Analytical Bidirectional Reflectance Distribution Function Research Articles

Assessment of the Hotspot Effect for the PROSAIL Model With POLDER Hotspot Observations Based on the Hotspot-Enhanced Kernel-Driven BRDF Model

The hotspot effect is a typical angular reflectance signature of vegetation canopies and contains important information for the retrieval of vegetation structural parameters. To date, the hotspot effect of various analytical bidirectional reflectance distribution function (BRDF) models (e.g., the PROSAIL model) has rarely been assessed by multiangular measurements with sufficient hotspot observations due to the lack of accurate hotspot measurements (for field measurements) or appropriate methods (for airborne and spaceborne measurements). In this paper, we develop a method to further improve the hotspot effect of the kernel-driven model and design a framework to utilize the improved kernel-driven model as a bridge to assess the hotspot effect of the PROSAIL model with Polarization and Directionality of the Earth Reflectance (POLDER) hotspot observations. The results indicate that the proposed method further improves the fits between the models and the observations in the vicinity of the hotspot direction, particularly in the rare situations where the geometric-optical scattering component governs the target reflectance. In addition, the hotspot signature indicated by the PROSAIL multiangular data shows a larger variability than that of POLDER observations. $C_{1}$ and $C_{2}$ in the improved kernel-driven model can be used as benchmarked parameters to qualify the amplitude and width of the hotspot effect for the simulated multiangular data of physical BRDF models and thus present the potential for the assessment and analysis of the hotspot effect of physical models, which, in return, helps retrieve the structural parameters of vegetation canopies from hotspot signatures.

In-vessel viewing system prototype performance measurements and simulation of measurement quality across the ITER in-vessel components

The In-Vessel Viewing and Metrology System (IVVS) is a fundamental tool for the ITER machine operations, tasked with inspection of plasma facing surfaces (PFS) of in-vessel components for both damage and erosion.The IVVS design has evolved to include a hybrid viewing and metrology system, using Frequency Modulated (FM) lidar for absolute distance measurements, and amplitude modulated (AM) lidar for surface viewing A full-scale prototype has been built, and has produced line-of-sight range precision of <2 μm in the optimum scenario. Error analysis indicates that 3D precision from 2 to 400 μm should be available over surfaces from 0.5 to 10 m with 0–70° incidence angles, exceeding the ITER requirements.Performance was found to be highly sensitive to received power and surface reflectivity. To parameterize the reflectivity, the Bidirectional Reflectance Distribution Function (BRDF) of a divertor monoblock prototype was measured and an analytic BRDF model was developed. An IVVS simulator was developed and used both to analyse the in-vessel geometry and to predict the coverage of the PFS. We have shown that 85% of the PFS area can be covered if the IVVS meets performance requirements up to incidence angles of 65° and distances of 8 m.

Connecting measured BRDFs to analytic BRDFs by data-driven diffuse-specular separation

The bidirectional reflectance distribution function (BRDF) is crucial for modeling the appearance of real-world materials. In production rendering, analytic BRDF models are often used to approximate the surface appearance since they are compact and flexible. Measured BRDFs usually have a more realistic appearance, but consume much more storage and are hard to modify. In this paper, we propose a novel framework for connecting measured and analytic BRDFs. First, we develop a robust method for separating a measured BRDF into diffuse and specular components. This is commonly done in analytic models, but has been difficult previously to do explicitly for measured BRDFs. This diffuse-specular separation allows novel measured BRDF editing on the diffuse and specular parts separately. In addition, we conduct analysis on each part of the measured BRDF, and demonstrate a more intuitive and lower-dimensional PCA model than Nielsen et al. [2015]. In fact, our measured BRDF model has the same number of parameters (8 parameters) as the commonly used analytic models, such as the GGX model. Finally, we visualize the analytic and measured BRDFs in the same space, and directly demonstrate their similarities and differences. We also design an analytic fitting algorithm for two-lobe materials, which is more robust, efficient and simple, compared to previous non-convex optimization-based analytic fitting methods.

An adaptive parameterization for efficient material acquisition and rendering

One of the key ingredients of any physically based rendering system is a detailed specification characterizing the interaction of light and matter of all materials present in a scene, typically via the Bidirectional Reflectance Distribution Function (BRDF). Despite their utility, access to real-world BRDF datasets remains limited: this is because measurements involve scanning a four-dimensional domain at sufficient resolution, a tedious and often infeasibly time-consuming process. We propose a new parameterization that automatically adapts to the behavior of a material, warping the underlying 4D domain so that most of the volume maps to regions where the BRDF takes on non-negligible values, while irrelevant regions are strongly compressed. This adaptation only requires a brief 1D or 2D measurement of the material's retro-reflective properties. Our parameterization is unified in the sense that it combines several steps that previously required intermediate data conversions: the same mapping can simultaneously be used for BRDF acquisition, storage, and it supports efficient Monte Carlo sample generation. We observe that the above desiderata are satisfied by a core operation present in modern rendering systems, which maps uniform variates to direction samples that are proportional to an analytic BRDF. Based on this insight, we define our adaptive parameterization as an invertible, retro-reflectively driven mapping between the parametric and directional domains. We are able to create noise-free renderings of existing BRDF datasets after conversion into our representation with the added benefit that the warped data is significantly more compact, requiring 16KiB and 544KiB per spectral channel for isotropic and anisotropic specimens, respectively. Finally, we show how to modify an existing gonio-photometer to provide the needed retro-reflection measurements. Acquisition then proceeds within a 4D space that is warped by our parameterization. We demonstrate the efficacy of this scheme by acquiring the first set of spectral BRDFs of surfaces exhibiting arbitrary roughness, including anisotropy.

Sequential fitting-and-separating reflectance components for analytical bidirectional reflectance distribution function estimation.

We present a sequential fitting-and-separating algorithm for surface reflectance components that separates individual dominant reflectance components and simultaneously estimates the corresponding bidirectional reflectance distribution function (BRDF) parameters from the separated reflectance values. We tackle the estimation of a Lafortune BRDF model, which combines a nonLambertian diffuse reflection and multiple specular reflectance components with a different specular lobe. Our proposed method infers the appropriate number of BRDF lobes and their parameters by separating and estimating each of the reflectance components using an interval analysis-based branch-and-bound method in conjunction with iterative K-ordered scale estimation. The focus of this paper is the estimation of the Lafortune BRDF model. Nevertheless, our proposed method can be applied to other analytical BRDF models such as the Cook-Torrance and Ward models. Experiments were carried out to validate the proposed method using isotropic materials from the Mitsubishi Electric Research Laboratories-Massachusetts Institute of Technology (MERL-MIT) BRDF database, and the results show that our method is superior to a conventional minimization algorithm.

Evaluation of Atmospheric Effects on Land-Surface Directional Reflectance With the Coupled RAPID and VLIDORT Models

In order to assess atmospheric effects on the directional reflectance of land surface, we have developed a new approach coupling the 3-D radiosity-based land-surface model [radiosity applicable to porous individual objects (RAPID)] with the atmospheric radiative transfer (RT) model [vector linearized discrete ordinate RT (VLIDORT)]. RAPID is used to generate a lookup table of bidirectional reflectance distribution function (BRDF) elements required by VLIDORT for the surface boundary condition. To test the RAPID–VLIDORT model, we used five natural 3-D scenes along with five aerosol optical depths (AODs). Results for top-of-atmosphere radiances show semiempirical analytical BRDF models are insufficiently accurate to represent bidirectional reflectance factors (BRFs) in hotspot regions and over wide angular variations. The large impact of AOD on BRF hotspot also underlines the importance of precise atmospheric corrections for multiangular remote sensing of the earth’s surface.

Branch and bound algorithm for accurate estimation of analytical isotropic bidirectional reflectance distribution function models.

We present a reliable and accurate global optimization framework for estimating parameters of isotropic analytical bidirectional reflectance distribution function (BRDF) models. This approach is based on a branch and bound strategy with linear programming and interval analysis. Conventional local optimization is often very inefficient for BRDF estimation since its fitting quality is highly dependent on initial guesses due to the nonlinearity of analytical BRDF models. The algorithm presented in this paper employs L1-norm error minimization to estimate BRDF parameters in a globally optimal way and interval arithmetic to derive our feasibility problem and lower bounding function. Our method is developed for the Cook-Torrance model but with several normal distribution functions such as the Beckmann, Berry, and GGX functions. Experiments have been carried out to validate the presented method using 100 isotropic materials from the MERL BRDF database, and our experimental results demonstrate that the L1-norm minimization provides a more accurate and reliable solution than the L2-norm minimization.

Adaptive highlights stencils for modeling of multi-axial BRDF anisotropy

Directionally dependent anisotropic material appearance phenomenon is widely represented using bidirectional reflectance distribution function (BRDF). This function needs in practice either reconstruction of unknown values interpolating between sparse measured samples or requires data fidelity preserving compression forming a compact representation from dense measurements. Both properties can be, to a certain extent, preserved by means of analytical BRDF models. Unfortunately, the number of anisotropic BRDF models is limited, and moreover, most require either a demanding iterative optimization procedure dependent on proper initialization or the user setting parameters. Most of these approaches are challenged by the fitting of complex anisotropic BRDFs. In contrast, we approximate BRDF anisotropic behavior by means of highlight stencils and derive a novel BRDF model that independently adapts such stencils to each anisotropic mode present in the BRDF. Our model allows for the fast direct fitting of parameters without the need of any demanding optimization. Furthermore, it achieves an encouraging, expressive visual quality as compared to rival solutions that rely on a similar number of parameters. We thereby ascertain that our method represents a promising approach to the analysis and modeling of complex anisotropic BRDF behavior.

Modeling the BRDF from spectral reflectance measurements of metallic surfaces

The key quantity for expressing the directional optical effect of materials on the incident radiance is the bidirectional reflectance distribution function (BRDF). Our work is devoted to the BRDF spectral measurements, in order to render the synthetic images, mostly of the metallic paints. We measured the spectral reflectance off multiple paint samples then used the measured data to fit the analytical BRDF model, in order to acquire its parameters. Our contribution is in a mutual comparison and using the Cook–Torrance microfacet model as a fitting function for reflectance distribution evaluation. Results of analysis and the measurements were incorporated into the rendering process of car paint.

Metallic paint appearance measurement and rendering

Abstract Humans recognize objects visually on the basis of material composition as well as shape. To acquire a certain level of photorealism, it is necessary to analyze, how the materials scatter the incident light. The key quantity for expressing the directional optical effect of materials on the incident radiance is the bidirectional reflectance distribution function (BRDF). Our work is devoted to the BRDF measurements, in order to render the synthetic images, mostly of the metallic paints. We measured the spectral reflectance off multiple paint samples then used the measured data to fit the analytical BRDF model, in order to acquire its parameters. In this paper we describe the methodology of the image synthesis from measured data. Materials such as the metallic paints exhibit a sparkling effect caused by the metallic particles scattered within the paint volume. Our analysis of sparkling effect is based on the processing of the multiple photographs. Results of analysis and the measurements were incorporated into the rendering process of car paint

Refining Space Object Radiation Pressure Modeling with Bidirectional Reflectance Distribution Functions

High-fidelity orbit propagation requires detailed knowledge of the solar radiation pressure on a space object. The solar radiation pressure depends not only on the space object’s shape and attitude, but also on the absorption and reflectance properties of each surface on the object. These properties are typically modeled in a simplistic fashion, but are here described by a surface bidirectional reflectance distribution function. Several analytic bidirectional reflectance distribution function models exist, and are typically complicated functions of illumination angle and material properties represented by parameters within the model. In general, the resulting calculation of the solar radiation pressure would require a time-consuming numerical integration. This might be impractical if multiple solar radiation pressure calculations are required for a variety of material properties in real time; for example, in a filter where the particular surface parameters are being estimated. This paper develops a method to make accurate and precise solar radiation pressure calculations quickly for some commonly used analytic bidirectional reflectance distribution functions. In addition, other radiation pressures exist, including Earth albedo/Earth infrared radiation pressure, and thermal radiation pressure from the space object itself, and are influenced by the specific bidirectional reflectance distribution function. A description of these various radiation pressures and a comparison of the magnitude of the resulting accelerations at various orbital heights and the degree to which they affect the space object’s orbit are also presented. Significantly, this study suggests that, for space debris whose interactions with electro-magnetic radiation are described accurately with a bidirectional reflectance distribution function, then hitherto unmodeled torques would account for rotational characteristics affecting both tracking signatures and the ability to predict the orbital evolution of the objects.

Real-time rendering of colour-shift effect of metallic materials

The directional-dependent effects of the materials are responsible for our perception of certain materials being realistic or not. Some materials consist of colour pigments, and these cause directional-dependent colour variations (or colour-shifts). For instance, we can observe a colour-shift effect of metallic materials, which means the changing of colour from metallic colour to pigment colour depending on the direction of incident illumination and direction of view. The most common criticism of existing analytical Bidirectional Reflectance Distribution Function (BRDF) models is that these models are inadequate to generate colour-shift effect of materials for realistic real-time rendering. This paper introduces a visually plausible shading model to generate colour-shift effect of metallic materials by modifying specular component with illumination and view dependent sheen. The developed shaders have intuitive parameters, which can generate different kinds of metallic effects for real-time rendering, including visually plausible gold, brass, silver, bronze and copper effects for real-time rendering.

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 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 paper, 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 model 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.

An analytic BRDF model of canopy radiative transfer and its inversion

Radiative transfer modeling of the bidirectional reflectance distribution function (BRDF) of leaf canopies is a powerful tool to relate multiangle remotely sensed data to biophysical parameters of the leaf canopy and to retrieve such parameters from multiangle imagery. However, the approximate approaches for multiple scattering that are used in the inversion of existing models are quite limited, and the sky radiance frequently is simply treated as isotropic. This paper presents an analytical model based on a rigorous canopy radiative transfer equation in which the multiple-scattering component is approximated by asymptotic theory and the single-scattering calculation, which requires numerical integration to properly accommodate the hotspot effect, is also simplified. Because the model is sensitive to angular variation in sky radiance, the authors provide an accompanying new formulation for directional radiance in which the unscattered solar radiance and single-scattering radiance are calculated exactly, and multiple-scattering is approximated by the well-known delta two-stream approach. A series of validations against exact calculations indicates that both models are quite accurate, especially when the viewing angle is smaller than 55 degrees . The Powell algorithm is then used to retrieve biophysical parameters from multiangle observations based on both the canopy and the sky radiance distribution models. >