m MODIS BRDF/Albedo product resolution, and allows for future improvements through BRDF model refinement and error assessment.     

Real‐Time Linear BRDF MIP‐Mapping

We present a new technique to jointly MIP‐map BRDF and normal maps. Starting with generating an instant BRDF map, our technique builds its MIP‐mapped versions based on a highly efficient algorithm that interpolates von Mises‐Fisher (vMF) distributions. In our BRDF MIP‐maps, each pixel stores a vMF mixture approximating the average of all BRDF lobes from the finest level. Our method is capable of jointly MIP‐mapping BRDF and normal maps, even with high‐frequency variations, at real‐time while preserving high‐quality reflectance details. Further, it is very fast, easy to implement, and requires no precomputation.     

Efficient product sampling using hierarchical thresholding

We present an efficient method for importance sampling the product of multiple functions. Our algorithm computes a quick approximation of the product on the fly, based on hierarchical representations of the local maxima and averages of the individual terms. Samples are generated by exploiting the hierarchical properties of many low-discrepancy sequences, and thresholded against the estimated product. We evaluate direct illumination by sampling the triple product of environment map lighting, surface reflectance, and a visibility function estimated per pixel. Our results show considerable noise reduction compared to existing state-of-the-art methods using only the product of lighting and BRDF.