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

Drift — where it appears

The slow accumulation of small errors along a chain, where each step is measured from the last rather than from a fixed reference. It grows as the square root of the number of steps when the steps are independent, which is what separates a chain from a closed loop, and a copied drawing from a redrawn one.

Named by 9 essays across 2 fields — each of them below, with the objects they name alongside it.

0.30.50.7125×10⁻⁴0.0010.0020.0050.010.02how finely each point is read (px, log scale)worst camera-centre error, as a fraction of the track's mean radius (log)chained pairsadjusted togetheradjustment is 4.0–9.2× better6 views · identical observations

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.

manyviews · Drift -200204060050100150link along the streetscale error relative to the first link (%)average 28.6 %16 streets · ties by mean of ratios · marks read to 1 pxspread after 199 links ±7.3 %

A scale chain leans rather than wanders

A camera driven 200 m along a street, each pair's scale handed to the next through the points they share. Across sixteen streets the scale does not spread the way a random walk would — 7.3 per cent after 199 links, where independent ties would give 108 — and its average leans by an amount the choice of average decides, from +28.6 per cent to −12.2.

manyviews · Drift 02004005101520camera round the loopcamera-centre standard deviation from the start (mm)left openclosedlast camera ×6.5 better · worst 20 % better24 cameras · marks read to 1 px

Closing a loop mends its ends

Twenty-four cameras walked once round a ring of walls, every mark read to a pixel. Recognising the twenty-two points seen at both ends makes the last camera six and a half times better placed relative to the first — and the worst camera, across the ring, only a fifth better. A closure mends the ends of a walk and barely touches its far side.

manyviews · Drift start, heldworst: 86 along, 64 acrossellipses ×12 · worst camera 112 mmloop closed

A loop's far side is a length

The worst camera on a closed loop of twenty-four is 411 mm from certain along the line from the start and 64 mm across it. A picture taken across the ring from the start tripod measures directions and moves the worst camera from 418 mm to 405. One distance measured across the ring to 10 mm moves it to 74, and a four-metre length measured on the start wall to 112. What the far side of a loop lacks is not a connection but a length.

manyviews · Drift 0.6000.7000.800010203040generations of copyingthe drawing's depth-spacing ratiocopying the methodcopying the marksone hand error, two kinds of copyist9 lineages

What survives being copied

A workshop copying a drawing from a drawing is a random walk — the spread across lineages grows as the square root of the generation, with a fitted exponent of 0.5001. A workshop copying the method is not, and its exponent is 0.012, which is no growth at all, and after forty generations two lineages started from different originals end up 5 × 10⁻¹⁵ apart. Copying the marks loses the picture; copying the recipe loses the original and keeps the recipe.

conventions · Transmission 0.6000.7000.8000255075100generations of copyingthe pavement's depth-spacing ratiothe workshop's taste7% of proposals rejectedband ±0.04

The workshop that throws drawings away

Adding a rule that discards a drawing which looks wrong turns the mark copyist's spread from a growing random walk into a stationary process — the fitted exponent falls from 0.542 to 0.022, indistinguishable from the method copyist's 0.033 — and the two mechanisms then separate only by where they settle, 0.7002 against 0.8000, seven and a half spreads apart.

conventions · Transmission 0.050.10.250.51240200400length of the scale bar at the start (m, log scale)worst camera, along the line from the start (mm)open walkloop closedopen, no barclosed, no bara scale bar at the start, measured to 0.1 mmopen: flat from 0.5 m

A scale bar is worth its ends, not its tape

A length measured at the start of a walk round a ring pins the walk's scale — but only to the precision with which the pictures place the length's two ends, 3.4 mm here, whatever the tape says. Measured to a thirtieth of a millimetre or to three millimetres, a one-metre bar leaves the worst camera at the same 89 mm. So a short length is not a long one measured well: a bar under about 13 cm tells the walk less about its scale than the walk already knows. And on an open walk no length at the start does better than 214 mm, because what is left there is drift, not scale.

manyviews · Drift 01002003004000123gap between two 25 cm bars stood on one wall (m)worst camera, along the line from the start (mm)two short barsone bar over the spanno barone short bartwo 25 cm bars on end, measured to 0.1 mm, gap unmeasuredloop closed

Two short bars are not one long one

A long scale bar is awkward to carry, so the natural substitute is two short ones set far apart on the same wall. It does not work. Two 25 cm bars 3.5 metres apart leave the worst camera of a closed walk at 219 mm; one bar over the same span leaves it at 72. The gap between the bars is read by the pictures like any other distance, so it carries no scale — and the same holds for a long length measured as separate pieces. What does work is a tape read at every mark: pieces that share their ends add up to the whole, and pieces that do not, do not.

manyviews · Drift 02004002610141822the wall the 1 m bar is laid on, by the camera that faces itworst camera, along the line from the start (mm)open walk, one barloop closed, one baropen, no barclosed, no bara 1 m bar measured to 0.1 mm, moved round the ringflat: the bar fixes one scale

A length fixes the scale where it lies, and the worst camera nowhere

Move one measured metre round a ring of twenty-four cameras and the worst camera hardly notices: 199 to 225 millimetres on the open walk, 80 to 103 on the closed loop, wherever the bar lies. What moves is the scale. On the open walk a length is known to 0.41 per cent beside the bar and 1.58 per cent twenty walls away, and no longer bar at the start brings the far end below 1.53. A survey that must measure lengths everywhere on an open walk needs its references spread along it; one that closes its loop can put a single reference anywhere.

manyviews · Drift

Named alongside it

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

bundle adjustmentCovariancegauge freedomLoop closurescale ambiguityControl pointrandom walkBiascamera trackReference lengthAttributionConstant-ratio

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