We proposed a method for the detection of meaningful line segment configurations, based on the a contrario
framework. The method can detect complete or incomplete regular polygons from a set of line segments. We define the strength of a configuration based on its resemblance to regular polygons. A configuration is meaningful if the expectation of such occurrence would be very small in an image of random line segments. The method is tested on both synthetic images and real images and detects 92.8% of the polygon edges.