An efficient approach to automated geometry diagram parsing

(1) Lilavatibai Podar High School, Mumbai, Maharashtra, India, (2) e-Emphasys Technologies, Mumbai, Maharashtra, India
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An automated geometry problem solver can be a valuable tool in math education as a learning aid. An essential part of such a system is the ability to parse diagrams automatically, and diagram understanding by itself is an interesting research problem because of the rich and complex information that geometry diagrams convey and the many approaches one can take to extract that information. In this paper, we introduce Fast Geometry Diagram Parser (FastGDP), an efficient approach to geometry diagram understanding that uses clustering and corner information. We hypothesized that FastGDP would be significantly faster than the widely used GeoSolver tool at both primitive (line and circle) and point detection, because FastGDP does not require large numbers of computationally expensive pixel-level calculations. We further hypothesized that FastGDP would offer comparable performance to GeoSolver on point detection, due to FastGDP’s use of corner information. We expected FastGDP’s primitive detection performance to be marginally lower than that of GeoSolver due to the latter’s emphasis on over-generation of primitives and subsequent selection of the best detections. Our experiments on three datasets (combined n=169) showed that FastGDP is more than an order of magnitude faster than GeoSolver in most cases. We found that FastGDP reports comparable performance to GeoSolver on primitive detection and slightly lower performance on point detection. We believe that the speed advantage offered by FastGDP will provide greater flexibility when it is incorporated into an automated geometry problem solver, especially if FastGDP is used within the training loop of the solver.

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