Modified X-Y Cut for Re-Ordering Strokes of Online Handwritten Mathematical Expressions

This paper proposes a modified X-Y cut method for reordering strokes of online handwritten mathematical expression (ME) in order to make stroke order free recognition. To deal with overlapping, which causes problems in the X-Y cut method, we determine vertically ordered strokes by detecting vertical symbols and its upper/lower MEs. An upper ME and a lower ME are treated as MEs which are reordered recursively. Unordered strokes on the left side of a vertical symbol are reordered as horizontally ordered strokes. The remaining strokes are reordered recursively. The horizontally ordered strokes are reordered from left to right and the vertically ordered strokes are reordered from top to bottom. The results of evaluations of the reordering method on the CROHME 2014 database show that our ME recognition system incorporating this method outperforms all other systems that use only CROHME 2014 for training while the processing time is kept to a practical level.