Matching Sets Of Line Segments

We give approximation algorithms for matching two sets of line segments in constant dimension. We consider several versions of the problem: Hausdorff distance, bottleneck distance and largest common point set. We study these similarity measures under several sets of transformations: translations, rotations about a fixed point and rigid motions. As opposed to previous theoretical work on this problem, we match segments individually, in other words we regard our two input sets as sets of segments rather than unions of segments.