Open course ware

PROFESSOR: All right. The end of this lecture generated so much excitement that we've continued on into the start of the next segment. So I think we'd better begin. What I told you, as several people were clever enough to observe, that the number of planes between the origin and intercept plane is equal to A times B times C, where the intercept is A T1 out plus B T2 out equals C T3 out. That is true only if the numbers A, B, and C are mutually prime. If it's something like 4, 2, 1, you won't get that number of planes. You'll get a submultiple. And the reason for that is that some of the planes, when you generate them by these three different translations in different directions, some of them are mapped on top of existing planes. And I'm not going to attempt to prove this, but let me just tell you the result, that if A and B contain some common factor, p, and B and C contain some common factor, q, and in the worst possible case, A and C contains som...

[SQUEAKING] [RUSTLING] [CLICKING] PROFESSOR: End of the photogrammetry section. We'll just briefly talk about exterior orientation, which is the fourth of the photogrammetric subjects we are talking about. So what's this about? This is best illustrated by thinking about a drone flying above some terrain of which we have a detailed model. So we know where points are in some global coordinate system. And we have a camera perspective projection. We get images of those three points. And the question is, where are we? So p1, p2, p3 are known. Let's assume that the center of projection is p0. That's what we want to find. And we also would like to find the attitude of a plane in the world. So it's the same old thing, rotation plus translation, except in this case, we have a mix of 2D and 3D information. The coordinates of the points in the world are given in 3D. So we have a terrain model. The points corresponding in the image are in 2D. So let's see. One...