Sequential Covariance-weighted Quasiconvex solution to Mapping in Visual SLAM

Abstract

This paper presents a new sequential real time algorithm that solves the mapping problem in Visual SLAM. The considered problem is a particular example from the triangulation problem, that has direct applications to robotic vision domain. In other words, the problem is handled as 3D estimate problem. The estimation process is formulated as a minimization problem of quasiconvex objective function. The minimization process is realized using the well-known bisection algorithm. The bisection algorithm runs sequentially solving one convex feasibility problem in each iteration, trying to reduce the bound on the 3D estimate. New image measurements arrive after every new iteration, new convex visibility problem is solved, and the bounds on the 3D estimates are updated. These steps are repeated till convergence. We conducted a set of experiments to show the applicability to the general reconstruction (triangulation) problem as well as the application to mapping Visual SLAM.