Monocular visual odometry based on epipolar geometry

Abstract

In Visual Odometry, there are many approaches related to the optimization of pose and structure.Some allow for fine-grained use of the observations, like feature points, but require many parameters.This limits the density of structure reconstruction and the number of poses that can be optimized in real-time.In this work, we propose a lowparameter characterization of Visual Odometry that consists solely of poses and the locations of eipoles in pairs of images.We do that by formulating an indirect type of Bundle Adjustment that consists of replacing structure parameters like inverse point depths with epipoles from two-view geometry.Our formulation allows us to reconstruct the scene with the same density as any set of point associations provided.Furthermore, this reconstruction does not increase the number of parameters when the number of points increases, and it has a linear computational time cost on the number of points.To check if the proposed formulation fits real-world data, we build a feature-based (indirect) VO pipeline that minimizes the reprojection error concerning poses and epipoles.We employ secondorder gradients to optimize the poses in the algebra of SE(3) and the epipoles in their original space.Then, we perform odometry and structure reconstruction in the KITTI dataset.Experiments show that the proposed approach indeed fits real observations and has odometry results compatible with the literature while allowing for some control over structure without point parameters.