PLDD: Point-lines distance distribution for detection of arbitrary triangles, regular polygons and circles

• Present a general framework for detecting triangles, regular polygons, and circles.
• Locate the shape center just by voting on distance.
• The maximal time complexity is O(n2) at the worst condition for polygon detection.

In this paper, a general framework is presented for detection of arbitrary triangles, regular polygons, and circles, which is inspired by the common geometric property that the incenter of the shape is equidistant to the tangential lines of the contour points. The idea of point-lines distance distribution (PLDD) is introduced to compute the shape energy of each pixel. Then, shape centers can be exacted from the produced PLDD map, and shape radii are obtained simultaneously based on the distance distribution of the shape center. The shape candidates are thus determined and represented with three independent characteristics: shape center, shape radius, and contour points. Finally, distinguish different types of the shape from shape candidates using shape contour points information. Compared with exiting methods, the PLDD based method detects the shapes mainly using the inherent information of edge points, such as distance, and it is simple and general. Comparative experiments both on synthetic and natural images with the state of the art also prove that the PLDD based method performs more robustly and accurately with the maximal time complexity O(n2) at the worst condition.