A rule-based approach to form mathematical symbols in printed mathematical expressions

Abstract

Automated understanding of mathematical expressions (MEs) is currently a challenging task due to their complex two- dimensional (2D) structure. Recognition of MEs can be online or offline and in either case, the process involves symbol recognition and analysis of 2D structure. This process is more complex for offline or printed MEs as they do not have temporal information. In our present work, we focus on the recognition of printed MEs and assume connected components (ccs) of a given ME image are labelled. Our approach to ME recognition comprises three stages,namely symbol formation, structural analysis and generation of encoding form like LATEX. In this paper, we present symbol formation process, where multi-cc symbols (like =, ≡ etc.) are formed, identity of context-dependent symbols (like a horizontal line can be MINUS, OVERBAR, FRACTION etc.) are resolved using spatial relations. Multi-line MEs like matrices and enumerated functions are also handled in this stage. A rule-based approach is proposed for the purpose, where the heuristics based on spatial relations are represented in the form of rules (knowledge) and those rules are fired depending on input data (labelled ccs). As knowledge is isolated from data like an expert system in our approach, it allows for easy adaptability and extensibility of the process. Proposed approach also handles both single-line and multi-line MEs in an unified manner. Our approach has been tested on around 800 MEs collected from various mathematical documents and experimental results are reported on them. © 2011 Springer-Verlag.