# Handwritten Numeral Recognition Integrating Start–End Points Measure with Convolutional Neural Network

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## Abstract

**:**

## 1. Introduction

- This study proposes an improved HNR method focusing on similarly shaped numerals;
- Start-end points measure of a handwritten numeral image is integrated into the decision of CNN for HNR recognition.
- Enhanced recognition accuracy demonstrates the superiority of the proposed system over existing methods.

## 2. HNR Integrating Start-End Writing Measure with CNN (SEWM-CNN)

_{CNN}∈ {0, 1, …, 9}) for the highest probability is the outcome of a CNN-based system. In the proposed system, along with classification in CL

_{CNN}, its probability value (say CNN’s confidence level σ

_{CNN}) is also considered as a regulating element. Parallel to CNN’s classification operation, SEWM measures the start-end points of the numeral image, suggesting the CL

_{SEWM}numeral category for which measured start-end points are found close to reference start-end points of the numeral class. Finally, the output label or system’s classification (CL

_{Sys}) of the given numeral image is provided by comparing σ

_{CNN}with a predefined threshold value (σ

_{0}): CL

_{Sys}= CL

_{CNN}if σ

_{CNN}=> σ

_{0}; otherwise, CL

_{Sys}= CL

_{SEWM}. The following subsections describe the pre-processing of data and the three functional steps of the system.

#### 2.1. Dataset Selection and Pre-Processing

#### 2.2. Related Studies with ISI Datasets

#### 2.3. Classification with CNN

_{CNN}) and its class category (CL

_{CNN}) are the outcomes of CNN, which are proceeded for the system’s outcome. The detailed training operation of CNN, along with a description of its structure, is available in [22,38].

#### 2.4. Start–End Writing Measure from Numeral Image

- Extraction of Start-End Positions in a Numeral Image

- Determining Numeral-Wise Reference Start-End Points

_{i}, E

_{i}) is the calculated start and end positions for the given image; and the reference start and end position pairs of 10 numerals are (S

_{0}, E

_{0}), (S

_{1}, E

_{1}), ----, and (S

_{9}, E

_{9}). The distance with 0 numeral is:

_{0}= (DS

_{i,0}+ DE

_{i,0})/2,

_{i,0}(and DE

_{i,0}) are the Euclidian distance of the start (and end) points of the given image and reference points of numeral 0. Similarly, distances with other numeral references are D

_{1}, D

_{2},…, and D

_{9}

_{.}The outcome of the SEWM (i.e., CL

_{SEWM}) is the numeral for which distance is minimum, i.e., min{D

_{1}, D

_{2,}… D

_{9}}.

#### 2.5. System Outcome Considering CNN’s Confidence and Start–End Writing Measure

_{CNN}) in the classification of the input image. Suppose with σ

_{CNN}=> 0.7, classifying with such a high confidence value assures very low confidence levels of other categories, and the sum of those is 0.3 or less. On the other hand, classification with σ

_{CNN}<= 0.5 indicates that cthe onfidence level in any other category might be competitive. Competitive (as well as low confidence) in two different numeral categories for a numeral image indicates that CNN becomes confused when making a decision. Such a scenario is typical for similarly shaped numerals. In such a case, the decision from SEWM is considered as the final recognition category of the proposed SEWM-CNN system.

_{0}). The final system outcome will be CNN’s recognition category (i.e., CL

_{Sys}= CL

_{CNN}) if it classifies the image with a confidence level equal to or above σ

_{0}(i.e., σ

_{CNN}=> σ

_{0}). On the contrary, the outcome of SEWM is exposed as a system outcome (i.e., CL

_{Sys}= CL

_{SEWM}) for σ

_{CNN <}σ

_{0}. It is notable that such selection-based integration does not incur computational costs in system operation concerning CNN or SEWM.

_{CNN}= 1 with σ

_{CNN}= 0.54 and CL

_{SEWM}= 9 for the lowest distance of 7. If σ

_{0}= 0.6 (i.e., σ

_{CNN}<σ

_{0}), the system relies on SEWM and CL

_{Sys}= CL

_{SEWM}= 9. It seems the value of σ

_{0}between 0.5 and 0.8 is suitable in SEWM-CNN.

#### 2.6. Significance of the Proposed System

## 3. Experimental Studies

_{0}) of the system in decision-making between CNN and SEWM. Finally, the proficiency of the proposed SEWM-CNN is validated by comparing it with other prominent methods.

#### 3.1. Experimental Results and Analysis

_{0}value. It is notable that SEWM-CNN consistently outperformed CNN, and SEWM-CNN with σ

_{0}= 0.6 is shown to be the best. Nevertheless, accuracy declines after 80 iterations for any case, indicating overfitting. The best recognition accuracy of a method is considered and compared in Table 2.

_{0}= 0.6. The accuracy of SEWM-CNN for any other σ

_{0}value (i.e., 0.5, 0.7, or 0.8) is also better than CNN. A similar observation is also available for Devanagari in Table 2b; CNN is shown to have the best recognition accuracy at 99.10% for BS 16; SEWM-CNN with any σ

_{0}value achieved better accuracy than CNN. Similar to Bengali, SEWM-CNN achieved the best accuracy with σ

_{0}= 0.6, and the value is 99.23%. It is notable that SEWM-CNN considers decisions from the SEWM technique in relatively large numbers for higher σ

_{0}values (e.g., 0.8), and similar start-end reference points among several numerals might incur wrong decisions in several cases. On the other hand, for lower σ

_{0}values (e.g., 0.5), SEWM-CNN mostly considers CNN’s outcome as a system decision ignoring SEWM and hindering the use of the start-end reference measure. According to the results presented in Table 2, σ

_{0}= 0.6 is found to be the most suitable value for both Bengali and Devanagari numerals, although all other values are shown to improve the recognition accuracy of the system, rectifying CNN’s decision in a range.

_{0}value 0.6 are presented for the same BS value 16. According to Table 3a, there is a total of 41 test samples (out of 4000) Bengali dataset misclassified by CNN, and the number reduced to 32 for SEWM-CNN; hence, recognition accuracy improved from 98.98% to 99.20% as presented in Table 2a. CNN misclassified the Bengali numeral ১ as ৯ in 12 alone out of a total of 18 misclassified cases, as seen in Table 3a. On the contrary, SEWM-CNN misclassified ১ as ৯ in seven cases, and the total misclassified number was reduced to 16. The promising result has been found by SEWM-CNN in the case of ৯; all eight misclassified cases as ১ by CNN are rectified by SEWM-CNN, and the total misclassified number is now reduced from 10 to 2. It is already mentioned that numerals ১ and ৯ are similar in shape, even in printed form, and it is sometimes difficult to distinguish between them. Table 3b also shows a similar observation for Devanagari due to the SEWM total number of misclassified test samples reduced from 36 (out of 3763) to 29; hence, recognition accuracy improved from 99.10% to 99.23%, as presented in Table 2b. In individual numeral cases, interchangeable misclassifications between ४ and ५ and between ६ and ९ are reduced. Finally, the reduction of interchangeable misclassifications of the numerals clearly indicates the effectiveness of SEWM in improving performance in the proposed SEWM-CNN method.

#### 3.2. Performance Comparison

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Plamondon, R.; Srihari, S. Online and off-line handwriting recognition: A comprehensive survey. IEEE Trans. Pattern Anal. Mach. Intell.
**2000**, 22, 63–84. [Google Scholar] [CrossRef] [Green Version] - Wen, Y.; Lu, Y.; Shi, P. Handwritten Bangla numeral recognition system and its application to postal automation. Pattern Recognit.
**2007**, 40, 99–107. [Google Scholar] [CrossRef] - Das, N.; Sarkar, R.; Basu, S.; Kundu, M.; Nasipuri, M.; Basu, D.K. A genetic algorithm based region sampling for selection of local features in handwritten digit recognition application. Appl. Soft Comput.
**2012**, 12, 1592–1606. [Google Scholar] [CrossRef] - Nasir, M.K. Hand Written Bangla Numerals Recognition for Automated Postal System. IOSR J. Comput. Eng.
**2013**, 8, 43–48. [Google Scholar] [CrossRef] - Hassan, T.; Khan, H.A. Handwritten Bangla numeral recognition using Local Binary Pattern. In Proceedings of the 2015 International Conference on Electrical Engineering and Information Communication Technology (ICEEICT), Dhaka, Bangladesh, 21–23 May 2015; pp. 1–4. [Google Scholar] [CrossRef]
- Choudhury, T.; Rana, A.; Bhowmik, H.S. Handwritten Bengali Numeral Recognition using HOG Based Feature Extraction Algorithm. In Proceedings of the 5th International Conference on Signal Processing and Integrated Networks (SPIN), Noida, India, 20–23 February 2018; pp. 687–690. [Google Scholar] [CrossRef]
- Khan, H.A. MCS HOG Features and SVM Based Handwritten Digit Recognition System. J. Intell. Learn. Syst. Appl.
**2017**, 09, 21–33. [Google Scholar] [CrossRef] [Green Version] - Das, N.; Pramanik, S.; Basu, S.; Saha, P.K.; Sarkar, R.; Kundu, M.; Nasipuri, M. Recognition of handwritten Bangla basic characters and digits using convex hull based feature set. arXiv
**2009**, arXiv:1410.0478. [Google Scholar] [CrossRef] - Rajput, G.G.; Mali, S.M. Marathi handwritten numeral recognition using Fourier descriptors and normalized chain code. Int. J. Comput. Appl.
**2010**, 3, 141–145. [Google Scholar] - Romero, D.; Ruedin, A.; Seijas, L. Wavelet-based feature extraction for handwritten numerals. In International Conference on Image Analysis and Processing; Springer: Berlin/Heidelberg, Germany, 2009; pp. 374–383. [Google Scholar] [CrossRef] [Green Version]
- Seijas, L.M.; Segura, E.C. A Wavelet-based Descriptor for Handwritten Numeral Classification. In Proceedings of the International Conference on Frontiers in Handwriting Recognition, Bari, Italy, 18–20 September 2012; pp. 649–654. [Google Scholar]
- Almuttardi, B.; Ambarek, A.; Alshari, K. Handwritten Numeral Recognition Using Wavelet Transform and Neural Networks. In Proceedings of the IEEE International Conference on Cloud Computing Technology and Science (CloudCom 2013), Bristol, UK, 2–5 December 2013; pp. 146–158. [Google Scholar]
- Do, T.N.; Pham, N.K. March. Handwritten digit recognition using GIST descriptors and random oblique decision trees. In The National Foundation for Science and Technology Development (NAFOSTED) Conference on Information and Computer Science; Springer: Cham, Switzerland, 2015; pp. 1–15. [Google Scholar] [CrossRef]
- Belongie, S.; Malik, J.; Puzicha, J. Shape matching and object recognition using shape contexts. IEEE Trans. Pattern Anal. Mach. Intell.
**2002**, 24, 509–522. [Google Scholar] [CrossRef] [Green Version] - Shamim, S.M.; Miah, M.B.A.; Angona Sarker, M.R.; Al Jobair, A. Handwritten digit recognition using machine learning algorithms. Glob. J. Comput. Sci. Technol.
**2018**, 18, 17–23. [Google Scholar] [CrossRef] [Green Version] - Bernard, S.; Adam, S.; Heutte, L. Using Random Forests for Handwritten Digit Recognition. In Proceedings of the Ninth International Conference on Document Analysis and Recognition (ICDAR 2007), Parana, Brazil, 20–26 September 2007; Volume 2, pp. 1043–1047. [Google Scholar] [CrossRef] [Green Version]
- Pandeeswari, B.; Sutha, J.; Parvathy, M. A novel synthetic aperture radar image change detection system using radial basis function-based deep convolutional neural network. J. Ambient. Intell. Humaniz. Comput.
**2020**, 12, 897–910. [Google Scholar] [CrossRef] - Devi, K.U.; Gomathi, R. RETRACTED ARTICLE: Brain tumour classification using saliency driven nonlinear diffusion and deep learning with convolutional neural networks (CNN). J. Ambient. Intell. Humaniz. Comput.
**2020**, 12, 6263–6273. [Google Scholar] [CrossRef] - Rajagopalan, N.; Narasimhan, V.; Vinjimoor, S.K.; Aiyer, J. RETRACTED ARTICLE: Deep CNN framework for retinal disease diagnosis using optical coherence tomography images. J. Ambient. Intell. Humaniz. Comput.
**2020**, 12, 7569–7580. [Google Scholar] [CrossRef] - Hu, W.-C.; Wu, H.-T.; Zhang, Y.-F.; Zhang, S.-H.; Lo, C.-H. Shrimp recognition using ShrimpNet based on convolutional neural network. J. Ambient. Intell. Humaniz. Comput.
**2020**, 1–8. [Google Scholar] [CrossRef] - Ahamed, P.; Kundu, S.; Khan, T.; Bhateja, V.; Sarkar, R.; Mollah, A.F. Handwritten Arabic numerals recognition using convolutional neural network. J. Ambient. Intell. Humaniz. Comput.
**2020**, 11, 5445–5457. [Google Scholar] [CrossRef] - Akhand, M.A.H.; Ahmed, M.; Rahman, M.M.H.; Islam, M. Convolutional Neural Network Training incorporating Rotation-Based Generated Patterns and Handwritten Numeral Recognition of Major Indian Scripts. IETE J. Res.
**2018**, 64, 176–194. [Google Scholar] [CrossRef] [Green Version] - Akhand, M.A.H.; Ahmed, M.; Rahman, M.M.H. Convolutional Neural Network based Handwritten Bengali and Bengali-English Mixed Numeral Recognition. Int. J. Image Graph. Signal Process.
**2015**, 8, 40–50. [Google Scholar] [CrossRef] - Gupta, D.; Bag, S. CNN-based multilingual handwritten numeral recognition: A fusion-free approach. Expert Syst. Appl.
**2020**, 165, 113784. [Google Scholar] [CrossRef] - Fateh, A.; Fateh, M.; Abolghasemi, V. Multilingual handwritten numeral recognition using a robust deep network joint with transfer learning. Inf. Sci.
**2021**, 581, 479–494. [Google Scholar] [CrossRef] - Mahto, M.K.; Bhatia, K.; Sharma, R.K. Deep Learning Based Models for Offline Gurmukhi Handwritten Character and Numeral Recognition. ELCVIA Electron. Lett. Comput. Vis. Image Anal.
**2021**, 20, 69–82. [Google Scholar] [CrossRef] - Alqudah, A.; Alqudah, A.; Alquran, H.; Al-Zoubi, H.; Al-Qodah, M.; Al-Khassaweneh, M. Recognition of Handwritten Arabic and Hindi Numerals Using Convolutional Neural Networks. Appl. Sci.
**2021**, 11, 1573. [Google Scholar] [CrossRef] - Mushtaq, F.; Misgar, M.M.; Kumar, M.; Khurana, S.S. UrduDeepNet: Offline handwritten Urdu character recognition using deep neural network. Neural Comput. Appl.
**2021**, 33, 15229–15252. [Google Scholar] [CrossRef] - Dutta, P.; Muppalaneni, N.B. DigiNet: Prediction of Assamese handwritten digits using convolutional neural network. Concurr. Comput. Pract. Exp.
**2021**, 33, e6451. [Google Scholar] [CrossRef] - Bhattacharya, U. Offline Handwritten Bangla and Devanagari Numeral Databases. 2009. Available online: https://www.isical.ac.in/~ujjwal/download/database.html (accessed on 27 December 2022).
- Bhattacharya, U.; Chaudhuri, B. Handwritten Numeral Databases of Indian Scripts and Multistage Recognition of Mixed Numerals. IEEE Trans. Pattern Anal. Mach. Intell.
**2008**, 31, 444–457. [Google Scholar] [CrossRef] [PubMed] - Singh, P.; Verma, A.; Chaudhari, N.S. Devanagri Handwritten Numeral Recognition using Feature Selection Approach. Int. J. Intell. Syst. Appl.
**2014**, 6, 40–47. [Google Scholar] [CrossRef] - Arya, S.; Chhabra, I.; Lehal, G.S. Recognition of Devnagari Numerals using Gabor Filter. Indian J. Sci. Technol.
**2015**, 8, 1–6. [Google Scholar] [CrossRef] - Prabhanjan, S.; Dinesh, R. Handwritten Devanagari Characters and Numeral Recognition using Multi-Region Uniform Local Binary Pattern. Int. J. Multimedia Ubiquitous Eng.
**2016**, 11, 387–398. [Google Scholar] [CrossRef] - Guha, R.; Ghosh, M.; Singh, P.K.; Sarkar, R.; Nasipuri, M. M-HMOGA: A New Multi-Objective Feature Selection Algorithm for Handwritten Numeral Classification. J. Intell. Syst.
**2019**, 29, 1453–1467. [Google Scholar] [CrossRef] - Shopon, M.; Mohammed, N.; Abedin, M.A. Bangla handwritten digit recognition using autoencoder and deep convolutional neural network. In Proceedings of the 2016 International Workshop on Computational Intelligence (IWCI), Dhaka, Bangladesh, 11–13 December 2016; pp. 64–68. [Google Scholar] [CrossRef]
- Jia, Y.; Huang, C.; Darrell, T. Beyond spatial pyramids: Receptive field learning for pooled image features. In Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition, Washington, DC, USA, 16–21 June 2012; pp. 3370–3377. [Google Scholar] [CrossRef] [Green Version]
- Akhand, M.A.H. Deep Learning Fundamentals—A Practical Approach to Understanding Deep Learning Methods; University Grants Commission of Bangladesh: Dhaka, Bangladesh, 2021. [Google Scholar]
- Zhang, T.Y.; Suen, C.Y. A fast parallel algorithm for thinning digital patterns. Commun. ACM
**1984**, 27, 236–239. [Google Scholar] [CrossRef] - Chen, Y.-S.; Hsu, W.-H. A modified fast parallel algorithm for thinning digital patterns. Pattern Recognit. Lett.
**1988**, 7, 99–106. [Google Scholar] [CrossRef] - Akhand, M.; Ayon, S.I.; Shahriyar, S.; Siddique, N.; Adeli, H. Discrete Spider Monkey Optimization for Travelling Salesman Problem. Appl. Soft Comput.
**2019**, 86, 105887. [Google Scholar] [CrossRef] - Daszykowski, M.; Walczak, B. Density-Based Clustering Methods. In Comprehensive Chemometrics; Elsevier: Amsterdam, The Netherlands, 2009; pp. 635–654. [Google Scholar] [CrossRef]
- Ester, M.; Kriegel, H.P.; Sander, J.; Xu, X. A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise. In Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining, Portland, OR, USA, 2–4 August 1996; pp. 226–231. [Google Scholar]
- Wen, Y.; He, L. A classifier for Bangla handwritten numeral recognition. Expert Syst. Appl.
**2012**, 39, 948–953. [Google Scholar] [CrossRef] - Basu, D.K.; Nasipuri, M.; Kundu, M.; Basu, S.; Das, N.; Sarkar, R.; Mollah, A.F.; Saha, S. CMATERdb 3.1.1 & CMATERdb 3.2.1: Handwritten Bangla and Devanagari Numeral Databases; Center for Microprocessor Application for Training Education and Research, Jadavpur University: Kolkata, India, 2011. [Google Scholar]
- Kumar, R.; Ravulakollu, K.K. Handwritten devnagari digit recognition: Benchmarking on new dataset. J. Theor. Appl. Inf. Technol.
**2014**, 60, 543–555. [Google Scholar] - Singh P., K.; Sarkar, R.; Nasipuri, M. A Study of Moment Based Features on Handwritten Digit Recognition. Appl. Comput. Intell. Soft Comput.
**2016**, 2016, 1–17. [Google Scholar] [CrossRef] [Green Version] - Shopon, M.; Mohammed, N.; Abedin, M.A. Image augmentation by blocky artifact in Deep Convolutional Neural Network for handwritten digit recognition. In Proceedings of the 2017 IEEE International Conference on Imaging, Vision & Pattern Recognition (icIVPR), Dhaka, Bangladesh, 13–14 February 2017; pp. 1–6. [Google Scholar] [CrossRef]

**Figure 3.**Demonstration of writing start (* marked) and end (# marked) points identification on a sample image.

**Figure 4.**Numeral-wise start and end points marking on sample images; and start and end reference points marking on printed numerals.

English Numeral | Bengali Numeral | Sample Bengali Handwritten Numeral Images | Devanagari Numeral | Sample Devanagari Handwritten Numeral Images | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

0 | ০ | ० | ||||||||||

1 | ১ | १ | ||||||||||

2 | ২ | २ | ||||||||||

3 | ৩ | ३ | ||||||||||

4 | ৪ | ४ | ||||||||||

5 | ৫ | ५ | ||||||||||

6 | ৬ | ६ | ||||||||||

7 | ৭ | ७ | ||||||||||

8 | ৮ | ८ | ||||||||||

9 | ৯ | ९ |

**Table 2.**Test set recognition accuracy of CNN and proposed SEWM-CNN with different threshold values for different batch sizes.

(a) Bengali | |||||

Batch Size | Recognition accuracy (%) of CNN | Recognition accuracy (%) of proposed SEWM-CNN with different σ_{0} values | |||

0.5 | 0.6 | 0.7 | 0.8 | ||

8 | 98.98 | 99.13 | 99.20 | 99.10 | 99.03 |

16 | 98.98 | 99.03 | 99.20 | 99.03 | 99.0 |

32 | 98.60 | 98.70 | 98.85 | 98.83 | 98.65 |

64 | 98.58 | 98.68 | 98.80 | 98.73 | 98.60 |

128 | 98.43 | 98.58 | 98.65 | 98.60 | 98.48 |

(b) Devanagari | |||||

Batch Size | Recognition accuracy (%) of CNN | Recognition accuracy (%) of proposed SEWM-CNN with different σ_{0} values | |||

0.5 | 0.6 | 0.7 | 0.8 | ||

8 | 99.08 | 99.13 | 99.23 | 99.10 | 99.08 |

16 | 99.10 | 99.15 | 99.23 | 99.15 | 99.13 |

32 | 98.78 | 98.88 | 98.90 | 98.85 | 98.83 |

64 | 98.78 | 98.85 | 98.83 | 98.78 | 98.75 |

128 | 98.50 | 98.58 | 98.70 | 98.55 | 98.53 |

(a) Bengali | |||||

Bengali Numeral | Total Samples | CNN | SEWM-CNN | ||

Truly Classified | Misclassification to Other Numerals and Count | Truly Classified | Misclassification to Other Numerals and Count | ||

0 | 400 | 399 | ৫(1) | 399 | ৯(1) |

১ | 400 | 382 | ২(1)-৪(1)-৫(2)-৬(1)-৭(1)-৯(12) | 384 | ২(1)-৪(3)-৫(2)-৭(2)-৮(1)-৯(7) |

২ | 400 | 398 | ৫(1)-৯(1) | 399 | ৮(1) |

৩ | 400 | 400 | - | 399 | 0(1) |

৪ | 400 | 400 | - | 399 | ৫(1) |

৫ | 400 | 394 | ২(2)-৪(2)-৬(1)-৭(1) | 395 | ১(1)-২(1)-৭(1)-৮(1)-৯(1) |

৬ | 400 | 397 | ৩(1)-৫(2) | 398 | 0(1)-১(1) |

৭ | 400 | 399 | ৬(1) | 399 | ৪(1) |

৮ | 400 | 400 | - | 398 | ২(1)-৩(1) |

৯ | 400 | 390 | ১(8)-৬(1)-৭(1) | 398 | ৬(1)-৭(1) |

Total | 4000 | 3959 | 41 | 3968 | 32 |

(b) Devanagari | |||||

Devanagari Numeral | Total Samples | CNN | SEWM-CNN | ||

Truly Classified | Misclassification to Other Numerals and Count | Truly Classified | Misclassification to Other Numerals and Count | ||

० | 369 | 364 | ४(1)-७(3)-८(1) | 364 | ४(1)-७(3)-८(1) |

१ | 378 | 376 | ०(1)-३(1) | 376 | ०(1)-३(1) |

२ | 378 | 376 | १(1)-५(1) | 376 | १(1)-५(1) |

३ | 377 | 375 | ६(1)-९(1) | 374 | ५(1)-६(1)-९(1) |

४ | 376 | 372 | ०(1)-५(3) | 374 | ०(1)-५(1) |

५ | 378 | 370 | ३(1)-४(7) | 374 | ३(2)-४(2) |

६ | 374 | 367 | ३(1)-८(1)-९(5) | 370 | ३(1)-८(1)-९(2) |

७ | 378 | 377 | ०(1) | 377 | ०(1) |

८ | 377 | 376 | ५(1) | 374 | ५(2)-९(1) |

९ | 378 | 374 | ६(4) | 375 | ६(2)-८(1) |

Total | 3763 | 3727 | 36 | 3734 | 29 |

(a) Bengali | ||||

Sl. | Handwritten Image | CL_{CNN}-CL_{Sys}-True Category | Remarks on the Sample. N.B.: σ_{0} = 0.6 | |

Samples for SEWM rectified CNN’s Wrong Decision | 1 | ১-৯-৯ | σ_{CNN} = 0.53 and CL_{Sys} = CL_{SEWM} = 9 (i.e., ৯) | |

2 | ১-৯-৯ | σ_{CNN} = 0.54 and CL_{Sys} = CL_{SEWM} = 9 (i.e., ৯) | ||

3 | ৯-১-১ | σ_{CNN} = 0.46 and CL_{Sys} = CL_{SEWM} = 1 (i.e., ১) | ||

Samples for SEWM-CNN Misclassified | 4 | ৯-৯-১ | σ_{CNN} = 0.59 and CL_{Sys} = CL_{SEWM} = 9 (i.e., ৯) | |

5 | ৩-0-৬ | σ_{CNN} = 0.51 but CL_{Sys} = CL_{SEWM} = 0 (i.e.,0) | ||

6 | ৪-৪-৭ | σ_{CNN} = 0.67, so CL_{Sys} = CL_{CNN} = 4 (i.e., ৪) ignoring SEWM | ||

(b) Devanagari | ||||

Sl. | Handwritten Image | CL_{CNN}-CL_{Sys}-True Category | Remarks on the Sample. N.B.: σ_{0} = 0.6 | |

Samples for SEWM rectified CNN’s Wrong Decision | 1 | ४-५-५ | σ_{CNN} = 0.52 and CL_{Sys} = CL_{SEWM} = 5 (i.e., ५) | |

2 | ४-५-५ | σ_{CNN} = 0.55 and CL_{Sys} = CL_{SEWM} = 5 (i.e., ५) | ||

3 | ५-४-४ | σ_{CNN} = 0.49 and CL_{Sys} = CL_{SEWM} = 4 (i.e., ४) | ||

Samples for SEWM-CNN Misclassified | 4 | ८-८-० | σ_{CNN} = 0.48 and CL_{Sys} = CL_{SEWM} = 8 (i.e., ८) | |

5 | ९–९–६ | σ_{CNN} = 0.54 and CL_{Sys} = CL_{SEWM} = 9 (i.e., ९) | ||

6 | ०-०-१ | σ_{CNN} = 0.69, so CL_{Sys} = CL_{CNN} = 0 (i.e., ०) ignoring SEWM |

**Table 5.**Comparison of proposed SEWM-CNN with prominent methods for Bengali and Devanagari HNR in terms of recognition accuracy, dataset used and method’s significance.

Work Reference | Dataset, Ref.; Training and Test Samples | Recognition Accuracy | Method’s Significance in Feature Selection and Classification | |
---|---|---|---|---|

Bengali | Devanagari | |||

Wen et al., 2007 [2] | Postal system; 6000 and 10,000 | 95.05% | - | PCA-based feature selection and SVM for classification. |

Bhattacharya and Chaudhuri, 2009 [31] | ISI [30]; 19,392 and 4000 | 98.20% | 99.04% | Wavelet filter-based feature selection and cascade of four MLPs for classification. |

Wen and He, 2012 [44] | Postal system; 30,000 and 15,000 | 96.91% | - | Feature selection using eigenvalues and eigenvectors and classification using kernel and Bayesian discriminant. |

Das et al., 2012 [3] | CMATERdb 3.1.1 [45]; 4000 and 2000 | 97.70% | - | Feature selection in different stages using GA and classification using SVM. |

Nasir and Uddin, 2013 [4] | Self-prepared, 300 | 96.80% | - | Bayes’ theorem, k-means clustering and Maximum Posteriori for feature selection and SVM for classification. |

Kumar and Ravulakollu, 2014 [46] | CPAR-2012 [46]; 24,000 and 11,000 | - | 97.87% | Features are based on profile and gradient and classification using NNs (in ensemble and cascade manners) and KNN. |

Singh et al., 2014 [32] | Samples from ISI [30]; 1400 and 600 | - | 98.53% | Feature selection using information theoretic-based MRMR and classification using NNs and ensemble of NNs. |

Arya et al., 2015 [33] | ISI [30]; 19,798 and 3763 | - | 98.06% | Feature selection using Gabor filter and classification using KNN and SVM. |

Singh et al., 2016 [47] | CMATERdb 3.2.1 [45]; 2000 and 1000 | - | 98.92% | Moment based six different features and classification using MLP. |

Guha et al., 2019 [35] | Self-prepared + Samples from ISI [30]; 10,000 and 500 | 98.40% | 97.60% | Memory-Based Histogram + GA for feature selection and KNN for classification. |

98.05% | 95.05% | Memory-Based Histogram + GA for feature selection and MLPs for classification. | ||

Akhand et al., 2016 [23] | ISI [30]; 18,000 and 4000 | 98.45% | - | Standard CNN |

Shopon et al., 2016 [48] | ISI [30]; 19,313 and 3986 | 98.29% | - | Auto-encoder (AE) with CNN |

Akhand et al., 2018 [22] | ISI [30]; 18,000 and 4000 (Bengali)/3763 (Devanagari) | 98.98% | 99.31% | Ensemble of three CNNs; one is trained with available samples and other two used rotation based generated data. |

98.96% | 98.96% | CNN is trained using available data plus rotation based generated data. | ||

Proposed SEWM-CNN | ISI [30]; 18,000 and 4000 (Bengali)/3763 (Devanagari) | 99.20% | 99.23% | Start-end Writing Measure is integrated with CNN’s decision. |

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## Share and Cite

**MDPI and ACS Style**

Akhand, M.A.H.; Rahat-Uz-Zaman, M.; Hye, S.; Kamal, M.A.S.
Handwritten Numeral Recognition Integrating Start–End Points Measure with Convolutional Neural Network. *Electronics* **2023**, *12*, 472.
https://doi.org/10.3390/electronics12020472

**AMA Style**

Akhand MAH, Rahat-Uz-Zaman M, Hye S, Kamal MAS.
Handwritten Numeral Recognition Integrating Start–End Points Measure with Convolutional Neural Network. *Electronics*. 2023; 12(2):472.
https://doi.org/10.3390/electronics12020472

**Chicago/Turabian Style**

Akhand, M. A. H., Md. Rahat-Uz-Zaman, Shadmaan Hye, and Md Abdus Samad Kamal.
2023. "Handwritten Numeral Recognition Integrating Start–End Points Measure with Convolutional Neural Network" *Electronics* 12, no. 2: 472.
https://doi.org/10.3390/electronics12020472