Parametrized BRDF for atmospheric and topographic correction and albedo estimation in Jiangxi rugged terrain,China

A method is presented for bi‐directional reflectance distribution function (BRDF) parametrization for topographic correction and surface reflectance estimation from Landsat Thematic Mapper (TM) over rugged terrain. Following this reflectance, albedo is calculated accurately. BRDF is parametrized using a land‐cover map and Landsat TM to build a BRDF factor to remove the variation of relative solar incident angle and relative sensor viewing angle per pixel. Based on the BRDF factor and radiative transfer model, solar direct radiance correction, sky diffuse radiance and adjacent terrain reflected radiance correction were introduced into the atmospheric‐topographic correction method. Solar direct radiance, sky diffuse radiance and adjacent terrain reflected radiance, as well as atmospheric transmittance and path radiance, are analysed in detail and calculated per pixel using a look‐up table (LUT) with a digital elevation model (DEM). The method is applied to Landsat TM imagery that covers a rugged area in Jiangxi province, China. Results show that atmospheric and topographic correction based on BRDF gives better surface reflectance compared with sole atmospheric correction and two other useful atmospheric‐topographic correction methods. Finally, surface albedo is calculated based on this topography‐corrected reflectance and shows a reasonable accuracy in albedo estimation.     

Reflectance from images: a model-based approach for human faces

In this paper, we present an image-based framework that acquires the reflectance properties of a human face. A range scan of the face is not required. Based on a morphable face model, the system estimates the 3D shape and establishes point-to-point correspondence across images taken from different viewpoints and across different individuals' faces. This provides a common parameterization of all reconstructed surfaces that can be used to compare and transfer BRDF data between different faces. Shape estimation from images compensates deformations of the face during the measurement process, such as facial expressions. In the common parameterization, regions of homogeneous materials on the face surface can be defined a priori. We apply analytical BRDF models to express the reflectance properties of each region and we estimate their parameters in a least-squares fit from the image data. For each of the surface points, the diffuse component of the BRDF is locally refined, which provides high detail. We present results for multiple analytical BRDF models, rendered at novel orientations and lighting conditions.     

Generalizing the definition of the bi-directional reflectance distribution function

The fundamental quantity that characterizes the reflectance property of a surface is the bi-directional reflectance distribution function (BRDF), defined as the ratio of the radiance scattered by a surface into a specified direction to the unidirectional irradiance incident on a surface. Its standard definition was derived under very restrictive conditions and it has only the angles of illumination and measurement as dependent variables. Several recent papers have attempted to generalize the BRDF to include the spatial attributes of illumination and measurement in order to make it applicable to heterogeneous media. The various BRDF definitions proposed by these papers are shown to be special cases of a generalized form of the BRDF derived herein. The spatial attributes of illumination and measurement are included as part of the nomenclature of the generalized BRDF. It is also shown that the generalized BRDF obeys reciprocity when properly weighted by the areas of illumination and measurement.     

A Light Scattering Model for Layered Dielectrics with Rough Surface Boundaries

A new model for the scattering of light from layered dielectrics with rough surface boundaries is introduced. The model contains a surface scattering component together with a subsurface scattering component. The former component corresponds to the roughness on the upper surface boundary and is modeled using the modified Beckmann model. The latter component accounts for both refraction due to Fresnel transmission through the layer and rough scattering at the lower layer boundary. One interesting consequence of the model is that the peak radiance is deflected away from the specular direction, a behavior that is also evident in BRDF data from human skin. By allowing independent roughness parameters for each surface boundary and controlling the contributions from the two scattering components in the outgoing radiance using a balance parameter, we can achieve excellent fits of the model to the measured BRDF data. We experiment with BRDF data from skin surface samples (human volunteers) and show that the new model outperforms alternative variants of the Beckmann model and the Lafortune et al. reflectance model. As an application in computer graphics, we also show that realistic images of 3D surfaces can be generated using the new model, by setting the values of its physical parameters.     

Improved Diffuse Reflection Models for Computer Vision

There are many computational vision techniques that fundamentally rely upon assumptions about the nature of diffuse reflection from object surfaces consisting of commonly occurring nonmetallic materials. Probably the most prevalent assumption made about diffuse reflection by computer vision researchers is that its reflected radiance distribution is described by the Lambertian model, whether the surface is rough or smooth. While computationally and mathematically a relatively simple model, in physical reality the Lambertian model is deficient in accurately describing the reflected radiance distribution for both rough and smooth nonmetallic surfaces. Recently, in computer vision diffuse reflectance models have been proposed separately for rough, and, smooth nonconducting dielectric surfaces each of these models accurately predicting salient non-Lambertian phenomena that have important bearing on computer vision methods relying upon assumptions about diffuse reflection. Together these reflectance models are complementary in their respective applicability to rough and smooth surfaces. A unified treatment is presented here detailing important deviations from Lambertian behavior for both rough and smooth surfaces. Some speculation is given as to how these separate diffuse reflectance models may be combined.     

An Image based Measurement System for Anisotropic Reflection

This paper introduces an image based method for measuring bidirectional reflectance distribution functions (BRDF). The measurement system uses a CCD camera connected to a workstation to capture images from the material under investigation. The evaluation of the BRDF is performed in an image processing step, gathering BRDF values with a broad range of incident and reflected angles, followed by a fitting process, where these values are approximated by a chosen reflectance model. Absolute BRDF values are obtained by the usage of a diffuse reflectance standard. It is shown that the proposed measurement system produces very reasonable results compared to accurate measurements. Thus, it is an easy and cost efficient way to measure material properties needed for physically based rendering algorithms.     

一种Blinn-Phong BRDF红外反射模型的研究

针对红外场景仿真中辐射反射分量运算复杂、真实感欠缺等问题,提出一种Blinn-Phong BRDF红外反射模型,并基于Unity平台将其应用于三维红外仿真场景。该方法在对实测红外图像进行阈值分割的基础上,利用简化辐亮度运算和红外成像过程的仿真链路反演模型,求解目标表面温度值,根据红外辐射原理与可见光光照模型的理论相似性,将改进的Blinn-Phong光照模型移植到红外波段,并引入双向反射分布函数提高仿真精度,提出Blinn-Phong BRDF红外反射模型;最后基于该辐射反射模型构建零视距仿真场景,同时将仿真图像与实测图像进行比对,验证了反射模型的可信度和有效性。实验结果表明,提出的红外反射模型既有较高的仿真效率,又能够较好地模拟红外反射的高光现象,满足红外视景仿真对辐射反射的要求。     

Radiometric Consistency between Landsat 8 OLIand Sentinel-2 MSI Imagery in Mountainous Terrain

The combined use of multi\|sensor/multi\|temporal images provides more opportunities for long\|term land surface monitoring with high resolution and frequency requirements.However,as sensors differ in their orbital,spatial,or spectral configuration,uncertainty was introduced in the radiometric consistency of multi\|sourse images,and that becomes more outstanding in mountainous terrain with the sharp topographic relief.Therefore,a series of radiometric corrections need to be carry out before further application.The objective of this study was to indicate the radiometric consistency of Landsat\|8 OLI and Sentinel\|2 MSI images.Thus the radiometric differences between the corresponding bands of these two images acquired almost simultaneously by OLI and MSI over 2 areas at different latitude was calculated for the TOA reflectance images first.Then several radiometric corrections(atmospheric correction,BRDF correction and bandpass adjustment) were carried out successively and after each of them the radiometric differences were researched again to assess the performance of each correction method.The results first indicate that there is high radiometric consistency between OLI\|L1T and MSI\|L1C images with the R²greater than 0.9 for each band involved.Then higher consistency was found after the 6S atmospheric correction and C\|factor BRDF correction,while no remarkable improve was found after the fixed\|parameter bandpass adjustment.Furthermore,in area with great topographic relief,the radiometric consistency were higher for hillside facing the sun than hillside in shadow (the MAD of SWIR2 band was 0.010 and RMSD was 0.007 in sun\|light area,while the MAD was 0.005 and RMSD was 0.004 in shadowed area).The results point out that proper atmospheric correction,BRDF correction and bandpass adjustment could be used to improve the radiometric consistency,and topographic correction might also be carried out to balance the radiometric consistency differences between different hillsides.     

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.     

纹理物体表面反射参数的恢复

物体表面反射参数的恢复是新兴的逆向绘制技术的核心问题，提出一种恢复物体表面BRDF模型参数的方法，假定物体表面的BRDF模型可以近似分解为漫射纹理和整体不变的镜面反射分量，则每一点的反射参数可以用Phong模型来近似计算，首先选取物体表面的一片区域，利用该区域在不同视点光照条件下采样的几幅图像，计算得到该区域的平均镜面反射分量，作为整个物体表面的镜面反射分量，然后据此从物体表面各点的采样中分离出漫射分量，计算各点的漫反射参数，得到近似的BRDF模型，实验数据表明算法是有效的。     

Integration and Case Analysis of BRDF Model based on Linear Kernel\|driven Model#br#

Anisotropic reflectance is the intrinsic characteristic of an object surface.over the past few decades,various BRDF models have been developed for investigating the relationship between the vegetation canopy and reflectance anisotropy.This helps to retrieve biophysical parameters from the anisotropic reflectance patterns of vegetation canopy.In this study,for the purpose of assisting potential users to use these models,and to improve the understanding of the BRDF modeling,several BRDF models that are widely used in the remote sensing community have been integrated with the current version of the MaKeMAT (Multi\|angular Kernel\|driven Model Analysis Tool),based on the Interactive Data Language (IDL).This work retains all functions of the current version of the MaKeMAT model,meanwhile,adds some new functions by integrating these physical BRDF models.Undoubtedly,this work facilitates the potential users to process BRDF data and make further analysis in their work by operating a simpler visual interface.This helps to build a rapid communication between the kernel\|driven BRDF models and the physical BRDF models.Our initial results show that this model\|integration practice is a valuable reference for potential users to devise a similar technique.Our case study in coupling these physical BRDF models with the kernel\|driven models present a high correlation between them,with the determination of coefficients (R²) reaching 0.899~0.989 in the red and NIR bands.     

Linear approximation of Bidirectional Reflectance Distribution Functions

Various empirical and theoretical models of the surface reflectance have been introduced so far. Most of these models are based on functions with non-linear parameters and therefore faces some computational difficulties involved in non-linear optimization processes. In this paper, we introduce a new approach for approximating Bidirectional Reflectance Distribution Functions (BRDF) by employing response surface methodology. The proposed model employs principal component transformations of the explanatory variables which are essentially functions of incoming and outgoing light directions. The resulting model is linear and can be used to represent both isotropic and anisotropic reflectance for diffuse and glossy materials. Considering some widely used reflection models including the Ward model, the Ashikhmin–Shirley model and the Lafortune model, we demonstrate empirically that satisfactory approximations can be made by means of the proposed general, simple and computationally efficient linear model.     

Comparison of BRDF models with a fuzzy inference system for correction of bidirectional effects

With the advances in computing and imaging technology, the field of precision agriculture is rapidly becoming a practical means for farm management. An important step in the delivery of highly accurate images for farm managers is the within-image correction for viewing geometry effects. Reflected light on an imaging sensor is influenced by properties of view zenith angle, solar zenith angle, and relative azimuth. There are a number of models that describe this effect termed the bidirectional reflectance distribution function (BRDF) or more generically “viewing geometry effects.” In this paper, we compared three BRDF models (Roujean, Shibayama-Wiegand, and Dymond-Qi) with a fuzzy inference system (FIS) for three data sets for correction of geometric effects. One data set consisted of ground data collected at different viewing angles of a cotton crop. Another data set included six aircraft images of a corn plot in a different part of each image. The final data set was an aerial image of a planting density experiment of cotton. All the models performed reasonably well, but the FIS was the most consistent predictor of BRDF for all three data sets. For the ground data set, R² statistics for predicting the reflectance based on the trained models ranged from 0.53 to 0.93 for the BRDF models and from 0.94 to 0.97 for the FIS.     

Making Shaders More Physically Plausible

There is a need to develop shaders that not only “look good”, but are more physically plausible. From physical and geometric considerations, we review the derivation of a shading equation expressing rejected radiance in terms of incident radiance and the bidirectional reflectance distribution function (BRDF). We then examine the connection between this equation and conventional shaders used in computer graphics. Imposing the additional physical constraints of energy conservation and Helmholtz reciprocity allows us to create variations of the conventional shaders that are more physically plausible.     

Variability in surface BRDF at different spatial scales (30 m-500 m) over a mixed agricultural landscape as retrieved from airborne and satellite spectral measurements

Over the past decade, the role of multiangle remote sensing has been central to the development of algorithms for the retrieval of global land surface properties including models of the bidirectional reflectance distribution function (BRDF), albedo, land cover/dynamics, burned area extent, as well as other key surface biophysical quantities impacted by the anisotropic reflectance characteristics of vegetation. In this study, a new retrieval strategy for fine-to-moderate resolution multiangle observations was developed, based on the operational sequence used to retrieve the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 5 reflectance and BRDF/albedo products. The algorithm makes use of a semiempirical kernel-driven bidirectional reflectance model to provide estimates of intrinsic albedo (i.e., directional-hemispherical reflectance and bihemispherical reflectance), model parameters describing the BRDF, and extensive quality assurance information. The new retrieval strategy was applied to NASA's Cloud Absorption Radiometer (CAR) data acquired during the 2007 Cloud and Land Surface Interaction Campaign (CLASIC) over the well-instrumented Atmospheric Radiation Measurement Program (ARM) Southern Great Plains (SGP) Cloud and Radiation Testbed (CART) site in Oklahoma, USA. For the case analyzed, we obtained ~ 1.6 million individual surface bidirectional reflectance factor (BRF) retrievals, from nadir to 75° off-nadir, and at spatial resolutions ranging from 3 m to 500 m. This unique dataset was used to examine the interaction of the spatial and angular characteristics of a mixed agricultural landscape; and provided the basis for detailed assessments of: (1) the use of a land cover type-specific a priori knowledge in kernel-driven BRDF model inversions; (2) the interaction between surface reflectance anisotropy and instrument spatial resolution; and (3) the uncertainties that arise when sub-pixel differences in the BRDF are aggregated to a moderate resolution satellite pixel. Results offer empirical evidence concerning the influence of scale and spatial heterogeneity in kernel-driven BRDF models; providing potential new insights into the behavior and characteristics of different surface radiative properties related to land/use cover change and vegetation structure.     

LANDSAT test of diffuse reflectance models for aquatic suspended solids measurement

LANDSAT radiance data were used to test mathematical models relating diffuse reflectance to aquatic suspended solids concentration. Digital CCT data for LANDSAT passes over the Bay of Fundy, Nova Scotia were analyzed on a General Electric Co. Image 100 multispectral analysis system. Three data sets were studied separately and together in all combinations with and without solar angle correction. Statistical analysis and chromaticity analysis show that a nonlinear relationship between LANDSAT radiance and suspended solids concentration is better at curve-fitting than a linear relationship. In particular, the quasi-single-scattering diffuse reflectance model developed by Gordon and coworkers is corroborated. The Gordon model applied to 33 points of MSS 5 data combined from three dates produced r = 0.98.     

Effect of surface roughness,wavelength, illumination,and viewing zenith angles on soil surface BRDF using an imaging BRDF approach

Compared to non-imaging instruments, imaging spectrometers (ISs) can provide detailed information to investigate the influence of scene components on the bidirectional reflectance distribution function (BRDF) of a mixed target. The research reported in this article investigated soil surface reflectance changes as a function of scene components (i.e. illuminated pixels and shaded pixels), illumination and viewing zenith angles, and wavelength. Image-based BRDF data of both rough and smooth soil surfaces were acquired in a laboratory setting at three different illumination zenith angles and at four different viewing zenith angles over the full 360° azimuth range, at an interval of 20°, using a Specim V10E IS (Specim, Spectral Imaging Ltd., Oulu, Finland) mounted on the University of Lethbridge Goniometer System version 2.5 (ULGS-2.5). The BRDF of the smooth soil surface was dominated by illuminated pixels, whereas the shaded pixels were a larger component of the BRDF of the rough soil surface. As the illumination zenith angle was changed from 60° to 45° and then to 30°, the shadowing effect decreased, regardless of the soil surface. Soil surface reflectance was generally higher at the backscattering view zenith angles and decreased continuously to forward scattering view zenith angles in the light principal plane, regardless of the wavelength, due to the Specim V10E IS seeing more illuminated pixels in the backscattering angles than in the forward scattering angles. Higher soil surface reflectance was observed at higher illumination and viewing zenith angle combinations. For both soil surface roughness categories, the BRDF exhibited a greater range of values in the near-infrared than at the visible wavelengths. This research enhances our understanding of soil BRDF for various soil roughness and illumination conditions.     

Estimating the surface radiance function from single images

This paper describes a simple method for estimating the surface radiance function from single images of smooth surfaces made of materials whose reflectance function is isotropic and monotonic. The method makes implicit use of the Gauss map between the surface and a unit sphere. We assume that the material brightness is monotonic with respect to the angle between the illuminant direction and the surface normal. Under conditions in which the light source and the viewer directions are identical, we show how a tabular representation of the surface radiance function can be estimated using the cumulative distribution of image gradients. Using this tabular representation of the radiance function, surfaces may be rendered under varying light source direction by rotating the corresponding reflectance map on the Gauss sphere about the specular spike direction. We present a sensitivity study on synthetic and real-world imagery. We also present two applications which make use of the estimated radiance function. The first of these illustrates how the radiance function estimates can be used to render objects when the light and viewer directions are no longer coincident. The second application involves applying corrected Lambertian radiance to rough and shiny surfaces.     

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.     

Wavelet Radiative Transfer and Surface Interaction

Recently, there has been considerable interest in the representation of radiance in terms of wavelet basis functions. We will present a coordinate system called Nusselt coordinates which, when combined with wavelets, considerably simplifies computation of radiative transport and surface interaction. It also provides straightforward computation of the physical quantities involved.
We show how to construct a discrete representation of the radiative transport operator Τ involving inner products of smoothing functions, discuss the possible numerical integration techniques, and present an application. We also show how surface interaction can be represented as a kind of matrix product of the wavelet projections of an incident radiance and a bidirectional reflectance distribution function (BRDF).