Plane Geometry Figure Retrieval with Bag of Shapes

Digital education is serving an increasingly important function in most educational institutions, thus resulting in the production of a large number of digital documents online for education purposes. However, convenient ways to retrieve mathematic geometry questions are lacking because current retrieval systems largely rely on keywords instead of geometry figure images. This study focuses on plane geometry figure (PGF) image retrieval with the aim of retrieving relevant geometry images that contain more structural information than a question text stem. To fully use geometrical properties, a Bag-of-shapes (BoS) method is proposed to build the feature descriptor of an image. The BoS method contains either basic geometric primitives or dual-primitive structures along with several specific geometrical features for shape description. Based on the BoS feature descriptor, we apply cosine similarity with group feature weight as vector similarity measure for ranking to achieve high efficiency. For a PGF image query, the retrieval results are provided in an appropriate ranking order, which has high visual similarity with respect to human perception. Retrieval experiments and evaluation results show the effectiveness and efficiency of the proposed BoS shape descriptor.