Top-down online handwritten mathematical expression parsing with graph grammar

Abstract

In recognition of online handwritten mathematical expressions, symbol segmentation and classification and recognition of relations among symbols is managed through a parsing technique. Most parsing techniques follow a bottom-up approach and adapt grammars typically used to parse strings. However, in contrast to top-down approaches, pure bottom-up approaches do not exploit grammar information to avoid parsing of invalid subexpressions. Moreover, modeling math expressions by string grammars makes difficult to extend it to include new structures. We propose a new parsing technique that models mathematical expressions as languages generated by graph grammars, and parses expressions following a top-down approach. The method is general in the sense that it can be easily extended to parse other multidimensional languages, as chemical expressions, or diagrams. We evaluate the method using the (publicly available) CROHME-2013 dataset.