Two-View Geometry
What a second camera adds, what it cannot add, and how well it adds it.
One view constrains a point to a ray. A second view constrains it to another ray, and two rays meet — in principle. This topic is about the three things that complicate that sentence: the constraint holds before you know the point (the epipolar constraint), the recovered geometry has an irreducible scale ambiguity, and with noise the rays do not actually meet.
Each of those is a place where practitioners have a working recipe and a shaky picture. The figures here are built to repair the picture.
- 01 The epipolar constraint Core 1 interactive 11′ A point in one image restricts its match in the other to a line — before anything is known about depth. Repairs Memorising $x'^\top F x = 0$ without a picture of where the line comes from or why the epipole is special.
- 02 Triangulation and its uncertainty Core 1 interactive 10′ Two rays never meet. Where you say the point is, and how sure you are, both depend on the baseline. Repairs Thinking of triangulation as an intersection, and of depth error as a fixed percentage rather than as a quantity growing with the square of distance.
- 03 Recovering pose, and the scale you cannot recover Advanced 10′ Eight points give you the essential matrix; decomposing it gives four poses and no metres. Repairs Expecting a two-view reconstruction to be metric, and being surprised when the trajectory is "right but the wrong size".