Handwritten Formula Symbol Recognition Based on Multi-Feature Convolutional Neural Network

Dingbang Fang; Gui Feng; Haiyan Cao; Hengjie Yang; Xue Han; Yincheng Yi

doi:10.3788/LOP56.072001

Laser & Optoelectronics Progress, Volume. 56, Issue 7, 072001(2019)

Handwritten Formula Symbol Recognition Based on Multi-Feature Convolutional Neural Network

Dingbang Fang, Gui Feng^*, Haiyan Cao, Hengjie Yang, Xue Han, and Yincheng Yi

Xiamen Key Laboratory of Mobile Mutimedia Communications, College of Information Science and Engineering, Huaqiao University, Xiamen, Fujian 361021, China

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Figures & Tables(11)

Fig. 1. Class distribution of 101 symbols

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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

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Fig. 3. Structural diagram of DenseNet-SE network

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Fig. 4. Structural diagram of residual-dense block module

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Fig. 5. Validation accuracy comparison of DenseNet and DenseNet-SE

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Fig. 6. Accuracy comparison of DenseNet-SE test set and validation set

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Fig. 7. Symbols of misjudgment types in CROHME2016 test set

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Table 1. Distribution of CROHME experimental datasets

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Table 1. Distribution of CROHME experimental datasets

Dividing dataset	Dataset category	Image size /(cm×cm)	Scale
Dividing dataset	Dataset category	Image size /(cm×cm)	Previous quantity	Twisted quantity
Train	CROHME2016 train	48×48	85802	321301
Validation	CROHME2013 test	48×48	6082	—
Test	CROHME2016 test	48×48	10019	—
Test	CROHME2014 test	48×48	10061	—

Table 2. Time consumption and accuracy for each epoch test
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Table 2. Time consumption and accuracy for each epoch test
Model Traintime /s Trainbatch /s Validationaccuracy /%
DenseNet 307 0.112 91.08
DenseNet-SE 406 0.123 95.31

Table 3. Comparison between proposed method and different types of systems

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Table 3. Comparison between proposed method and different types of systems

System	CROHME2014 testaccuracy /%	CROHME2016 testaccuracy /%	Featureused
Ref. [6]	91.04	92.81	Online+offline
Ref. [5]	91.28	92.27	Online+offline
Ref. [3]	91.24	-	Online+offline
Ref. [4]	88.66	88.85	Online+offline
Ref. [8]	87.72	-	Offline
Ref. [7]	91.82	92.42	Offline
Proposed	93.38	92.93	Offline

Table 4. Symbols of TOP-10 error discrimination types in CROHME2016
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Table 4. Symbols of TOP-10 error discrimination types in CROHME2016
No. Symbollabel Totalsymbols Percentage ofnumber ofmisclassifiedsymbols /%
1 o 11 100
2 ρrime 11 100
3 C 31 96.77
4 τimes 72 88.89
5 Y 13 76.92
6 COMMA 82 76.83
7 s 21 71.43
8 . 21 71.43
9 ιn 3 66.67
10 r 40 65.00

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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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