E-Graph: Minimal Solution for Rigid Rotation with Extensibility Graphs

Minimal solutions for relative rotation and translation estimation tasks have been explored in different scenarios, typically relying on the so-called co-visibility graph. However, how to build direct rotation relationships between two frames without overlap is still an open topic, which, if solved, could greatly improve the accuracy of visual odometry. In this paper, a new minimal solution is proposed to solve relative rotation estimation between two images without overlapping areas by exploiting a new graph structure, which we call Extensibility Graph (E-Graph). Differently from a co-visibility graph, high-level landmarks, including vanishing directions and plane normals, are stored in our E-Graph, which are geometrically extensible. Based on E-Graph, the rotation estimation problem becomes simpler and more elegant, as it can deal with pure rotational motion and requires fewer assumptions, e.g. Manhattan/Atlanta World, planar/vertical motion. Finally, we embed our rotation estimation strategy into a complete camera tracking and mapping system which obtains 6-DoF camera poses and a dense 3D mesh model. Extensive experiments on public benchmarks demonstrate that the proposed method achieves state-of-the-art tracking performance.