Robust unambiguous parametrization of the essential manifold

Analytic manifolds were recently used for motion averaging, segmentation and robust estimation. Here we consider the epipolar constraint for calibrated cameras, which is the most general motion model for calibrated cameras and is encoded by the essential matrix. The set of all essential matrices forms the essential manifold. We provide a theoretical characterization of the geometry of the essential manifold and develop a parametrization which associates each essential matrix with a unique point on the manifold. Our work provides a more complete theoretical analysis of the essential manifold than previous work in this direction. We show the results of using this parametrization with real data sets, while previous work concentrated on theoretical analysis with synthetic data.