Measured Bidirectional Reflectance Distribution Function Data Research Articles

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.

Adaptive B-spline volume representation of measured BRDF data for photorealistic rendering

Abstract Measured bidirectional reflectance distribution function (BRDF) data have been used to represent complex interaction between lights and surface materials for photorealistic rendering. However, their massive size makes it hard to adopt them in practical rendering applications. In this paper, we propose an adaptive method for B-spline volume representation of measured BRDF data. It basically performs approximate B-spline volume lofting, which decomposes the problem into three sub-problems of multiple B-spline curve fitting along u-, v-, and w-parametric directions. Especially, it makes the efficient use of knots in the multiple B-spline curve fitting and thereby accomplishes adaptive knot placement along each parametric direction of a resulting B-spline volume. The proposed method is quite useful to realize efficient data reduction while smoothing out the noises and keeping the overall features of BRDF data well. By applying the B-spline volume models of real materials for rendering, we show that the B-spline volume models are effective in preserving the features of material appearance and are suitable for representing BRDF data.

Forward Reflection Characteristics of Typical Smooth Building Walls and the Simulation Analysis

Non-line-of-sight optical imaging technology is a novel application of imaging technology developed recently, achieving the effective imaging of the corner, basements and other scenes which are difficult to be directly observed by traditional vision with intermediate reflective surface. Smooth building walls, such as tiles and marbles, are typical intermediate reflective surfaces. Because reflecting surface is neither ideal specular reflective nor Lambertian reflective, the reflection characteristics of the intermediate reflective surface have a significant impact on the non-line-of-sight imaging. Based on the test data of the spectral bidirectional reflectance distribution function (BRDF) of common smooth tiles, the surface transfer function and angle spread function of smooth tiles are established according to the Harvey-Shack surface scatter theory in the paper. And the descriptions of the characteristics of specular reflection and forward scattering are implemented. Furthermore, according to the measured BRDF data at a certain wavelength for a certain angle of incidence, we can predict the reflection and scattering distribution at any other wavelengths or for other incident angles. The simulation results indicate that the curves fitted by the model basically are in agreement with the measured data, so that the simulation of the specular reflection and the forward scattering in the model is valid.

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.

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.

BRDF Measurement Modelling using Wavelets for Efficient Path Tracing

Abstract Physically based rendering needs numerical models from real measurements, or analytical models from material definitions, of the Bidirectional Reflectance Distribution Function (BRDF). However, measured BRDF data sets are too large and provide no functionalities to be practically used in Monte Carlo path tracing algorithms. In this paper, we present a wavelet‐based generic BRDF model suitable for both physical analysis and path tracing. The model is based on the separation of spectral and geometrical aspect of the BRDF and allows a compact and efficient representation of isotropic, anisotropic and/or spectral BRDFs. After a brief survey of BRDF and wavelet theory, we present our software architecture for generic wavelet transform and how to use it to model BRDFs. Then, modelling results are presented on real and virtual BRDF measurements. Finally, we show how to exploit the multiresolution property of the wavelet encoding to reduce the variance by importance sampling in a path tracing algorithm. ACM CSS: I.3.7 Computer Graphics—Three‐Dimensional Graphics and Realism

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.

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.

Bidirectional reflectance and specularity of twelve spacecraft thermal control materials

Many spacecraft external payloads are sensitive to focused solar heating caused by specular reflections from exterior thermal control surfaces. This paper presents a method of calculating specularity using bidirectional reflectance distribution function (BRDF) input. Definitions are presented for directional and hemispherical specularity as a function of the conical half-angle surrounding the specular ray. Measured BRDF data are presented for commonly used thermal control materials including plastic films and paints. Angles of incidence range from 5 to 78 deg and data are taken both in and out of the plane of incidence. Most measurements are made at a wavelength of 0.488 /urn, though measurements for two white paints are also made at 1.06, 3.39, and 10.63 ftm. The BRDF values are found to increase with both angle of incidence and wavelength. A numerical code is described that integrates BRDF data to yield both directional and hemispherical specularity as a function of cone half-angle around the specular ray. Specularity results are presented for all 12 materials studied.