Existing line segment detectors tend to break up perceptually distinct line segments into multiple segments. We propose an algorithm for merging such broken segments to recover the original perceptually accurate line segments. The algorithm proceeds by grouping line segments on the basis of angular and spatial proximity. Then those line segment pairs within each group that satisfy unique, adaptive mergeability criteria are successively merged to form a single line segment. This process is repeated until no more line segments can be merged. We also propose a method for quantitative comparison of line segment detection algorithms. Results on the York Urban dataset show that our merged line segments are closer to human-marked ground-truth line segments compared to state-of-the-art line segment detection algorithms.