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

vertical vanishing point — where it appears

3 essays name this object, across 2 fields. What follows is each of them, and the objects they name alongside it.
horizon — the eye's own heightbase — 0 mhorizon crossing — 1.62 mtop — 3.40 m recoveredthe vertical vanishing point is 8586 px above this framerecovered 3.400 m · true 3.400 m1.8 cm per pixel of click error

A height, out of one photograph

Four points on a vertical, one cross-ratio, and the height of something nobody measured. The only metric input is the photographer's own eye height, because the horizon is at eye level and that is the one piece of perspective folklore that is exactly true.

metrology · height level — the top is cut off0.00° of spreadtilted 13°4.55° of spreadshifted 95 px0.00° of spreada shift moves every point by exactly the shift95.0 px, and no direction at all

The principal point is not the centre

Every textbook that computes a focal length from two vanishing points supplies the middle of the frame as the principal point. On a shifted or cropped picture that is wrong, and it costs one and a half per cent of the answer at a fifth of a frame's shift.

lens · shift 05101550100150200distance from the camera (metres)error in the recovered height, per pixel of click error (%)6 m — 0.55%25 m — 2.27%60 m — 5.43%120 m — 10.84%one pixel, on a 690 px picturelinear in distance

How wrong a measurement from one picture can be

The formula divides by a difference of two nearly equal numbers when the object is tall, which looked like the instability and is not. Measured, a taller object is recovered better and a more distant one worse — half a per cent per pixel at six metres and eleven per cent at a hundred and twenty. The argument that was wrong is as much the finding as the curve that replaced it.

metrology · height

Named alongside it

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

Vanishing pointCross ratioHorizonPicture planesingle-view metrologyConditioningerror propagationFocal lengthPhotogrammetrypoint at infinityPrincipal pointSensitivity

All concepts