Multi-Scale Attention with Dense Encoder for Handwritten Mathematical Expression Recognition

Handwritten mathematical expression recognition is a challenging problem due to the complicated two-dimensional structures, ambiguous handwriting input and variant scales of handwritten math symbols. To settle this problem, we utilize the attention based encoder-decoder model that recognizes mathematical expression images from two-dimensional layouts to one-dimensional LaTeX strings. We improve the encoder by employing densely connected convolutional networks as they can strengthen feature extraction and facilitate gradient propagation especially on a small training set. We also present a novel multi-scale attention model which is employed to deal with the recognition of math symbols in different scales and save the fine-grained details that will be dropped by pooling operations. Validated on the CROHME competition task, the proposed method significantly outperforms the state-of-the-art methods with an expression recognition accuracy of 52.8% on CROHME 2014 and 50.1% on CROHME 2016, by only using the official training dataset

Context-based Multi-stage Offline Handwritten Mathematical Symbol Recognition using Deep Learning

We propose a multi-stage machine learning (ML) architecture to improve the accuracy of offline handwritten mathematical symbol recognition. In the first stage, we train and assemble multiple deep convolutional neural networks to classify isolated mathematical symbols. However, certain ambiguous symbols are hard to classify without the context information of the mathematical expressions where the symbols belong. In the second stage, we train a deep convolutional neural network that further classifies the ambiguous symbols based on the context information of the symbols. To further improve the classification accuracy, in the third stage, we develop a set of rules to classify the ambiguity or otherwise the syntax of the mathematical expressions will be violated. We evaluate the proposed method by using the Competition on Recognition of Online Handwritten Mathematical Expressions (CROHME) dataset. The proposed method results the state-of-the-art accuracy of 94.04%, which is 1.62% improvement compared with the previous single-stage approach

On-line Recognition of Handwritten Mathematical Symbols

This paper presents a classification system which uses the pen trajectory to classify handwritten symbols. Five preprocessing steps, one data multiplication algorithm, five features and five variants for multilayer Perceptron training were evaluated using 166898 recordings. The evaluation results of 21 experiments were used to create an optimized recognizer. This improvement was achieved by supervised layer-wise pretraining (SLP) and adding new features

Augmented incremental recognition of online handwritten mathematical expressions

This paper presents an augmented incremental recognition method for online handwritten mathematical expressions (MEs). If an ME is recognized after all strokes are written (batch recognition), the waiting time increases significantly when the ME becomes longer. On the other hand, the pure incremental recognition method recognizes an ME whenever a new single stroke is input. It shortens the waiting time but degrades the recognition rate due to the limited context. Thus, we propose an augmented incremental recognition method that not only maintains the advantage of the two methods but also reduces their weaknesses. The proposed method has two main features: one is to process the latest stroke, and the other is to find the erroneous segmentations and recognitions in the recent strokes and correct them. In the first process, the segmentation and the recognition by Cocke-Younger-Kasami (CYK) algorithm are only executed for the latest stroke. In the second process, all the previous segmentations are updated if they are significantly changed after the latest stroke is input, and then, all the symbols related to the updated segmentations are updated with their recognition scores. These changes are reflected in the CYK table. In addition, the waiting time is further reduced by employing multi-thread processes. Experiments on our dataset and the CROHME datasets show the effectiveness of this augmented incremental recognition method, which not only maintains recognition rate even compared with the batch recognition method but also reduces the waiting time to a very small level

Recognition of on-line handwritten mathematical expressions using 2D stochastic context-free grammars and hidden Markov models

[EN] This paper describes a formal model for the recognition of on-line handwritten mathematical expressions using 2D stochastic context-free grammars and hidden Markov models. Hidden Markov models are used to recognize mathematical symbols, and a stochastic context-free grammar is used to model the relation between these symbols. This formal model makes possible to use classic algorithms for parsing and stochastic estimation. In this way, first, the model is able to capture many of variability phenomena that appear in on-line handwritten mathematical expressions during the training process. And second, the parsing process can make decisions taking into account only stochastic information, and avoiding heuristic decisions. The proposed model participated in a contest of mathematical expression recognition and it obtained the best results at different levels. 2012 Elsevier B.V. All rights reserved.Work supported by the EC (FEDER/ FSE) and the Spanish MEC/MICINN under the MIPRCV ‘‘Consolider Ingenio 2010’’ program (CSD2007-00018), the MITTRAL (TIN2009-14633-C03-01) project, the FPU Grant (AP2009-4363), and by the Generalitat Valenciana under the Grant Prometeo/2009/014.Álvaro Muñoz, F.; Sánchez Peiró, JA.; Benedí Ruiz, JM. (2014). Recognition of on-line handwritten mathematical expressions using 2D stochastic context-free grammars and hidden Markov models. Pattern Recognition Letters. 35:58-67. https://doi.org/10.1016/j.patrec.2012.09.023S58673