Parallel line grouping based on interval graphs

Abstract

We use an interval graph to model the uncertainty of line slopes in a digital image. We propose two different algorithms that group lines into classes of lines that are parallel, or almost parallel. This grouping is strongly based on the Helly-type property of parallelism in the digital plane: a group of lines is digitally parallel if and only if each pair of lines is digitally parallel. As a result, the extraction of parallel groups is reduced to the extraction of cliques in the interval graph generated by the slope intervals. Likewise, the extraction of lines that are almost parallel becomes equivalent to the detection of subgraphs that resemble cliques. © Springer-Verlag Berlin Heidelberg 2000.