Depolarized Reflectance Modeling

Abstract

Polarimetric imaging is a growing topic of interest in computer vision for resolving the toughest edge cases and adversarial problems in detection and reconstruction where traditional RGB imaging falls short. The greater the fidelity of these polarimetric models, the more effectively they can be applied to both the forward problem of computer graphics modeling and the inverse problems of computer vision tasks. Polarization information has a long history of use in computer vision, particularly in the form of bi-directional reflectance distribution functions (BRDFs) which describe the profile of light scattered from an object as a function of macrosurface normal, illumination direction, and observation direction. Polarimetric interpretations of the seminal Cook and Torrance (1981) microfacet BRDF model are represented as Stokes vector or Mueller matrix functions, and describes smooth and spectrally invariant materials well. However, higher albedo and increased surface roughness generally relate to an increase depolarization, so the pBRDF microfacet model does not describe these rough and varying albedo materials as well. This dissertation describes a framework for designing partial Mueller polarimeters and developing Mueller pBSDF models for highly depolarizing, roughly textured, colored materials. A type of ``triply degenerate" materials is identified and leveraged to improve polarimetric accuracy of a two-component pBSDF model and polarimetric measurement techniques. ``Triple degeneracy" refers to the case when the eigenspectrum of a Cloude coherency matrix, calculated from a Mueller matrix, consists of a unique largest eigenvalue and three approximately equal smaller eigenvalues. Triple degeneracy is identified in each of the Mueller matrix measurement data sets analyzed in this dissertation. The Mueller matrices analyzed in this work are all taken using the RGB950, a large aperture rotating retarder Mueller matrix imaging polarimeter developed by the University of Arizona and Axometrics, Inc. in Huntsville, Alabama. This polarimeter is designed to study highly diffuse objects. A 10 cm aperture fixed polarizer and rotating retarder form the generator optics and, together with the lightbox source, output a high polarized radiance that is suited for analyzing large samples of highly diffuse, low albedo materials. The red (662±22 nm), green (524±34 nm), and blue (451±19 nm) illumination channels enable computer vision task performance assessment between traditional RGB imaging and polarimetric imaging. The inverse problems of metamer discrimination and partial Mueller polarimeter are addressed through analysis of the diffuse white materials Mueller matrix measurements data set. Partial Mueller polarimetry uses fewer than sixteen polarized measurements to capture crucial polarimetric information of a sample under observation, and can aid in the design of faster, smaller polarimeters for specific tasks. The diffuse white materials set is curated purposefully to be metameric or difficult to distinguish in traditional RGB imaging and highly diffuse to further challenge polarimetric imaging. Depolarization parameters and the second largest coherency eigenvalue are shown to be the most effective parameters for metamer classification. The inverse problem of surface texture estimation and forward problem of accurate Mueller pBRDF modeling are addressed through analysis of the rough, opaque, colored plastics Mueller matrix measurements data set. The wavelength-dependence of the Fresnel reflection component of the microfacet pBRDF model is demonstrated using near-specular measurements of four different roughened red plastics under red and blue illumination. Analysis on the full opaque plastics data set (five colors, nine textures, and RGB illumination at off-specular geometries) shows that treating the polarized component of the Mueller BRDF model as a wavelength-independent parameter is a poor assumption for depolarizing materials with spectrally varying albedo over wavelength. In both data sets, a relationship of triple degeneracy is observed in the eigenspectrum of the related coherency matrix to these Mueller matrices. This triple degeneracy relationship is leveraged to improve polarimetric accuracy of a newly proposed two-component pBSDF model that characterizes Mueller pBSDFs using the largest coherency eigenvalue. This novel re-parameterized Mueller pBSDF model is compared to a hypothetical-ray-path-based three-component Mueller pBSDF model and shown to be well-suited to describing rougher surface textures. Finally, a method of directly measuring the largest coherency eigenvalue of a triply degenerate back-scattering material is demonstrated through simulation.