Fuzzy Visibility Graph for Structural Analysis of Online Handwritten Mathematical Expressions

This paper presents a fuzzy visibility graph representation for handwritten mathematical expressions (HME) computed over segmented symbols using learned fuzzy landscape (FL) models. The learned FL models define the relative positioning of a pair of symbols using both their morphology, their typology and their context. A Random Forest Classifier uses this relative positioning to qualify relationships between symbols. The valued fuzzy visibility graph with the FL membership is produced from this classifier's output. This graph offers an explicit representation of the HME bi-dimensional structure which is then parsed with a set of rules to produce the recognized HME. We evaluate the performance of this system on the task of HME structure recognition using provided segmented symbols with experimental results on both CROHME 2014 and 2016 datasets. We obtain results up to par with the state-of-the-art thus proving that our fuzzy visibility graphs are a strong representation for mathematical expression parsing.