Concept

bundle adjustment — where it appears

5 essays name this object, across one field. What follows is each of them, and 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
× 4.6e+6seven flatand the rest stiffsingular value ÷ the largest, log scale, smallest firstσ₈/σ₇ = 4.6e+6168 parameters · 528 residuals

Seven numbers no picture can name

Shift a whole reconstruction by a metre and a half, turn it half a radian, scale it by 2.7, and every photograph of it stays where it was to a hundredth of a billionth of a pixel. Move one point by fifty millimetres and they move by two thirds of a pixel.

manyviews · gauge
-3-2.50-2-0.600-0.400-0.20000.200how 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
-10-50012345iterationreprojection error (px, log scale)exact marksread to 1 px4.67 px → 0.3324 px in 5 iterationsexact marks reach 1.3e-11 px

Where the adjustment stops

Given exact marks the reprojection error falls to a hundredth of a billionth of a pixel, which is arithmetic. Given the same marks read to a whole pixel it falls to a third of a pixel and stays there, and a solver that reached zero on those would be fitting the rounding.

manyviews · bundle
-2.80-2.6034567number 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

Named alongside it

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

camera trackgauge freedomBaselineJacobianReprojection errorSimilaritystructure from motionConditioningConvergenceCorrespondenceDriftLevenberg–Marquardt

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