If the lens has a second radial term the solver does not model, does self-calibrating bundle adjustment still recover the surface?

research/sensing-bak2

Rendering with k1 = −0.2 and k2 swept from −0.2 to +0.4, a bundle adjustment solving for the focal and k1 only returns 0.0015 object radii, the same as one that also solves k2, against 0.0022–0.0030 with no distortion model; the lens parameters are not separately identified (k1 stays near −0.16, k2 sits about 0.16 low) and the gain vanishes by 2 px noise. Synthetic only

5 tests

What it found

Follows sensing-bafocal, whose fitted radial law was the rendering law, and takes its “model mismatch” next step. Images are rendered on the sensing-ba rig (12 views, 0.5 px noise, every pose wrong) with x_d = x(1 + k₁r² + k₂r⁴). With k₁ = −0.2 and k₂ from −0.2 to +0.4, an adjustment with no distortion model costs 0.0024–0.0030 (focal free) and 0.0022–0.0027 (focal held), while fitting the focal and k₁ alone gives 0.0015 in every case, equal to fitting k₂ as well. The parameters are not recovered separately: the k₁ estimate is −0.158 whatever the true k₂ and the k₂ estimate moves with the truth but sits about 0.16 below it, and the focal ends 1.1% off; surface error is insensitive to this. The benefit disappears by 2 px of noise (0.0061 for all three), and at 6 views the focal is 4% off. Limits: synthetic, the lens-parameter ranges are swept, not measured from a device; one object; correct matches; 6 seeds per cell; what the one-term model gets right is the surface, not the lens parameters.

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.