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[SQUEAKING] [RUSTLING] [CLICKING] BERTHOLD HORN: Let's have a quick review of what we learned about photometry. So there are a number of concepts, one of which was irradiance. And we use the symbol E for it. And it was power per unit area. And it's a way of talking about light falling on a surface. And it's what we measure in the image plane and convert to what's commonly called a gray level. So the quantity of interest here is directly used when we're imaging. But it's also, of course, a measure of light falling on the objects that we're imaging. Then we talked about intensity, which applies to a point source. And it describes the power per unit solid angle. And so we had to define the solid angle. And it's the quantity that typically varies with the direction. So if you have a good old incandescent light bulb, it's very low intensity in the direction of the base, because that's blocked by the base and some higher intensity in othe...

[SQUEAKING] [RUSTLING] [CLICKING] BERTHOLD HORN: We're starting to talk about what determines brightness in an image and how we can exploit that. And we introduced the idea of a gradient space. Why? Well, because brightness is going to depend on the illumination, obviously, and it's going to depend on the geometry of the situation, including surface orientation. Obviously, the amount of light falling on the surface will, per unit area, will depend on its orientation. And then different types of surfaces will reflect that light in different ways. In any case, we expect that the brightness we observe in an image is going to depend on the surface orientation of the corresponding patch on an object. And so we need to talk about the orientation of the patch. And we had unit normals, and then we had p and q, but these are just convenient shorthands for those slopes in the image, slopes on the surface. So those are derivatives of height rather than derivatives of brightn...