A New Approach for Understanding of Structure of Printed Mathematical Expression

This paper introduces a new approach for automatic understanding of structure of printed mathematical expression (ME). The method is consisted of three periods, i.e. matrix analysis, sub-expression analysis and script expression analysis. In matrix analysis (sub-expression analysis), a ME (sub-expression) is decomposed into several basic matrixes (sub-expressions) and some sub-expressions (script expressions) by reconstructing the ME global structure, and then every basic matrix (sub-expression) is analyzed from bottom to up. In script analysis, graph rewriting algorithm is adopted to build script relation trees among symbols within a script expression. In order to calculate spatial relations' confidence between two symbols, spatial relation model is built based on Gaussian Mixture Model (GMM). The experiments were implemented on a database with 3268 images and the results show that the proposed method works well. Top-1 prefect analysis accuracy reaches 92.3%.