Minimal Metric Structure and Motion from Three Affine Images

Structure and motion from minimal data is essential to bootstrap robust methods based on random sampling such as RANSAC or LMS. Let us consider the affine camera model and make the hypotheses of zero skew and unity aspect ratio. In this case, at least 4 points in 3 images are necessary to recover structure and motion. We propose a parametrization based on metric structure rather than camera motion parameters which have been previously used. The structure of 4 points is computed in closed-form by solving a quadratic equation. Unstable configurations are also investigated. Experimental results on simulated data and real images demonstrate that our algorithm allows fast estimation when included in a robust estimation process.