Traditional structure from motion is hard in indoor environments with only a few detectable point features. These environments, however, have other useful characteristics: they often contain severable visible lines, and their layout typically conforms to a Manhattan world geometry. We introduce a new algorithm to cluster visible lines in a Manhattan world, seen from two different viewpoints, into coplanar bundles. This algorithm is based on the notion of “characteristic line”, which is an invariant of a set of parallel coplanar lines. Finding coplanar sets of lines becomes a problem of clustering characteristic lines, which can be accomplished using a modified mean shift procedure. The algorithm is computationally light and produces good results in real world situations.