On Indexing Line Segments

In several image applications, it is necessary to retrieve specific line segments born a potentially very large set. In this paper, we consider the problem of indexing straight line segments to enable efficient retrieval of all line segments that (i) go through a specified point, or (ii) intersect a specified line segment. We propose a data organization, based on the Hough transform, that can be used to solve both retrieval problems efficiently. In addition, the proposed structure can be used for approximate retrievals, finding all line segments that pass close to a specified point. We show, through analysis and experiment, that the proposed technique always does as well as or better than retrieval based on minimum bounding rectangles or line segment end-points.