A Theory of
Joint Light and Heat Transport
for Lambertian Scenes

Theory: Light to Heat Transport

Visible cameras capture scattered light to form images.
What happened to the absorbed light?

When light gets absorbed, it becomes heat. This heat is then exchanged with the environment via radiation and convection, and through the object via conduction. Unlike light, heat is independent of wavelength as it is exchanged via molecular vibrations. We can observe heat at a point by capturing its thermal radiation, which is simply light at Long-Wave Infrared (LWIR, \(8-14\mu \textrm{m} )\) that depends only on the surface temperature and emissivity. Tracing back through the heat transport, we can estimate the absorbed light at that point.

We can analytically estimate absorbed light per-pixel from short thermal transients.

Application: Intrinsic Image Decomposition

Single image intrinsic image decomposition is an ill-posed problem.
Can absorbed light help?

In the general case, a scene point can be illuminated by multiple light sources, and the light can be scattered multiple times before reaching the camera. This makes the problem of intrinsic image decomposition ill-posed. But all the complexities of light transport are also present in absorbed light!

For Lambertian scenes, knowing absorbed light makes
single view intrinsic image decomposition a well-posed problem
for arbitrary shapes and lighting!

We simply apply energy conservation at each pixel independently. We have generalized the results to wavelength dependent albedo and camera response in the paper. Our method can be extended to non-Lambertian scenes if we can compute total scattered light at each pixel from a single visible image.