一种基于分块树的手写数学公式结构分析算法

A Structural Analysis Approach to Online Handwritten Mathematical Expression

本文源于一个手写数学公式识别系统,该系统实现了手写数学公式到文本公式的自动转化。文中提出了一种基于分块树的数学公式结构分析方法,该方法首先根据其内部结构特征将数学表达式分解为若干子模块,并采用树型结构对每个子模块内部字符之间的结构关系进行表示,最终形成整个表达式的树型表示。该方法定义了一系列的字符结构属性,将字符及属性值作为结构分析的结果,这些属性值再现了公式的结构特征,并很容易被系统的公式文本显示部分所利用。另外,该方法对传统的字符空间关系类型进行了简化,减小了识别误差,而引入的分块处理方式更加适合具有根式和分式等多层嵌套结构公式的处理,并且具有较强的可扩展性。

This paper is based on an online handwritten mathematical expression recognition system. In this paper,we propose a structural analysis approach for mathematical expressions based on the partitioned tree transformation approaches. The approach firstly divides the mathematical expression into several subexpressions ,according to its internal structural information . Then,with a tree transformation it displays the spatial relations of all the characters of each subexpression. In this algorithm,the spatial relation types are greatly simplified,and the algorithm can deal with the expression with a nested structure .Moreover,it can be easily enhanced to suit for different kinds of applications.