Concept

camera track — where it appears

The path a moving camera took, recovered from the pictures it made along the way rather than measured while it moved. It is determined only up to a similarity, so a recovered track has a shape and no size until one length in the scene is supplied.

Named by 7 essays across one field — each of them below, with the objects they name alongside it.

view 1view 6the scene, in plan — recovered points and cameras over the true onesreprojection 0.332 px · track 2.0e-3264 observations, 168 parameters

The track and the scene together

Six photographs go in and one hundred and sixty-eight numbers come out — every camera's position and orientation and every point's place in space, solved for at once. Nothing in the solve was ever told where a camera or a point was.

manyviews · Bundle
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
0.0020.00334567number of viewsworst camera-centre error (fraction of the track's mean radius, log scale)7 flat7 flat7 flat7 flat7 flat60° sweep, filled in12° per view, wideningfilled in: 1.1e-3 → 2.0e-3widened: 3.2e-3 → 1.8e-3

Another picture of the same sweep

Going from three views to seven across the same sixty degrees leaves the reconstruction exactly where it started, and at one point makes it worse. What a reconstruction is short of is angular spread, not photographs.

manyviews · Spread
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
89°in plan · the mark's size is the angle at the pointthe track covers 60°

The spread a point gets

A track of sixty degrees gives no point of the scene sixty degrees. The nearest receive 89 and the furthest 41, a factor of 2.2, and their errors run from 1.5 to 8.4 millimetres — following the angle at the point as its −1.68 power, with 94 per cent of the variation explained. The arc a track covers is one number for forty-four different situations and predicts none of them.

manyviews · Spread
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
in plan · ellipses 25× actual sizewithin 8.4° of the mean sight

Split the track and the needles turn

A point triangulated from a track of cameras is not known equally well in every direction: its error is a needle, long along the direction its lines of sight barely constrain. That direction is not the mean line of sight but the lines of sight weighted by how near each camera is — and it can be turned. Two groups of cameras more than a right angle apart swing every needle across, and the same six pictures of a facade then measure its depth four times better.

manyviews · Spread

Named alongside it

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

bundle adjustmentCovariancegauge freedomBaselineConditioningDriftTriangulationDepth uncertaintyLoop closurestructure from motionSubtended angleControl point

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