  Visual-Inertial Odometry (VIO) algorithms typically rely on a point cloud
representation of the scene that does not model the topology of the
environment. A 3D mesh instead offers a richer, yet lightweight, model.
Nevertheless, building a 3D mesh out of the sparse and noisy 3D landmarks
triangulated by a VIO algorithm often results in a mesh that does not fit the
real scene. In order to regularize the mesh, previous approaches decouple state
estimation from the 3D mesh regularization step, and either limit the 3D mesh
to the current frame or let the mesh grow indefinitely. We propose instead to
tightly couple mesh regularization and state estimation by detecting and
enforcing structural regularities in a novel factor-graph formulation. We also
propose to incrementally build the mesh by restricting its extent to the
time-horizon of the VIO optimization; the resulting 3D mesh covers a larger
portion of the scene than a per-frame approach while its memory usage and
computational complexity remain bounded. We show that our approach successfully
regularizes the mesh, while improving localization accuracy, when structural
regularities are present, and remains operational in scenes without
regularities.
