Same Measurements, Different Velocity Risk: Complementary Rolling-Shutter Readouts under Clock Uncertainty

Lunshuo Tian, Dongheng Liu, Mingwei Ma

Camera rigs with identical measurement budgets can have different velocity estimation rates when exposure timing is uncertain. We establish this distinction for rolling-shutter reconstruction with two calibrated moving anchors, unknown scene points, and independently unknown auxiliary poses and clocks. On the same fixed local physical class near a separated lateral rig, repeated readouts have worst-case squared velocity risk at least of order $σρ_{\mathrm{eff}}$, whereas complementary readouts have minimax risk of order $σ^2$, for a fixed admissible clock displacement $ρ_{\mathrm{eff}}>0$ as the noise standard deviation $σ$ tends to zero. A finite physical compensation path gives the lower bound; a nonlinear velocity inverse proves complementary stability. All motion, structure, pose, and clock nuisances remain unknown. We identify mounting configurations in which both designs become regular and quantify the risk floor induced by metric uncertainty. We quantify full-parameter domains with independent 6-ms clocks and test in-domain reconstruction under paired noise and a depth-offset intervention. Raster studies examine image formation and calibration sensitivity.