Generating Handwritten Mathematical Expressions From Symbol Graphs: An End-to-End Pipeline
Authors: Yu Chen, Fei Gao, Yanguang Zhang, Maoying Qiao, Nannan Wang

In this paper we explore a novel challenging generation task i.e. Handwritten Mathematical Expression Generation (HMEG) from symbolic sequences. Since symbolic sequences are naturally graph-structured data we formulate HMEG as a graph-to-image (G2I) generation problem. Unlike the generation of natural images HMEG requires critic layout clarity for synthesizing correct and recognizable formulas but has no real masks available to supervise the learning process. To alleviate this challenge we propose a novel end-to-end G2I generation pipeline (i.e. graph - layout - mask - image) which requires no real masks or nondifferentiable alignment between layouts and masks. Technically to boost the capacity of predicting detailed relations among adjacent symbols we propose a Less-is-More (LiM) learning strategy. In addition we design a differentiable layout refinement module which maps bounding boxes to pixel-level soft masks so as to further alleviate ambiguous layout areas. Our whole model including layout prediction mask refinement and image generation can be jointly optimized in an end-to-end manner. Experimental results show that our model can generate high-quality HME images and outperforms previous generative methods. Besides a series of ablations study demonstrate effectiveness of the proposed techniques. Finally we validate that our generated images promisingly boosts the performance of HME recognition models through data augmentation. Our code and results are available at: https://github.com/AiArt-HDU/HMEG.