Concept

Overfitting — where it appears

Letting a model absorb noise by having more freedom than the data supports, so the residual falls and the answer worsens. The tell is that the residual improves while a quantity computed from the fit gets worse, which is why a fit is judged on something it was not fitted to.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

-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
a centretrue measurediminutionbounded depthstraight linesperspectivehandscrollisometricdimetrictrimetriccavaliercabinetelevationmilitaryfilled means the system keeps itmeasured from each system's own projectionno row is filled in both of the first two

Each system answers its own question

A comparison in which every system wins its own column proves nothing if the columns were chosen after the systems. The test that makes it a result is whether any system wins something it was not designed for — and two of them do.

choices · Exclusion
horizoncorrect from 19 cm, at 160 mm wide2 centres · 2.12 px

How many lamps a drawing has

The shadow field recovers a lamp by intersecting drawn lines. Two lamps make that a partition rather than an intersection — and two centres fit any bundle better than one, on a one-lamp drawing as readily as on a two-lamp one, so a count is a decision that needs a noise level before it exists. A criterion built on a penalty instead of a noise level returns four.

light · Twolamps
how clearly each line belongs to one pencil2 lamps, 5 posts251.5 px100% assigned right3 lamps, 5 posts12.1 px73% assigned right4 lamps, 5 posts38.6 px40% assigned right0.5 px of clicking, lamps spread over 2 mthe counting of unknowns cannot see this

The drawing does not run out of lines

Every post supplies a line to every lamp, so a drawing of five posts offers ten lines to two lamps and twenty to four — the unknowns and the constraints grow together and two posts fix any number of lights. What runs out is the partition, whose margin falls from 251 pixels to six as the share of lines assigned correctly falls from all to just over half.

light · Lightrecovery

Named alongside it

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

ResidualConditioningCorrespondenceIdentifiabilityleast-squares intersectionLight recoveryPencilPoint lightAxis scalebundle adjustmentConformalConvergence

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