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Scale Exploiting Minimal Solvers for Relative Pose with Calibrated Cameras

We present efficient minimal solvers for the estimation of relative pose between two calibrated images. The proposed method exploits known scale ratios of feature matches which are intrinsically provided by scale invariant feature detectors with scale-space pyramids (e.g. SIFT). Since we are using scale, the number of required feature matches is reduced and consequently fewer inliers are needed. In our paper, we derive two solvers each related to one of the two possible minimal sets: Our 1+3 point algorithm estimates relative pose from four feature matches with one known scale, while our 2+1 point algorithm computes relative pose from three feature matches with two known scales. We embed the proposed methods into RANSAC with two inlier classes, and present an efficient RANSAC modification for less reliable scales. Finally, we analyze performance and robustness in synthetic data, and evaluate our RANSAC approach on real data in comparison to RANSAC based on the five point algorithm.