A Multi-Candidate Mathematical Expression Recognition System

A multi-candidate mathematical expression (ME) recognition system is proposed. The system includes three main components: image preprocessing, symbol segmentation and structure analysis. During the symbol segmentation period, a three-stage segmentation method based on dynamic programming (DP) is proposed. In the initial segmentation based on DP algorithm, the ME image is segmented into several blocks. In the vertical segmentation, each block is segmented into some blobs. In the horizontal segmentation based on DP algorithm, every blob is segmented into symbols. During the structure analysis period, hierarchical structure is adopted to analyze structure of ME. The hierarchical structure analysis method consists of three steps, i.e., matrix analysis, sub-expression analysis and script expression analysis. In matrix analysis (sub-expression analysis), an ME is decomposed into several basic matrixes (basic sub-expressions) and some sub-expressions (script expressions) by reconstructing the ME (sub-expression) global structure, and then every basic matrix (sub-expression) is analyzed from bottom to up. In script analysis, a graph rewriting algorithm is adopted to build script relation trees among symbols within a script expression. A spatial relation model is built to calculate spatial relations' confidence between two symbols. The experiments are implemented on a database with 3268 ME images and the results show that the proposed system works well. Top-1 ME recognition accuracy reaches 78.2%.