A pinhole twin of a radially distorted camera mis-ranges the near field: how far off does a twin-trained braking policy stop, and does focal calibration fix it?

What it found

With Brown distortion x_d=x(1+k₁r²) and a camera at height h, the pinhole twin reads floor range off by exactly 1/(1+k₁h²/R²): for k₁=−0.3, h=0.5 m that is +15.4% at 0.75 m, +8.1% at 1 m and +0.5% at 4 m. A policy trained to stop at 1.0 m stops at 0.909 m (16.4 cm short at 0.75 m; the first-order formula understates this at large ρ). Least-squares focal calibration (s=1+3k₁ρ_max²/5) moves the error rather than removing it: near-field 8.1% → 3.2% but a new 4.4% far-field under-read, and a 4 m stop lands 17 cm long. One image of a known grid identifies k₁ (RMS 0.001 at 0.002 normalised-pixel noise). Stylised: one distortion term, axis-column floor points, known grid pose, no real lens.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

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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.