Analysis of Stroke Intersection for Overlapping PGF Elements

Query-by-figure is an effective retrieval approach for educational documents. However, complex geometric diagrams in the field of mathematics education remain as obstacles in current retrieval systems. This study aims to explore a query method for plane geometric figures (PGFs) via sketched figures on smart mobile devices. We adopt an undirected graph model to describe PGFs and a divide-and-conquer strategy to analyze the relationships among strokes. Our main contribution is the detailed analysis of the stroke intersection that frequently occurs in PGFs. Numerous accurate elements obtained through overlapping analysis are then selected to construct strong descriptors for PGFs. Only the compressed query features, instead of a query figure, are transmitted to an image-based retrieval system located on a remote server, where the sketched PGF is finally recognized with low delay response. The experiments show that the proposed method achieves high efficiency and provides users with good interactive experience.