Contrastive learning has gained significant attention recently as it can learn a representation from a large amount of unlabeled training data to improve downstream tasks. While the existing approaches mainly focus on standard tasks of image classification and object detection, they are not easily applied to structured prediction problems. In this paper, we propose an unsupervised pre-trained model, called PrimCLR, for handwritten mathematical expression recognition. For a formula recognition model of encoder-decoder architecture, a pre-trained representation is obtained by PrimCLR, where the contrastive loss is computed from pairs of patches so as to better discriminate primitives. The pre-trained representation is transferred to downstream formula recognition with supervised fine-tuning. Experiments show that pre-training by PrimCLR can significantly improve the formula recognition performance, and PrimCLR shows superiority to conventional contrastive learning methods. Our model achieves state-of-the-art performance on standard datasets CROHME 2016 and CROHME 2019.

Recent handwritten mathematical expression recognition (HMER) approaches treat the problem as an image-to-markup generation task where the handwritten formula is translated into a sequence (e.g. LaTeX). The encoder-decoder framework is widely used to solve this image-to-sequence problem. However, (i) for structured mathematical formula, the hierarchical structure neither in the formula nor in the markup has been explored adequately. In addition, (ii) existing image-to-markup methods could not explicitly segment mathematical symbols in the formula corresponding to each target markup token. In this paper, we address the above issues by formulating the HMER as a graph-to-graph (G2G) learning problem. Graph is more flexible and general for structure representation and learning compared with image or sequence. At the core of our method lies the embedding of input formula and output markup into graphs on primitives, with Graph Neural Networks (GNN) to explore the structural information, and a novel sub-graph attention mechanism to match primitives in the input and output graphs. We conduct extensive experiments on CROHME datasets to demonstrate the benefits of the proposed G2G model. Our method yields significant improvements over previous SOTA image-to-markup systems. Moreover, it explicitly resolves the symbol segmentation problem while still being trained end-to-end, making the whole system much more accurate and interpretable.

This paper presents the competition on Offline Recognition and Spotting of Handwritten Mathematical Expressions (OffRaSHME) held at the 17th International Conference on Frontiers in Handwriting Recognition (ICFHR 2020). Handwritten Mathematical Expression Recognition (HMER) has wide potential applications and is capturing increasing attention in recent years. Previous HMER competitions mainly focused on online datasets or offline datasets that are converted from online data. In this competition, we have collected a dataset of offline handwritten mathematical expressions by scanning papers that contain expressions. Moreover, we labeled the offline dataset at symbol level, i.e., the bounding boxes of each symbol are also provided, to facilitate the research of HMER. At last, 19,749 offline handwritten mathematical expressions are collected for training, and 2,000 ones are provided for evaluating the participating systems. In the competition, 7 teams submitted 8 systems for the task of offline HMER, among which 5 systems only use the provided datasets without any extra data while 3 systems use extra data. The winner team achieved a recognition accuracy of 79.85% (without extra data) and 81.85% (with extra data) on the offline formula recognition task.