Curvature as a Baseline: Monocular Pose Measurement of Cylindrical Objects with Dual Colour Stripe Markers

Thin cylindrical objects offer little space for planar markers. We propose a dual-colour-stripe marker that uses the known curvature of an object to improve pose measurement with a single camera. The boundary between two colours provides a long centre line, while dots and printed edges supply features at different depths. We analyse how this depth separation improves the estimation of rotation about the cylinder axis, or roll. For a camera-facing marker at 15 cm, the Cramér-Rao lower bound on roll standard deviation is 2.00°for a flat marker, 0.38°for a single curved marker and 0.21°for a wrap-around marker. Monte Carlo roll RMS errors are within about 10% of the corresponding standard-deviation bounds. A first-order relation connects the sagitta of the curved marker to the roll sensitivity provided by a stereo baseline. The analytical and simulation results explain how curvature improves monocular measurement and provide a basis for designing marker geometry.