Detection of Overlapped Quadrangles in Plane Geometric Figures

Digital plane geometric figures (PGFs) are important resources of digital education, especially in mathematical pedagogy. The related applications, such as recognition and retrieval system on geometric figure images, have not been fully exploited. Special quadrangles, including rectangles, parallelograms, and trapezoids, are important components of PGFs, and extracting these special quadrangles is a prerequisite task. In this paper, we focus on the detection of overlapped quadrangles in PGFs using the proposed one-pass detection algorithm based on the geometric symmetrical property of involved shapes. We also introduce a method to refine the detected geometric primitives by significance analysis in order to optimize the shape descriptor. Experimental results show that the proposed method for special quadrangle detection is accurate and efficient, and is ready for further use in PGF retrieval systems.