Baseline direction measurement for active optical imaging systems

We propose a closed-form method for measuring the baseline direction in active optical imaging systems, including projector-camera and laser-emitter imaging configurations. The method uses two planar homographies induced by observing a planar target at different system-to-plane distances, enabling analytic estimation without iterative optimization, emitter intrinsics, or prior knowledge of the plane normal. Specifically, we show that the scaled homography difference admits a rank-one factorization whose column space gives the baseline direction, and we recover the direction by selecting the scale that best satisfies the rank-one condition. Simulations demonstrate strong numerical stability: under sub-pixel Gaussian noise ( σ < 0.5 px), the mean angular error remains below 1 ∘ , while for severe noise ( σ = 2.0 px), it stays below 3 ∘ . Public-data experiments on calib_small , cartman , and MT yield dataset-level mean angular errors of 0.459 ∘ , 1.067 ∘ , and 1.506 ∘ , respectively. In the tested custom imaging–emitter setup, checkerboard and stripe-based correspondences produce angular errors of 0.801 ∘ and 0.968 ∘ , respectively. The results indicate that the proposed method provides a compact and robust solution for flexible baseline-direction measurement in optical metrology and active optical imaging systems.