Recognition of Spatial Relations in Mathematical Formulas

A critical issue in recognition of mathematical expressions is the identification of the spatial relations of the symbols or/and sub-expressions that comprise the entire mathematical formula. This paper addresses the problem of structural analysis of mathematical expressions by constructing appropriate feature vectors to represent the spatial affinity of the objects (mathematical symbols or sub-expressions) under examination and employing two popular machine learning techniques: (i) Support Vector Machines (SVM) and (ii) Artificial Neural Networks (ANN) to recognize the spatial relation between these objects. In order to evaluate the proposed techniques, we use Math Brush, a large publicly available dataset of mathematical expressions with annotated spatial relations, and a subset of spatial relations derived from the mathematical expressions the CROHME 2012 dataset. The experimental results give an overall mean error rate of 2.8% for the SVM and 3.4% for the ANN classifiers respectively, which are at par with other approaches evaluated on the same datasets.