BRDF

An Intro to Bidirectional Reflectance Distribution Function

Objects appear different when viewed from different angles and illuminated from different directions because of how light interacts with the object’s surface. The surface of an object reflects and absorbs light in different ways depending on its texture, color, and shape. When an object is illuminated, light waves bounce off its surface and are scattered in different directions. How the light is scattered depends on the angle of incidence of the light and the object’s surface properties.

Reflection happens when a beam of light hits a nontransparent surface and gets redirected. The magnitude and direction of that redirected beam of light depend on the surface material and the surface irregularities. Depending on the surface material some colors of the light can get absorbed and other colors reflected. If the surface is smooth, then we have “specular reflection” for the reflected colors of light. That is when almost all of the light is reflected in a single direction, like the type of reflection from surfaces like mirror, water, metallic surface. If the surface is not smooth “diffuse reflection” happens. That is when the light gets scattered in all directions. It can get reflected more in one direction and less reflected in another direction. A perfect diffuse surface is called a “Lambertian surface” which scatters the light equally in every directions ( in computer graphics we call this “isotropic”).

Bidirectional Reflectance Distribution Function (BRDF) represents spectrally-resolved reflectance of a surface as a function of (A) illumination angle and (B) observation angle. The surface has structural properties and optical properties such as transmission, reflection, absorption, emission, shadow-casting, multiple scattering, mutual shadowing.

BRDF is a mathematical function that describes how light reflects off a surface in different directions. It is typically denoted as f(θi, θr, ϕi, ϕr), where:

• θi is the angle between the incident light and the surface
• θr is the angle between the reflected light and the surface
• ϕi is the angle between the incident light and a reference plane
• ϕr is the angle between the reflected light and the same reference plane

Geometrical view of parameters defining a BRDF expression

It is a ratio of the reflected radiance (i.e., the amount of light reflected per unit area per unit solid angle) to the incident radiance (i.e., the amount of light arriving at the surface per unit area per unit solid angle) for a given pair of the incident and reflected directions.

The BRDF function can be different for different materials and surfaces and depend on other factors such as polarization and wavelength of the incident light. It is an essential tool for computer graphics and computer vision applications, where it is used to model and simulate the appearance of different materials under various lighting conditions.

These photographs view the same surfaces from different angles. And different looks of the same surface is because of the BRDF concept we explained above. Because these surfaces are not specular or Lambertian, changes in illumination or view angles make a big difference how a camera or eyes observe these surfaces. They look so different! (Photograph Credit: Don Deering)

When we view an object, our eyes receive the scattered light waves, which are then processed by our brain to create an image. When we change our viewing angle or the direction of illumination, the way the light interacts with the object’s surface changes, which results in a different pattern of light waves being scattered and reaching our eyes. This results in a distinct visual appearance of the object. For example, as we see in the images above textured objects or surfaces may appear to have different patterns of shadows and highlights when viewed from different angles, creating an additional visual experience for the viewer.