Surface illuminance flow

We introduce the concept of "surface illuminance flow" in two steps. First we reiterate the notion of the "light vector", and then proceed to decompose the light vector into a scalar "normal illuminance" and a vector "surface illuminance flow". The scalar normal illuminance generates the familiar illuminance pattern that is often known as the "shading". The vector surface illuminance flow is irrelevant for smooth surfaces (which probably explains why it is conventionally ignored) but it generates the texture due to surface mesorelief. We show how observation of the illuminance induced texture leads to robust inferences of the surface illuminance flow direction modulo 180°. This makes surface illuminance flow a property that is observable in natural scenes. Much like optical flow, the surface illuminance flow is largely due to a global property that exists independent of local structure, namely the direction of the general illuminating beam (sunlight or light from the overcast sky in a typical outdoors scene). However, due to the fact that there exists "true screening" in radiometry (thus removing any hope for a "field theory" of radiometry) the local scene structure has an influence on the local light field. Such "vignetting" is a main cause of the complexity of radiometry, the other cause being the ever present multiple scatterings. This complicates matters but also introduces additional sources of information. We illustrate instances of the observation of illuminance flow in scenes. We also present a database of roughly spherical objects, illuminated in a number of standard ways that we have used to study illuminance flow over actual rough objects.