A Theory of Joint Light and Heat Transport for Lambertian Scenes

We present a novel theory that establishes the relation-ship between light transport in visible and thermal infrared, and heat transport in solids. We show that heat generated due to light absorption can be estimated by modeling heat transport using a thermal camera. For situations where heat conduction is negligible, we analytically solve the heat transport equation to derive a simple expression relating the change in thermal image intensity to the absorbed light intensity and heat capacity of the material. Next, we prove that intrinsic image decomposition for Lambertian scenes becomes a well-posed problem if one has access to the ab-sorbed light. Our theory generalizes to arbitrary shapes and unstructured illumination. Our theory is based on ap-plying energy conservation principle at each pixel indepen-dently. We validate our theory using real-world experi-ments on diffuse objects made of different materials that ex-hibit both direct and global components (inter-reflections) of light transport under unknown complex lighting.