Plane Geometry Figure Retrieval Based on Bilayer Geometric Attributed Graph Matching

With the development of computer-aided education and digital library, there have emerged large numbers of digital documents online for education purposes. However, it is far from convenient to retrieve mathematic geometry questions because current retrieval systems largely rely on keywords instead of geometry figure images. We focus on plane geometry figure (PGF) image retrieval aiming at retrieving relevant geometry images that hold more similar geometric attributes and structure properties than a question text stem. Motivated by Attribute Graph (AG), and aiming to catch more delicate local geometric attributes and overall structure layout, we propose a Bilayer Geometric Attributed Graph (Bilayer-GAG) matching method to retrieve the relevant PGF images. The root node of Bilayer-GAG catches the spatial relationships among its children - the graph elements of the second layer, the second layer contains curvilinear geometric primitives and linear nested AGs that consist of nodes and edges with geometric signatures. Then we calculate the overall matching cost in three perspectives and finally retrieve top-k relevant Bilayer-GAGs. For a PGF image query, the retrieval results are shown in an appropriate ranking order, which has high visual similarity with respect to human perception. Retrieval experiments results show the effectiveness and efficiency of the proposed Bilayer-GAG.