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

error propagation — where it appears

3 essays name this object, across 3 fields. What follows is each of them, and the objects they name alongside it.
025507510010203040true depth (m)depth reported from the disparity, with a 1 px reading error5.86–7.33 m13.96–26.69 m23.76–126.49 mat 40 m: +86.5 m against −16.2 munbounded past 58.5 m

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.

depth · disparity 00.50011.502-0.400-0.20000.200k₁departure of the cross-ratio from the world's value (%)pinhole1.29%the pinhole's own error, on the same four points2e-16 — the control

A lens destroys the invariant

The cross-ratio is the one thing a projection preserves, and everything checkable on this site is checked with it. A lens returns it one and a third per cent out where the pinhole is exact to fifteen digits — and the height error that follows tracks a quantity nobody would guess.

lens · distortion 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.

Cross ratioFocal lengthHorizonSensitivitysingle-view metrologyVanishing pointBaselineConditioningDepth uncertaintyDisparityPrincipal pointProjective invariant

All concepts