In this paper, we introduce Track, Attend and Parse (TAP), an end-to-end approach based on neural networks for online handwritten mathematical expression recognition (OHMER). The architecture of TAP consists of a tracker and a parser. The tracker employs a stack of bidirectional recurrent neural networks with gated recurrent units (GRU) to model the input handwritten traces, which can fully utilize the dynamic trajectory information in OHMER. Followed by the tracker, the parser adopts a GRU equipped with guided hybrid attention (GHA) to generate LaTeX notations. The proposed GHA is composed of a coverage based spatial attention, a temporal attention and an attention guider. Moreover, we demonstrate the strong complementarity between offline information with static-image input and online information with ink-trajectory input by blending a fully convolutional networks based watcher into TAP. Inherently unlike traditional methods, this end-to-end framework does not require the explicit symbol segmentation and a predefined expression grammar for parsing. Validated on a benchmark published by the CROHME competition, the proposed approach outperforms the state-of-the-art methods and achieves the best reported results with an expression recognition accuracy of 61.16% on CROHME 2014 and 57.02% on CROHME 2016, using only official training dataset.

Recently, recognition of online handwritten mathematical expression has been greatly improved by employing encoder-decoder based methods. Existing encoder-decoder models use string decoders to generate LaTeX strings for mathematical expressions recognition. However, in this paper, we importantly argue that string representations might not be the most natural for mathematical expressions -- mathematical expressions are inherently tree structures other than flat strings. For this purpose, we propose a novel sequential relation decoder (SRD) that aims to decode expressions into tree structures for online handwritten mathematical expressions recognition. At each step of tree construction, a sub-tree structure composed of a relation node and two symbol nodes is computed based on previous sub-tree structures. This is the first work that builds a tree structure based decoder for encoder-decoder based mathematical expression recognition. Compared with string decoders, a decoder that better understands tree structures is crucial for mathematical expression recognition as it brings a more reasonable learning objective and improves overall generalization ability. We demonstrate how the proposed SRD outperforms state-of-the-art string decoders through a set of experiments on CROHME database, which is currently the largest benchmark for online handwritten mathematical expression recognition.

The problem of document structure reconstruction refers to converting digital or scanned documents into corresponding semantic structures. Most existing works mainly focus on splitting the boundary of each element in a single document page, neglecting the reconstruction of semantic structure in multi-page documents. This paper introduces hierarchical reconstruction of document structures as a novel task suitable for NLP and CV fields. To better evaluate the system performance on the new task, we built a large-scale dataset named HRDoc, which consists of 2,500 multi-page documents with nearly 2 million semantic units. Every document in HRDoc has line-level annotations including categories and relations obtained from rule-based extractors and human annotators. Moreover, we proposed an encoder-decoder-based hierarchical document structure parsing system (DSPS) to tackle this problem. By adopting a multi-modal bidirectional encoder and a structure-aware GRU decoder with soft-mask operation, the DSPS model surpass the baseline method by a large margin. All scripts and datasets will be made publicly available at https://github.com/jfma-USTC/HRDoc.