• Laser & Optoelectronics Progress
  • Vol. 56, Issue 7, 072001 (2019)
Dingbang Fang, Gui Feng*, Haiyan Cao, Hengjie Yang..., Xue Han and Yincheng Yi|Show fewer author(s)
Author Affiliations
  • Xiamen Key Laboratory of Mobile Mutimedia Communications, College of Information Science and Engineering, Huaqiao University, Xiamen, Fujian 361021, China
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    DOI: 10.3788/LOP56.072001 Cite this Article Set citation alerts
    Dingbang Fang, Gui Feng, Haiyan Cao, Hengjie Yang, Xue Han, Yincheng Yi. Handwritten Formula Symbol Recognition Based on Multi-Feature Convolutional Neural Network[J]. Laser & Optoelectronics Progress, 2019, 56(7): 072001 Copy Citation Text show less
    Class distribution of 101 symbols
    Fig. 1. Class distribution of 101 symbols
    Images randomly generated after original images passing through elastic distortion model. (a) Original images; (b) images randomly generated for first time; (c) images randomly generated for second time
    Fig. 2. Images randomly generated after original images passing through elastic distortion model. (a) Original images; (b) images randomly generated for first time; (c) images randomly generated for second time
    Structural diagram of DenseNet-SE network
    Fig. 3. Structural diagram of DenseNet-SE network
    Structural diagram of residual-dense block module
    Fig. 4. Structural diagram of residual-dense block module
    Validation accuracy comparison of DenseNet and DenseNet-SE
    Fig. 5. Validation accuracy comparison of DenseNet and DenseNet-SE
    Accuracy comparison of DenseNet-SE test set and validation set
    Fig. 6. Accuracy comparison of DenseNet-SE test set and validation set
    Symbols of misjudgment types in CROHME2016 test set
    Fig. 7. Symbols of misjudgment types in CROHME2016 test set
    Dividing datasetDataset categoryImage size /(cm×cm)Scale
    Previous quantityTwisted quantity
    TrainCROHME2016 train48×4885802321301
    ValidationCROHME2013 test48×486082
    TestCROHME2016 test48×4810019
    CROHME2014 test48×4810061
    Table 1. Distribution of CROHME experimental datasets
    ModelTraintime /sTrainbatch /sValidationaccuracy /%
    DenseNet3070.11291.08
    DenseNet-SE4060.12395.31
    Table 2. Time consumption and accuracy for each epoch test
    SystemCROHME2014 testaccuracy /%CROHME2016 testaccuracy /%Featureused
    Ref. [6]91.0492.81Online+offline
    Ref. [5]91.2892.27Online+offline
    Ref. [3]91.24-Online+offline
    Ref. [4]88.6688.85Online+offline
    Ref. [8]87.72-Offline
    Ref. [7]91.8292.42Offline
    Proposed93.3892.93Offline
    Table 3. Comparison between proposed method and different types of systems
    No.SymbollabelTotalsymbolsPercentage ofnumber ofmisclassifiedsymbols /%
    1o11100
    2ρrime11100
    3C3196.77
    4τimes7288.89
    5Y1376.92
    6COMMA8276.83
    7s2171.43
    8.2171.43
    9ιn366.67
    10r4065.00
    Table 4. Symbols of TOP-10 error discrimination types in CROHME2016
    Dingbang Fang, Gui Feng, Haiyan Cao, Hengjie Yang, Xue Han, Yincheng Yi. Handwritten Formula Symbol Recognition Based on Multi-Feature Convolutional Neural Network[J]. Laser & Optoelectronics Progress, 2019, 56(7): 072001
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