Visual Plane
every picture states the point it is correct from
Concept

scale ambiguity — where it appears

2 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
a room 2.8 m across, eye 1.6 m up1 mthe same plan, 137× bigger137 midenticalpicturesthe picture — both scenes, drawn twice, one on top of the otherlargest disagreement 1e-13 px over 8 verticesone length has to come from outside the picture

The one thing a single view cannot give

Make the world a hundred and thirty-seven times larger and move the eye a hundred and thirty-seven times further away, and the picture does not change by a measurable amount. Every ratio in a scene is recoverable from one photograph and no size is, and that is not a caveat about the method — it is the shape of the method.

metrology · scale 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.

Reference lengthSimilarityBaselineCorrespondenceDemonstrationFocal lengthProjective invariantreconstruction ambiguityRelative posesingle-view metrologyTriangulation

All concepts