Fresnel Microfacet BRDF:
Unification of Polari-Radiometric Surface-Body Reflection

Tomoki Ichikawa, Yoshiki Fukao,
Shohei Nobuhara, and Ko Nishino
Kyoto University

Computer vision applications have heavily relied on the linear combination of Lambertian diffuse and microfacet specular reflection models for representing reflected radiance, which turns out to be physically incompatible and limited in applicability. In this paper, we derive a novel analytical reflectance model, which we refer to as Fresnel Microfacet BRDF model, that is physically accurate and generalizes to various real-world surfaces. Our key idea is to model the Fresnel reflection and transmission of the surface microgeometry with a collection of oriented mirror facets, both for body and surface reflections. We carefully derive the Fresnel reflection and transmission for each microfacet as well as the light transport between them in the subsurface. This physically-grounded modeling also allows us to express the polarimetric behavior of reflected light in addition to its radiometric behavior. That is, FMBRDF unifies not only body and surface reflections but also light reflection in radiometry and polarization and represents them in a single model. Experimental results demonstrate its effectiveness in accuracy, expressive power, image-based estimation, and geometry recovery.

• Fresnel Microfacet BRDF: Unification of Polari-Radiometric Surface-Body Reflection
  T. Ichikawa, Y. Fukao, S. Nobuhara, and K. Nishino,
  in Proc. of Conference on Computer Vision and Pattern Recognition CVPR’23, Jun., 2023.
  [ paper ][ supp. material ][ project ][ code/data ]

Overview

We derive a novel analytical reflectance model that is physically accurate and generalizes to various real-world surfaces. Our key idea is to build up from the very atomic behavior of light reflection, namely Fresnel reflection. We model surface microgeometry with a collection of oriented mirror facets, both for body and surface reflections. We carefully derive the Fresnel reflection and transmission for each microfacet as well as the light transport between them in the subsurface. By modeling the full Fresnel behavior of light for an analytically oriented distribution of mirror microfacets, we arrive at a generalized reflection model that subsumes past representative models as special cases. This physically-grounded modeling allows us to describe the polarimetric behavior of reflected light by a rough surface, in addition to its radiometric behavior. As a result, our novel reflectance model, which we refer to as Fresnel Microfacet BRDF model (FMBRDF), unifies not only body and surface reflections but also light reflection in radiometry and polarization in a single model.

As our FMBRDF model is physically-based, it provides an intuitive interpretation of polarization of surface reflection. Polarimetric image interpretation is notoriously difficult but our model lets us map key characteristics to its physically explicable parameters. Our model describes both the polarimetric and radiometric behaviors of light reflected by a surface. This allows us to estimate its parameters from a single polarimetric image captured with a known directional light of an object of known geometry and then use those parameters to analyze and synthesize not just polarimetric but also radiometric appearance of that surface.

Results

Polarimetric accuracy shown with DoLP values plotted as a function of the angle between the global surface normal and the viewing direction. Each graph shows the fitting results for one of the lighting conditions. The number under the graph is the root mean square error. Our FMBRDF model accurately captures the characteristics of the DoLP distributions both for surface and body reflections regardless of the surface roughness and color.

Radiometric accuracy shown with intensity values as a function of the angle between the global surface normal and the light source direction. Each graph shows the fitting results for one of the lighting conditions. The number at the top of the graph is the RMSE. Our FMBRDF model accurately represents both surface and body reflections regardless of the surface roughness and color.

Radiometric fitting results on objects with nonLambertian diffuse reflectance. The microfacet correlation function enables our model to represent Oren-Nayar diffuse reflection caused by rough mesogeometry.

Radiometric renderings using BRDF parameters estimated from single polarimetric images (ours), DoLP images (ours only polarization), and radiometric images (others). The number under the rendered image is the RMSE from the observation divided by the average of observed radiance. In contrast to BRDFs estimated with only radiance, FMBRDF estimated with radiance and polarization results in accurate radiometric appearance both in surface and body reflection for different surfaces.