Bidirectional reflectance distribution function

Summary

The bidirectional reflectance distribution function (BRDF; f_{\text{r}}(\omega_{\text{i}},, \omega_{\text{r}}) ) is a function of four real variables that defines how light is reflected at an opaque surface. It is employed in the optics of real-world light, in computer graphics algorithms, and in computer vision algorithms. The function takes an incoming light direction, \omega_{\text{i}}, and outgoing direction, \omega_{\text{r}} (taken in a coordinate system where the surface normal \mathbf n lies along the z-axis), and returns the ratio of reflected radiance exiting along \omega_{\text{r}} to the irradiance incident on the surface from direction \omega_{\text{i}}. Each direction \omega is itself parameterized by azimuth angle \phi and zenith angle \theta, therefore the BRDF as a whole is a function of 4 variables. The BRDF has units sr−1, with steradians (sr)

Official source

https://en.wikipedia.org/wiki/Bidirectional_reflectance_distribution_function

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Realistic modeling of the bidirectional reflectance distribution function (BRDF) of scene objects is a vital prerequisite for any type of physically based rendering. In the last decades, the availability of databases containing real-world material measurements has fueled considerable innovation in the development of such models. However, previous work in this area was mainly focused on increasing the visual realism of images, and hence ignored the effect of scattering on the polarization state of light, which is normally imperceptible to the human eye. Existing databases thus only capture scattered flux, or polarimetric BRDF datasets are too directionally sparse (e.g., in-plane) to be usable for simulation. While subtle to human observers, polarization is easily perceived by any optical sensor (e.g., using polarizing filters), providing a wealth of additional information about shape and material properties of the object under observation. Given the increasing application of rendering in the solution of inverse problems via analysis-by-synthesis and differentiation, the ability to realistically model polarized radiative transport is thus highly desirable. Polarization depends on the wavelength of the spectrum, and thus we provide the first polarimetric BRDF (pBRDF) dataset that captures the polarimetric properties of real-world materials over the full angular domain, and at multiple wavelengths. Acquisition of such reflectance data is challenging due to the extremely large space of angular, spectral, and polarimetric configurations that must be observed, and we propose a scheme combining image-based acquisition with spectroscopic ellipsometry to perform measurements in a realistic amount of time. This process yields raw Mueller matrices, which we subsequently transform into Rusinkiewicz-parameterized pBRDFs that can be used for rendering. Our dataset provides 25 isotropic pBRDFs spanning a wide range of appearances: diffuse/specular, metallic/dielectric, rough/smooth, and different color albedos, captured in five wavelength ranges covering the visible spectrum. We demonstrate usage of our data-driven pBRDF model in a physically based renderer that accounts for polarized interreflection, and we investigate the relationship of polarization and material appearance, providing insights into the behavior of characteristic real-world pBRDFs.

ASSOC COMPUTING MACHINERY2020

Device for Determining a Bidirectional Reflectance Distribution Function of a Subject

Loïc Arnaud Baboulaz, Gaël Georges Soudan, Martin Vetterli

The present invention relates to a device (10) for determining a bidirectional reflectance distribution function of a subject (S) comprising: a light source (LS) for producing an incident light (li) and directing said incident light (li) onto a subject (S) at a predetermined zenith angle (θi) and at a predetermined azimuth angle (φi); means for displacing said light source (LS) at any location on the periphery of a hemispherical area centered on the subject (S); means (C) for measuring the bidirectional reflectance distribution function of the subject (S) from one fixed location, said fixed location being preferably aligned with a normal direction (Z) defined by the subject (S); a control unit adapted to control said displacing means and/or said measuring means; wherein said displacing means comprises: an arc-shaped arm (12) at one end of which is fixedly connected the light source (LS), said arc-shaped arm being slideably connected to a first support (14) through sliding means, thus permitting the adjustment of said zenith angle (θi); and means for pivoting said first support (14) about said normal direction (Z), thus permitting the adjustment of said azimuth angle (φi).

2016

An Adaptive Parameterization for Efficient Material Acquisition and Rendering

Wenzel Alban Jakob

One of the key ingredients of any physically based rendering system is a detailed specification characterizing the interaction of light and matter of all materials present in a scene, typically via the Bidirectional Reflectance Distribution Function (BRDF). Despite their utility, access to real-world BRDF datasets remains limited: this is because measurements involve scanning a four-dimensional domain at sufficient resolution, a tedious and often infeasibly time-consuming process. We propose a new parameterization that automatically adapts to the behavior of a material, warping the underlying 4D domain so that most of the volume maps to regions where the BRDF takes on non-negligible values, while irrelevant regions are strongly compressed. This adaptation only requires a brief 1D or 2D measurement of the material's retro-reflective properties. Our parameterization is unified in the sense that it combines several steps that previously required intermediate data conversions: the same mapping can simultaneously be used for BRDF acquisition, storage, and it supports efficient Monte Carlo sample generation. We observe that the above desiderata are satisfied by a core operation present in modern rendering systems, which maps uniform variates to direction samples that are proportional to an analytic BRDF. Based on this insight, we define our adaptive parameterization as an invertible, retro-reflectively driven mapping between the parametric and directional domains. We are able to create noise-free renderings of existing BRDF datasets after conversion into our representation with the added benefit that the warped data is significantly more compact, requiring 16KiB and 544KiB per spectral channel for isotropic and anisotropic specimens, respectively. Finally, we show how to modify an existing gonio-photometer to provide the needed retro-reflection measurements. Acquisition then proceeds within a 4D space that is warped by our parameterization. We demonstrate the efficacy of this scheme by acquiring the first set of spectral BRDFs of surfaces exhibiting arbitrary roughness, including anisotropy.

ASSOC COMPUTING MACHINERY2018

An Adaptive Parameterization for Efficient Material Acquisition and Rendering

Wenzel Alban Jakob

ASSOC COMPUTING MACHINERY2018

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ASSOC COMPUTING MACHINERY2020