Robust method of determining microfacet BRDF parameters in the presence of noise via recursive optimization

Michael W Bishop,Samuel D Butler,Michael A Marciniak

doi:10.1117/1.oe.60.9.094103

Abstract

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%.

Highlights

Light reflected off surfaces can be modeled according to the direction of the incoming light, light direction upon reflection, and surface normal
An unsupervised, yet reliable recursive optimization routine was proposed as an improved approach for consistent determination of bidirectional reflectance distribution function (BRDF) parameter values
A modified Cook–Torrance model with a semi-empirical directional volume term was used with the recursive optimization method and validated against three synthetic test datasets, as well as implemented on scatterometry measurements of several materials

Summary

Introduction

Light reflected off surfaces can be modeled according to the direction of the incoming light, light direction upon reflection, and surface normal Such a description is widely employed in scene generation, medical imaging, multi-layer color printing, resource monitoring, weather modeling, and paint development industries.[1,2,3,4,5,6,7] For a complete dataset, one must make assumptions about the direction, magnitude, and wavelength dependency of light reflection off the observed material. Such a reflection description is given by a bidirectional reflectance distribution function (BRDF). The BRDF, fr, is defined as the ratio of the reflected radiance (Ls) to the incident irradiance (Ei) as[8] f ðω^ ; ω^ ; λÞ 1⁄4 dLdEðω^ðω^; ω^; λ;ÞλÞ ; EQ-TARGET;temp:intralink-;e001;116;167 r i s si s ii (1)

Methods

Results

Conclusion