Understanding mathematical expressions using procedure-oriented transformation

摘要

A system for understanding mathematical expressions is presented. The mathematical expressions scanned from a printed document are recognized and transformed into one-dimensional (1D) strings according to the format of a publication system. After separating all symbols in an input mathematical expression, 13 features are utilized to represent each symbol. In order to reduce the computational time, a coarse classification algorithm is applied to reduce the number of candidates. Then for each input symbol, the character with the highest similarity is selected as the candidate symbol. Since some of the symbols in an arithmetical expression may touch each other, a dynamic programming algorithm which uses structural features is adopted to identify correct characters from connected symbols. In the expression formation stage, a procedure-oriented method is proposed to translate the recognized symbols from a two-dimensional (2D) space into a 1D character string. A total of 105 mathematical expressions have been used as training data and 50 expressions as testing data. The experimental results have demonstrated the feasibility of the understanding system.