Experimental and Theoretical Basis for a Closed-Form Spectral BRDF Model

The microfacet class of BRDF models is frequently used to calculate optical scatter from realistic surfaces using geometric optics, but has the disadvantage of not being able to consider wavelength dependence. This dissertation works toward development of a closed-form approximation to the BRDF that is suitable for hyperspectral remote sensing by presenting measured BRDF data of 12 different materials at four different incident angles and up to seven different wavelengths between 3.39 and 10.6 micrometer. The data was intended to be fit to various microfacet BRDF models to determine an appropriate form of the wavelength scaling. However, when fitting the microfacet models to measured data, the results indicated a breakdown in the microfacet model itself. To overcome this deficiency, elements of microfacet BRDF models are compared to elements of scalar wave optics BRDF models, which inherently contain a wavelength dependence. This analysis led to a theoretical understanding of how to modify microfacet BRDF models to maintain the simplicity of a closed-form model, while better approximating the underlying physics

Practical Multiple Scattering for Rough Surfaces

Microfacet theory concisely models light transport over rough surfaces. Specular reflection is the result of single mirror reflections on each facet, while exact computation of multiple scattering is either neglected, or modeled using costly importance sampling techniques. Practical but accurate simulation of multiple scattering in microfacet theory thus remains an open challenge. In this work, we revisit the traditional V-groove cavity model and derive an analytical, cost-effective solution for multiple scattering in rough surfaces. Our kaleidoscopic model is made up of both real and virtual V-grooves, and allows us to calculate higher-order scattering in the microfacets in an analytical fashion. We then extend our model to include nonsymmetric grooves, allowing for additional degrees of freedom on the surface geometry, improving multiple reflections at grazing angles with backward compatibility to traditional normal distribution functions. We validate the accuracy of our model against ground-truth Monte Carlo simulations, and demonstrate its flexibility on anisotropic and textured materials. Our model is analytical, does not introduce significant cost and variance, can be seamless integrated in any rendering engine, preserves reciprocity and energy conservation, and is suitable for bidirectional methods

Robust Method of Determining Microfacet BRDF Parameters in the Presence of Noise via Recursive Optimization

Accurate bidirectional reflectance distribution function (BRDF) models are essential for computer graphics and remote sensing performance. The popular microfacet class of BRDF models is geometric-optics-based and computationally inexpensive. Fitting microfacet models to scatterometry measurements is a common yet challenging requirement that can result in a model being fit as one of several unique local minima. Final model fit accuracy is therefore largely based on the quality of the initial parameter estimate. This makes for widely varying material parameter estimates and causes inconsistent performance comparisons across microfacet models, as will be shown with synthetic data. We proposed a recursive optimization method for accurate parameter determination. This method establishes an array of local minima best fits by initializing a fixed number of parameter conditions that span the parameter space. The identified solution associated with the best fit quality is extracted from the local array and stored as the relative global best fit. This method is first applied successfully to synthetic data, then it is applied to several materials and several illumination wavelengths. This method proves to reduce manual parameter adjustments, is equally weighted across incident angles, helps define parameter stability within a model, and consistently improves fit quality over the high-error local minimum best fit from lsqcurvefit by an average of 71%

Enhanced BRDF Modeling Using Directional Volume Scatter Terms

Accurate Bidirectional Reflectance Distribution Function (BRDF) models provide critical scatter behavior for computer graphics and remote sensing performance. The popular microfacet class of BRDF models is geometric-based and computationally inexpensive compared to wave-optics models. Microfacet models commonly account for surface scatter and Lambertian volume scatter, but not directional volume scatter. This work proposes directional volume scatter modeling for enhanced performance over all observation regions. Five directional volume models are incorporated into the modified Cook-Torrance microfacet model. Additionally, a semi-empirical directional volume term is presented based on the Beckmann microfacet distribution and a modified Fresnel reflection term. High fidelity, low density data from 15 datasets are fit to each hybrid model using a recursive optimization method then compared to the baseline Cook-Torrance model. By including a directional volume term, analysis shows fit quality is improved based on the square of the mean standard error (MSE2) by as much as 78% and backscatter agreement is improved by as much as 92%. Including the semi-empirical, Oren-Nayar, or Beard-Maxwell directional volume term reduced backscatter MSE2 across datasets exhibiting high volume scatter by an average of 52%, 46%, and 26% respectively. Directional volume terms showed statistically insignificant improvement for low volume scatter materials, while full model improvements were apparent across all high volume scatter visually diffuse materials. Results suggest directional volume scatter modeling can consistently improve full model fit quality with emphasized model agreement for backscatter observations. These results validate directional volume scatter significance and are expected to lead to enhanced remote sensing and scene generation

Measurement, modeling and perception of painted surfaces : A Multi-scale analysis of the touch-up problem

Real-world surfaces typically have geometric features at a range of spatial scales. At the microscale, opaque surfaces are often characterized by bidirectional reflectance distribution functions (BRDF), which describes how a surface scatters incident light. At the mesoscale, surfaces often exhibit visible texture - stochastic or patterned arrangements of geometric features that provide visual information about surface properties such as roughness, smoothness, softness, etc. These textures also affect how light is scattered by the surface, but the effects are at a different spatial scale than those captured by the BRDF. Through this research, we investigate how microscale and mesoscale surface properties interact to contribute to overall surface appearance. This behavior is also the cause of the well-known touch-up problem in the paint industry, where two regions coated with exactly the same paint, look different in color, gloss and/or texture because of differences in application methods. At first, samples were created by applying latex paint to standard wallboard surfaces. Two application methods- spraying and rolling were used. The BRDF and texture properties of the samples were measured, which revealed differences at both the microscale and mesoscale. This data was then used as input for a physically-based image synthesis algorithm, to generate realistic images of the surfaces under different viewing conditions. In order to understand the factors that govern touch-up visibility, psychophysical tests were conducted using calibrated, digital photographs of the samples as stimuli. Images were presented in pairs and a two alternative forced choice design was used for the experiments. These judgments were then used as data for a Thurstonian scaling analysis to produce psychophysical scales of visibility, which helped determine the effect of paint formulation, application methods, and viewing and illumination conditions on the touch-up problem. The results can be used as base data towards development of a psychophysical model that relates physical differences in paint formulation and application methods to visual differences in surface appearance

A Comparative Study of the Bidirectional Reflectance Distribution Function of Several Surfaces as a Mid-wave Infrared Diffuse Reflectance Standard

The Bi-Directional Reflectance Distribution Function (BRDF) has a well defined diffuse measurement standard in the ultraviolet, visible, and near infrared (NIR), Spectralon(trade name). It is predictable, stable, repeatable, and has low surface variation because it is a bulk scatterer. In the mid-wave IR (MWIR) and long-wave IR (LWIR), there is not such a well-defined standard. There are well-defined directional hemispherical reflectance (DHR) standards, but the process of integrating BRDF measurements into DHR for the purpose of calibration is problematic, at best. Direct BRDF measurement standards are needed. This study use current calibration techniques to ensure valid measurements and then systematically investigates the BRDF and its variation for eight potential MWIR diffuse BRDF standards. Diffuseness, repeatability, and reflectance are all considered as required parameters necessary for a di use MWIR BRDF standard. This document shows comparatively that Spectralon is an excellent candidate for a diffuse MWIR BRDF standard