Concept

reconstruction ambiguity — where it appears

4 essays name this object, across 3 fields. What follows is each of them, and the objects they name alongside it.
× 4.6e+6seven flatand the rest stiffsingular value ÷ the largest, log scale, smallest firstσ₈/σ₇ = 4.6e+6168 parameters · 528 residuals

Seven numbers no picture can name

Shift a whole reconstruction by a metre and a half, turn it half a radian, scale it by 2.7, and every photograph of it stays where it was to a hundredth of a billionth of a pixel. Move one point by fifty millimetres and they move by two thirds of a pixel.

manyviews · gauge
points in front of both camerasR₁, t0 of 44180° from the truthR₁, t reversed0 of 44180° from the truthR₂, t44 of 44chosenR₂, t reversed0 of 44180° from the truththe chosen pose is the true one to 0.0e+0°cheirality, not algebra, picks it

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.

twoviews · cheirality
-10-50-2-10baseline (m, log scale)worst deviation in the recovered shape (log scale)exact pointsread to 1 pxat 2 mm: 4.7e-9 exact, 2.9e+1 read to 1 px6e+9× apart

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.

depth · baseline
as recovered0.308 across× 3.4 — same two pictures1.046 acrossworst ratio deviation 6.3e-14size fixed only by a supplied 0.80 m

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.

twoviews · scale

Named alongside it

The objects these essays reach for when they reach for this one.

BaselineCorrespondenceRelative poseSimilaritybundle adjustmentCamera matrixCheiralityConditioningDegeneracyEntrance pupilEpipoleEssential matrix

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