Baseline — where it appears
The image of the other eye
Two photographs of one courtyard, and in each of them a point that is the other camera. It is computed from forty-four matched marks and nothing else, and it lands on the projection of the other eye to about a billionth of a pixel.
Depth is a reciprocal
Two eyes measure a shift in the picture, and depth is that shift divided into a constant. So a fixed error in what is read maps to an interval in what is reported that is not centred on the answer, and at forty metres runs sixteen metres nearer and eighty-six further.
The range a pair cannot see past
A stereo rig has a distance beyond which it cannot say "no further than", and the distance is fixed before anything is built. It is the focal length times the baseline divided by the reading precision, and for a human pair of eyes it is fifty-eight and a half metres.
Eight points and the basis they are read in
The linear system that recovers a fundamental matrix is written in whatever coordinates the marks were read in, and pixel coordinates are a bad choice. Centring and scaling them first is worth nothing at a quarter-pixel reading and a factor of thirty at four.
Two rays that do not meet
Triangulation is described everywhere as the intersection of two rays, and two rays in space do not intersect. Read the same two marks to a whole pixel and they miss by 2.77 mm at seven metres, which is a real length and is the part a residual will not report.
A chain and an adjustment
Composing pairwise poses along a sequence is supposed to drift. Measured over five links it wanders instead — one chain ends closer to the truth than its own worst link — and the real cost of chaining turns out to be something else entirely.
Four cameras fit, and one of them can see
The essential matrix does not determine a camera pair. It determines four, all of which reproject every correspondence exactly, and the thing that picks one is not more algebra — it is the assumption that the photographer could see what was photographed.
A turn of the head is not a step sideways
The textbook says a short baseline makes reconstruction ill-conditioned. Measured, the algebra does not notice — a two-millimetre baseline recovers the courtyard to nine digits from exact marks. What fails is the ratio of baseline to reading error, and it fails without refusing.
A wrong match is not a small error
Move one correspondence of forty-four by thirty pixels and the recovered geometry is wrong for every other point — the typical one by half a pixel, from a fit that was exact to a part in ten trillion. Least squares has nowhere to put a bad row except across all of them.
Another picture of the same sweep
Going from three views to seven across the same sixty degrees leaves the reconstruction exactly where it started, and at one point makes it worse. What a reconstruction is short of is angular spread, not photographs.
Two views give shape and no size
Every pairwise distance ratio in a courtyard recovered from two photographs matches the real one to fourteen digits. The courtyard's actual size is not merely uncertain — it is absent, and a reconstruction three and a half times larger fits the same two pictures exactly as well.
Named alongside it
The objects these essays reach for when they reach for this one.
CorrespondenceFundamental matrixConditioningFocal lengthreconstruction ambiguityRelative poseResidualTriangulationbundle adjustmentCamera matrixcamera trackDepth uncertainty