  In this work, we propose a purely geometrical approach for the robust
matching of line segments for challenging stereo streams with severe
illumination changes or High Dynamic Range (HDR) environments. To that purpose,
we exploit the univocal nature of the matching problem, i.e. every observation
must be corresponded with a single feature or not corresponded at all. We state
the problem as a sparse, convex, L1-minimization of the matching vector
regularized by the geometric constraints. This formulation allows for the
robust tracking of line segments along sequences where traditional
appearance-based matching techniques tend to fail due to dynamic changes in
illumination conditions. Moreover, the proposed matching algorithm also results
in a considerable speed-up of previous state of the art techniques making it
suitable for real-time applications such as Visual Odometry (VO). This, of
course, comes at expense of a slightly lower number of matches in comparison
with appearance based methods, and also limits its application to continuous
video sequences, as it is rather constrained to small pose increments between
consecutive frames. We validate the claimed advantages by first evaluating the
matching performance in challenging video sequences, and then testing the
method in a benchmarked point and line based VO algorithm.
