This work is concerned with the matching of straight lines between two stereo image pairs by reprojection. While we will focus on visual odometry in the realm of simultaneous mapping and localization, the techniques are also relevant to monocular and stereo 3D object detection and tracking. Our first contribution is an adaptation of the Iterative Closest Point (ICP) algorithm to the domain of lines. We argue that a naive "Iterative Closest Line" derivation cannot deliver similar performance. In contrast, our novel Iterative Closest Multiple Lines (ICML) algorithm allows efficient line matching while even reducing the amount of local minima during iterative optimization with its consideration of several weighted matches. The second contribution is a fast and robust hypothesize-andtest algorithm which can act as a fallback for challenging frame pairs where pure gradient-based optimization fails. In several differently textured scenes, we demonstrate robust performance, even in very sparse cases where proven feature point based methods fail. In comparison to edge-point ICP, we see speed improvements of more than an order of a magnitude and reduced susceptibility for local minima.

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