Can a lidar twin give each beam an independent visibility probability, or do neighbouring beams share occluders?

What it found

For a Poisson field of occluders of radius ρ, beams a distance s apart are both clear with probability exp(−μ(2ρ+min(s,2ρ))), which equals p² exactly when s ≥ 2ρ; any set of beams has the closed form exp(−μ·union length). An independent-beam twin therefore matches the mean number of clear beams but understates the variance and the blind probability: with 8 beams at 25 cm and single-beam visibility 0.5 (occluder diameter 1 m) the exact blind probability is 0.0815 against the twin’s 0.0039 (20.9×, 97× at 5 cm), and reaching a blind probability of 0.01 needs 16 beams instead of 7 (not reachable with 16 at 10 cm). The twin is exact once the spacing exceeds the occluder diameter, and an ensemble twin that samples occluder fields reproduces the exact value (0.0815 vs 0.0815 ± 0.0006). Stylised: one-dimensional lateral projection, binary opaque occluders, no lidar data.

A figure from its own output

Paper, code and results

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

More in Digital twins & sim-to-real

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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.