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A Metric for Line Segments
December 1993 (vol. 15 no. 12)
pp. 1312-1318

This correspondence presents a metric for describing line segments. This metric measures how well two line segments can be replaced by a single longer one. This depends for example on collinearity and nearness of the line segments. The metric is constructed using a new technique using so-called neighborhood functions. The behavior of the metric depends on the neighborhood function chosen. In this correspondence, an appropriate choice for the case of line segments is presented. The quality of the metric is verified by using it in a simple clustering algorithm that groups line segments found by an edge detection algorithm in an image. The fact that the clustering algorithm can detect long linear structures in an image shows that the metric is a good measure for the groupability of line segments.

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Index Terms:
line segments; metric; collinearity; nearness; neighborhood functions; clustering algorithm; edge detection; groupability measure; geometry; image recognition
P.F.M. Nacken, "A Metric for Line Segments," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 12, pp. 1312-1318, Dec. 1993, doi:10.1109/34.250848
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