Describe the BRDF, its advantage over Lambertian, and critical CV tasks

What's really being asked

This question probes whether you understand that light-surface interaction is fundamentally a directional phenomenon rather than a point property. Interviewers want to see that you know reflectance is a function, not a constant, and that you can articulate the mathematical and practical consequences of using a physically accurate model versus a convenient approximation. At the senior level, they are also checking if you can connect this physical foundation to downstream vision algorithms and their failure modes.

The full answer

A good answer hits four things in order. First, define the BRDF as the ratio of reflected radiance exiting along a direction to the irradiance arriving from an incident direction, which gives it units of inverse steradians. Second, explain that it is a function of four real variables, typically parameterized by the azimuth and zenith angles of both the incoming and outgoing light directions. Third, contrast this with the Lambertian model, which assumes the surface looks equally bright from all viewing angles and is therefore the special isotropic case where the BRDF collapses to a constant albedo divided by pi. Fourth, name computer vision tasks where the Lambertian assumption breaks down, such as photometric stereo and shape-from-shading, because specular highlights, interreflections, or grazing angles make the observed intensity depend on viewer position.

The mistakes people make

The most common red flag is treating the BRDF as a texture map, RGB albedo, or scalar value rather than a directional distribution. Another weak pattern is saying Lambertian is wrong without explaining that it is actually a valid special case of the BRDF. Some candidates also confuse radiance and irradiance or omit the sr^-1 units, which signals a shaky grasp of the physical quantities involved.

What usually comes next

An interviewer might push you to name a specific BRDF model beyond Lambertian, such as the Phong, Blinn-Phong, Cook-Torrance, or Oren-Nayar models. They could ask how you would acquire or estimate a BRDF from images, how the BRDF complicates inverse rendering, or why the rendering equation integrates over the hemisphere of incoming directions. You might also be asked to explain Helmholtz reciprocity, which states that swapping incoming and outgoing directions leaves the BRDF unchanged.

A concrete example

Consider photometric stereo with three point lights. Under a Lambertian assumption, the brightness variation across images depends only on the surface normal and light direction, so three equations suffice to solve for the normal. If the surface is glossy, the same pixel appears brighter when the camera happens to lie near the perfect reflection direction of one light. A Lambertian solver would misinterpret that extra brightness as a tilted normal, producing a dent or bump that does not exist. Only by accounting for a view-dependent BRDF can the reconstruction remain accurate.