Bidirectional Reflectance Distribution Function Research Articles

Mitigating Illumination-, Leaf-, and View-Angle Dependencies in Hyperspectral Imaging Using Polarimetry

Automation of plant phenotyping using data from high-dimensional imaging sensors is on the forefront of agricultural research for its potential to improve seasonal yield by monitoring crop health and accelerating breeding programs. A common challenge when capturing images in the field relates to the spectral reflection of sunlight (glare) from crop leaves that, at certain solar incidences and sensor viewing angles, presents unwanted signals. The research presented here involves the convergence of 2 parallel projects to develop a facile algorithm that can use polarization data to decouple light reflected from the surface of the leaves and light scattered from the leaf’s tissue. The first project is a mast-mounted hyperspectral imaging polarimeter (HIP) that can image a maize field across multiple diurnal cycles throughout a growing season. The second project is a multistatic fiber-based Mueller matrix bidirectional reflectance distribution function (mmBRDF) instrument which measures the polarized light-scattering behavior of individual maize leaves. The mmBRDF data was fitted to an existing model, which outputs parameters that were used to run simulations. The simulated data were then used to train a shallow neural network which works by comparing unpolarized 2-band vegetation index (VI) with linearly polarized data from the low-reflectivity bands of the VI. Using GNDVI and red-edge reflection ratio we saw an improvement of an order of magnitude or more in the mean error ( ϵ ) and a reduction spanning 1.5 to 2.7 in their standard deviation ( ϵ σ ) after applying the correction network on the HIP sensor data.

BRDF Data for Coniferous Forests Acquired from Multispectral Camera Onboard a Unmanned Aerial Vehicle

Bidirectional reflectance distribution function (BRDF) is a distribution of directional reflectance for varying viewing and solar geometry. BRDF of a target is important in processing optical image data from satellites, because the observed radiance has great dependency on the direction (or angle) of reflection. It is desirable that the BRDF of any targets is characterized for rigorous BRDF correction of satellite data, since the sun-sensor-target geometry of satellites often varies in a very limited range, limiting the full characterization of target BRDF. This study provides BRDF data set for typical coniferous forests in Korea, by using a multispectral camera onboard a unmanned aerial vehicle (UAV). By operating the UAV in a goniometer-like way, reflectance data for all possible viewing zenith and azimuth angles were obtained. The BRDF data collected from the 3 campaigns in different days were visualized in a polar-coordinate, together with the standard deviation calculated for each zenith/azimuth bin made in 1˚ interval. The data sets demonstrated reflectance distribution over the wide range of angles with sound data quality, suggesting commonly known BRDF characteristics for forests such as strong back-scattering and hot spot area in the viewing zenith angle near the solar zenith angle. This data set is expected to be utilized for the BRDF correction of various satellites including Agro-forest satellite of Korea which is to be launched in 2025 that has similar spectral bands with the ones used in this study.

Infrared polarization model optimization and radiation characteristics of camouflage coatings

To investigate the polarization characteristics of the infrared radiation form camouflage a coating surface, an improved model for the two-component polarized bidirectional reflectance distribution function (pBRDF) is established. A new form of the geometric attenuation factor is used instead of the traditional Blinn shielding function, and diffuse scattering component caused by the rough surface is also taken into account in the micro mirro model. The expression of the degree of linear polarization (DOLP) of the infrared radiation is derived by using the optimized pBRDF, the valid of which is proved by experimental data. The numerical calculations results of DOLP of the three coatings are in good agreement with the experimental data. The expression is numerically evaluated and the influence of coating surface roughness, the effect of geometric attenuation diffuse scattering on the infrared DOLP is discussed. The greater the surface roughness of the coating is, the more obvious are the geometric attenuation effect and diffuse scattering effect caused by the roughness. These results provide theoretical and technical support for the realization of military camouflage, anti-camouflage, target recognition, and other fields.

Analyzing GOES-R ABI BRDF-adjusted EVI2 time series by comparing with VIIRS observations over the CONUS

The Advanced Baseline Imager (ABI) instruments onboard the Geostationary Operational Environmental Satellite-R series (GOES-R) provide new opportunities to expand their applications in global terrestrial ecology and environmental sciences. It offers a 5–15 min temporal resolution and 0.5–1 km spatial resolution that greatly benefit those environmental applications where spatial resolution can be compromised in favor of more frequent imagery. However, ABI captures reflected radiation at varying sun positions throughout the day, causing significant diurnal variations. The varying off-nadir view across ABI full disk presents further challenges for generating comparable and consistent vegetation observations, such as the two-band Enhanced Vegetation Index (EVI2). To address these challenges, three Bidirectional Reflectance Distribution Function (BRDF) models (RossThick-LiSparse-Reciprocal (RTLSR), Walthall, and Tian models) are examined to generate high-quality BRDF-adjusted EVI2 based on GeoNEX GOES-16 ABI surface reflectance. The ABI BRDF retrievals are then systematically compared to the corresponding VIIRS (Visible Infrared Imaging Radiometer Suite) Nadir BRDF-Adjusted Reflectance (NBAR) products (VNP43 V001) retrieved from RTLSR model. The viewing geometry effects are further analyzed over various land cover types using time series analysis, Pearson Correlation Coefficients (PCC), and Relative Difference (RD) between ABI and VIIRS high-quality time series inversions. The results indicate that the RTLSR model fits well the diurnal ABI observed reflectance and EVI2 values (even for the hot-spot phenomena), and outperforms the Walthall and Tian models for generating ABI high-quality BRDF retrievals with consistently low Root Mean Square Error (RMSE<0.02) and Weight of Determination (WoD < 0.5) across the CONUS. The annual proportion of ABI high-quality BRDF retrievals with a 3-day moving window using the RTLSR model is spatially and statistically comparable to that of VIIRS NBAR with a 16-day retrieval period. Compared to the time series of high-quality VIIRS NBAR EVI2, the BRDF adjusted ABI EVI2 time series still show considerable impacts of view zenith angles over evergreen forest, shrubland, and savanna pixels. However, such impacts are not significant over spatially homogeneous pixels such as cropland and deciduous forests. These results emphasize the need for BRDF correction when considering the impact of off-nadir observations from geostationary satellites on vegetation monitoring. They also demonstrate the advantages of geostationary satellites in capturing rapid changes in greenness trajectories.

The influence of BRDF effects and representativeness of training data on tree species classification using multi-flightline airborne hyperspectral imagery

Airborne hyperspectral imagery provides detailed spatial and spectral information that can be used for tree species classification, but its application in practical forest inventories over large areas is limited. This study investigates the impact of (i) bidirectional reflectance distribution function (BRDF) effects on multi-flightline airborne imagery and (ii) the selection strategy for training data on tree species classification accuracy over large forested areas. Hyperspectral imagery was acquired using the Chinese Academy of Forestry’s LiDAR, CCD, and Hyperspectral system (CAF-LiCHy) over the Mengjiagang Forest Farm (MFF, ∼155 km2) in northeastern China, which includes common keystone coniferous species in northern China’s temperate-boreal ecozones. A kernel-driven BRDF model based on mNDVI704.50 stratification was applied to airborne hyperspectral data acquired from multi-flightlines. We developed three training data selection strategies, namely #1 sampling over the entire area, #2 localized sampling over the area for each flight date, and #3 gradually decreasing sampling in size. Additionally, two validation assessment strategies were respectively employed: independent data over the entire area and independent data in areas with inconsistent classification labeling between using BRDF corrected and uncorrected hyperspectral imagery. These strategies were implemented to perform a comprehensive cross-comparison of tree species classification accuracy using BRDF corrected and uncorrected airborne hyperspectral imagery. The study found that the representativeness of the training data (in terms of solar-viewing geometry distribution and size) has a stronger impact on the classification accuracy of tree species than the BRDF effects in airborne hyperspectral imagery. By utilizing BRDF corrected hyperspectral imagery with a majority of representative training data, the mean overall accuracy of tree species classification improves by ≤ 2.9 % compared to uncorrected imagery. Notably, BRDF correction has improved classification accuracy by 11.5 % in inconsistently labeled areas, mainly concentrated in the spatial overlap regions of adjacent flightlines. These findings provide valuable insights for improving tree species classification accuracy in large forested areas using multi-flightline airborne hyperspectral imagery.

Effect of beryllium topography on BRDF measurements

The Bidirectional Reflectance Distribution Function (BRDF) of beryllium is important for a ray-tracing simulation to evaluate the effect of reflected light on optical diagnostics in the fusion device ITER. However, the BRDF for beryllium has not been investigated yet and is currently lacking. To fill this gap, this study measured BRDFs of beryllium specimens with different topographies using goniophotometers and optimized optical reflection models. Additionally, various surface topographic parameters were computed, and their correlation with parameters for the optical reflection models was explored. As a result, it was found that topographic parameters related to slope offer a certain correlation with the parameters of the reflection model. This can be useful for determining the optical reflection properties of materials for which direct BRDF measurements are not possible.

Design of an image-based BRDF measurement method using a catadioptric multispectral capture and a real-time Lambert calibration.

By utilizing a catadioptric system and a calibration Lambertian sample, a compact measurement method of bidirectional reflectance distribution function (BRDF) has been proposed for rapid and accurate measurement. With the help of an ellipsoidal dome mirror, a hyperboloid mirror, and a high-resolution camera, spatial reflectance distributions from reflected directions with a large field of view (FOV) can be obtained. The built-in Lambertian standard allows for real-time calibration to account for fluctuations in the illumination spectrum, effectively reducing the measurement drift and achieving a high accuracy. Moreover, a multispectral camera captures images at 8 spectral bands for accurate spectral color reconstruction from different directions. To verify the method, a prototype capable of fast, high-resolution measurements with a large FOV has been developed for characterizing the scattering properties of objects. It achieves a measured angular range up to 160°. Multispectral BRDF data for each sample can be obtained within 5 minutes with an angular resolution of less than 0.6°. Eight ceramic samples with different colors were selected for the verification of measurement accuracy, and their mean relative bias of BRDF measurement was found to be as low as 2.5%.

Aerosol retrieval over snow using the RemoTAP algorithm

Abstract. In order to conduct accurate aerosol retrieval over snow, the Remote Sensing of Trace Gases and Aerosol Products (RemoTAP) algorithm developed by SRON Netherlands Institute for Space Research is extended with a bi-directional reflection distribution function (BRDF) for snow surfaces. The capability of the extended algorithm is validated with both synthetic measurements and real satellite measurements from the Polarization &amp;amp; Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar (PARASOL), and a comparison has been made to retrievals with the baseline RemoTAP (without a snow kernel). For retrievals with real PARASOL observations, we use pixels over Aerosol Robotic Network (AERONET) stations for validation and we use the MODIS snow cover products to identify pixels over snow. We evaluate the retrieved aerosol optical thickness (AOT) at 550 nm (τ550), single-scattering albedo (SSA) at 550 nm (ω550) and Ångström exponent (AE) for 440–870 nm (AE440−870). The experiments with both synthetic and real data show that the extended RemoTAP maintains capability for snow-free pixels and has obvious advantages in accuracy and the fraction of successful retrievals for retrieval over snow, especially over surfaces with snow cover &gt;75 %. According to the real-data experiment, we find that the retrieval algorithm has difficulty in fitting the PARASOL 1020 nm band, where snow reflectance is significantly lower than that for the visible bands. When we perform a four-band retrieval (490, 565, 670, 865 nm) with the extended RemoTAP, we obtain a good retrieval result for τ550, ω550 and AE440−870. Therefore, the four-band retrieval with the extended RemoTAP is recommended for aerosol retrieval over snow.

Апроксимація дистрибутивної функції відбивної здатності поверхні поліном третього степеня

In the article a bidirectional reflectance distribution function based on a polynomial of the third degree is developed. The main disadvantages of Schlick, Phong, Blinn reflectance models are analyzed. The approximation of Blinn-Phong model by a cubic polynomial is proposed to improve the productivity of three-dimensional image formation. Formulas for the coefficients of the approximation cubic polynomial are calculated. The disadvantages of using the proposed cubic polynomial for reproducing the glare’s attenuation zone are considered. A function for high-precision reproduction of this zone is proposed, formulas of its coefficients are calculated. A combined function, combining a cubic polynomial for reproducing the glare’s epicenter zone and a function for reproducing the attenuation zone, is proposed. The plot of the combined function is built. It is shown that the combined function reproduces the glare’s epicenter and attenuation zones with small relative and absolute errors. The developed reflectance model provides a highly-productive formation of three-dimensional scenes in computer graphics systems. The proposed distribution function of surface reflectivity can be used in computer graphics systems.

BRDF modeling and optimization of a target surface based on the gradient descent algorithm

Addressing the current challenges in modeling and optimizing the bidirectional reflectance distribution function (BRDF) for the target surface, an improved six-parameter semi-empirical model is proposed based on an existing five-parameter semi-empirical model. In comparison with the original five-parameter model, the new, to the best of our knowledge, model considers reciprocity, and the results demonstrate that as the incident angle increases, the fitting accuracy of the six parameters gradually surpasses that of the five parameters. Additionally, this paper employs a machine learning optimization algorithm, namely, the gradient descent method, for optimizing the BRDF. The algorithm was comprehensively compared with other optimization methods, revealing that for the same dataset, the gradient descent method exhibited the smallest fitting errors. Subsequently, utilizing this algorithm for fitting experimental data resulted in errors consistently within 3%, confirming the reliability and accuracy of this optimization algorithm.

An overview of BRDF models in computer graphics

This paper aims to provide an overview of the Bidirectional Reflectance Distribution Function (BRDF) and the various parametric numerical models, known as BRDF models, used to make it easier and more efficient to use BRDF data in computer graphics. It introduces the basics of BRDF and classifies and describes some well-known BRDF models, including their advantages and disadvantages. The paper also covers the concept of data-driven models, which can achieve a high degree of realism by directly acquiring and using measured BRDF data in the rendering process.

Enhancing Leaf Area Index Estimation with MODIS BRDF Data by Optimizing Directional Observations and Integrating PROSAIL and Ross–Li Models

The Leaf Area Index (LAI) is a crucial vegetation parameter for climate and ecological models. Reflectance anisotropy contains valuable supplementary information for the retrieval of properties of an observed target surface. Previous studies have utilized multi-angular reflectance data and physically based Bidirectional Reflectance Distribution Function (BRDF) models with detailed vegetation structure descriptions for LAI estimation. However, the optimal selection of viewing angles for improved inversion results has received limited attention. By optimizing directional observations and integrating the PROSAIL and Ross–Li models, this study aims to enhance LAI estimation from MODIS BRDF data. A dataset of 20,000 vegetation parameter combinations was utilized to identify the directions in which the PROSAIL model exhibits higher sensitivity to LAI changes and better consistency with the Ross–Li BRDF models. The results reveal significant variations in the sensitivity of the PROSAIL model to LAI changes and its consistency with the Ross–Li model over the viewing hemisphere. In the red band, directions with high sensitivity to LAI changes and strong model consistency are mainly found at smaller solar and viewing zenith angles. In the near-infrared band, these directions are distributed at positions with larger solar and viewing zenith angles. Validation using field measurements and LAI maps demonstrates that the proposed method achieves comparable accuracy to an algorithm utilizing 397 viewing angles by utilizing reflectance data from only 30 directions. Moreover, there is a significant improvement in computational efficiency. The accuracy of LAI estimation obtained from simulated multi-angle data is relatively high for LAI values below 3.5 when compared with the MODIS LAI product from two tiles. Additionally, there is also a slight improvement in the results when the LAI exceeds 4.5. Overall, our results highlight the potential of utilizing multi-angular reflectance in specific directions for vegetation parameter inversion, showcasing the promise of this method for large-scale LAI estimation.

Towards Scalable Multi-View Reconstruction of Geometry and Materials.

In this paper, we propose a novel method for joint recovery of camera pose, object geometry and spatially-varying Bidirectional Reflectance Distribution Function (svBRDF) of 3D scenes that exceed object-scale and hence cannot be captured with stationary light stages. The input are high-resolution RGB-D images captured by a mobile, hand-held capture system with point lights for active illumination. Compared to previous works that jointly estimate geometry and materials from a hand-held scanner, we formulate this problem using a single objective function that can be minimized using off-the-shelf gradient-based solvers. To facilitate scalability to large numbers of observation views and optimization variables, we introduce a distributed optimization algorithm that reconstructs 2.5D keyframe-based representations of the scene. A novel multi-view consistency regularizer effectively synchronizes neighboring keyframes such that the local optimization results allow for seamless integration into a globally consistent 3D model. We provide a study on the importance of each component in our formulation and show that our method compares favorably to baselines. We further demonstrate that our method accurately reconstructs various objects and materials and allows for expansion to spatially larger scenes. We believe that this work represents a significant step towards making geometry and material estimation from hand-held scanners scalable.

Retrieving BRDFs from UAV-based radiometers for fiducial reference measurements: caveats and recommendations

Surface Bidirectional reflectance distribution function (BRDF) is a key intrinsic geophysical variable depending only on the characteristics of the observed medium. It is therefore the most suitable measurand to support the definition of fiducial reference measurements (FRM). Field acquisition of surface reflectance data relies on substantial assumptions and simplifications, often without accounting for their impact. For example, the BRDF is a theoretical concept and can never be measured in the field. In contrast, the hemispherical conical reflectance factor (HCRF), which is the measurand obtained during field campaigns, is impacted by all scene elements and is not intrinsic to the surface. This study analyses the impact of four parameters (atmospheric scattering, measurement device field of view cropping, acquisition duration, non-Lambertian reference panels) on HCRF estimation. Simulations are performed on a 3D vegetation scene, using the new radiative transfer model Eradiate. It is found that among the aforementioned parameters, atmospheric scattering alone leads to a relative root-mean-square error (RRMSE) of more than 10% between HCRF and reference Bidirectional reflectance factor (BRF).

Modeling and analysis of spectral polarization BRDF based on Microfacet theory

The polarization bidirectional reflectance distribution function (p-BRDF) model derived from the microfacet theory is utilized for ascertaining wavelength dependent terms in the model. The spectral p-BRDF model of a given object surface is established according to the spectral models of the complex refractive index and the width parameter. Each parameter in the spectral p-BRDF model has a clear physical meaning, making it more physical than Cook-Torrance BRDF model. The particle swarm optimization algorithm combined with in-plane BRDF experimental data is used for analyzing the spectral p-BRDF of a brass surface in the visible light band. The results show that the BRDF calculated by the model is in good agreement with the experimental data, which is validated by the adjusted R2, the optimal value is 0.9872. The peak value of BRDF is found to increase with increase in wavelength for different polarization states. There exists a certain incident angle at which the BRDF initially increases and then decreases as the reflection angle is increased. The BRDF peak appears in the direction of specular reflection, and all the BRDF peaks increase with the increase in the incident angle. The polarization state, wavelength, surface roughness, and permittivity are found to be the important factors affecting the distribution of BRDF on the object surface. A combination of the spectral p-BRDF model and limited experimental data related to the object surface under different testing conditions can be used to predict the spatial reflection characteristics of the surface of a given object.

GF-1 WFV Surface Reflectance Quality Evaluation in Countries along “the Belt and Road”

The GaoFen-1 wide field of view (GF-1 WFV) has produced level 1 digital number data globally; however, most applications have focused on China, and data quality outside China has not been validated. This study presents a preliminary assessment of the 2020 GF-1 WFV surface reflectance data for Nepal, Azerbaijan, Kenya, and Sri Lanka along “the Belt and Road” route using Sentinel-2 Multi-Spectral Instrument (MSI), Landsat-8 Operational Land Image (OLI), and Moderate Resolution Imaging Spectroradiometer (MODIS) data. A method for obtaining the GF-1 WFV surface reflectance data was also proposed, with steps including atmospheric correction, cross-radiation calibration, and bidirectional reflectance distribution function correction. The results showed that WFV surface reflectance data was not significantly different from MSI, OLI, and MODIS surface reflectance data. In the visible and near-infrared bands, for most landcover types, the bias was less than 0.02, and the precision and root mean square error were less than 0.04. When the landcover types were forest and water, the MSI, OLI, and MODIS surface reflectance data were higher than that of WFV in the near-infrared band. The results of this study provide a basis for assessing the global application potential of GF-1 WFV.

Accuracy evaluation of reflectance, normalized difference vegetation index, and normalized difference water index using corrected unmanned aerial vehicle multispectral images by bidirectional reflectance distribution function and solar irradiance

Accuracy evaluation of reflectance, normalized difference vegetation index, and normalized difference water index using corrected unmanned aerial vehicle multispectral images by bidirectional reflectance distribution function and solar irradiance

A Kalman-filtering-based BRDF online measurement method for variable temperature surfaces

Bidirectional Reflectance Distribution Function (BRDF) at variable temperature is important in many applications such as thermal imaging and target detection. However, ensuring long-term stable high temperature control is complex and energy consuming, making online measurements essential. Existing BRDF systems are mainly designed for room temperature measurements, and the widely used quadrature demodulator requires a large amount of stored measurement data and complicate post-processing calculations. In this paper, the Kalman-based demodulator was modified by adding a forgetting factor to improve the demodulation speed and flexibility. This demodulator was implemented on FPGA in both numerical simulations and experiments. The detection of BRDF was demodulated online, reducing measurement time and resource consumption by half compared to the quadrature demodulator. The proposed demodulator can be utilized for further analysis of high-temperature BRDF characteristics of material surfaces.

Modeling reflection by structured building-integrated photovoltaics

Evaluating the reflection of solar radiation by Building Integrated Photovoltaics (BIPV) with structured front-glass is challenging for two reasons. First, the resulting irregular scattering of light cannot be accounted for by simple reflection models. Second, the locations where the evaluation needs to take place cannot be predicted by simple geometric considerations, as in the case of mirror-like reflection. The detailed modelling of a BIPV module featuring a periodical, linear structure based on the scanning of its surface is described. The application of the model is demonstrated in the assessment of solar reflection by a concave array of the modules. The stochastic sampling of the BIPV modules from each location in a dense sensor grid, that is required to ensure that no local concentration of reflected solar radiation is missed, is supported by re-orienting the sensors. Rather than relying on a data-driven Bidirectional Reflectance Distribution Function (BRDF) model of limited directional resolution, the geometric structure of the front-glass is modelled by modulating the normal of a mirror-like surface. The method allows an accurate and dense simulation with moderate computational demand.

Interpolation Method for Measurement Data of Bidirectional Reflectance Distribution Function Using by Machine Learning

Interpolation Method for Measurement Data of Bidirectional Reflectance Distribution Function Using by Machine Learning