Does a wide field of view make the second radial lens term identifiable in self-calibrating bundle adjustment?

research/sensing-bak2wide

Moving the camera in and shortening the focal length (800 to 400 px) raises the largest normalised radius from 0.34 to 0.85, and the spread of the fitted k2 over seeds falls from 0.33 to 0.02 with its mean within 0.01 of truth; the surface then needs k2 (0.0027 with k1 only against 0.0020 with both). Synthetic only

4 tests

What it found

Takes the next step of sensing-bak2, where k₂ was invisible on a narrow field of view. The camera is moved in (distance 4 to 2) and the focal length shortened with it (800 to 400 px) so the object keeps its pixel size, which raises the largest normalised radius of a visible point from 0.34 to 0.85. The standard deviation of the fitted k₂ over 6 seeds falls from 0.33 to 0.02 and its mean is within 0.01 of the true +0.1 from distance 2.5 on; k₁ is recovered to −0.195 against a true −0.2. The surface now needs the second term: at distance 2 a k₁-only adjustment costs 0.0027 object radii against 0.0020 with k₂ (0.0055 against 0.0022 at k₂ = −0.2), and ignoring distortion costs 0.0082–0.0118. At 2 px of noise the two fits meet at 0.0081–0.0083. Limits: synthetic, lens values swept not measured, one object, the closer camera adds perspective so field of view and range are not separated, no decentring or principal-point error, correct matches, 6 seeds.

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.