An instantaneous-exposure twin of a finite-exposure camera certifies detection at every speed: what is the real speed limit, and what does a blur-matched filter buy back?

research/blur-twin

An instantaneous-exposure twin of a finite-exposure camera certifies detection at every speed; a moving bar is an exact trapezoid (peak C·min(1, w/d)), a twin-tuned peak detector has a hard speed limit wC/(σz), and a blur-matched box filter raises it quadratically (5–55×).

9 tests

What it found

A bar of width w moving d = vT px during the exposure is imaged as an exact trapezoid (peak C·min(1, w/d), energy Cw conserved), matching a 2000-sub-exposure simulation to its quantisation. A single-pixel peak detector that the twin certifies at Pd = 1 everywhere loses power as soon as d > w (at w = 6, C/σ = 10: Pd 1.00 → 0.28 at d = 24), with speed limit d* = wC/(σz) (13.7 px). A box filter of length d collects all of Cw at noise cost √d, output Cw/(σ√d)·(1−w/4d), so the limit grows quadratically in SNR: 5–55× faster over 12 settings, but it needs the speed, and a filter tuned on the twin (length w) still drops to Pd 0.26 at d = 60. Stylised: 1-D, known location, constant velocity, white Gaussian noise, no real footage.

A figure from its own output

Figure produced by research/blur-twin: detection — blur-twin/experiments/detection.svg, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.