Log in

Machine learning and non-machine learning methods in mathematical recognition systems: Two decades’ systematic literature review

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

Tools based on machine learning (ML) have seen widespread application in the prediction and categorization of mathematical symbols and phrases. The purpose of this work is to conduct a comprehensive analysis of the machine learning and non-machine learning strategies that are currently in use for the recognition of mathematical expressions. (MEs). The authors collected and analyzed research studies on the recognition of MEs (and closely related models and issues as well), which are published from January 2000 to December 2022 in the SLR. The review has nominated 98 primary studies out of the extracted 202 studies after heedful filtering using inclusion/exclusion criteria and quality assessment. The pertinent data is derived from IEEE explore, Science Direct, Wiley, Scopus, ACM Digital Library, etc. For assiduously reviewing and synthesizing the data, the authors used grounded theory and other qualitative and quantitative techniques. The analysis reveals that the support vector machine as an ML model with CROHME as the dataset and expression recognition rate as an accuracy metric is frequently used in the chosen studies. Recognition is typically fragmented down into three stages—segmenting symbols, recognizing symbols, and analyzing structures—in non-ML studies. In conclusion, this work aims to synthesize the results of existing research to provide a summary of the state-of-the-art in recognizing handwritten MEs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

Data Availability

My manuscript has no associated data.

References

  1. Afshan N, Afshar Alam M, Ali Mehdi S (2017) An Analysis of Mathematical Expression Recognition Techniques. Int J Adv Res Comput Sci 8(5):2021–2026 www.ijarcs.info

    Google Scholar 

  2. Aggarwal R, Harit G, Tiwari A (2020) Structural analysis of offline handwritten mathematical expressions. Proceedings of 3rd International Conference on Computer Vision and Image Processing. (Springer, Singapore) 1024:213–225

  3. Ahmed M, Ward R, Kharma N (2004) Solving mathematical problems using knowledge-based systems. Math Comput Simul 67(1–2):149–161. https://doi.org/10.1016/j.matcom.2004.05.015

    Article  MathSciNet  Google Scholar 

  4. Ali A, Gravino C (2019) A systematic literature review of software effort prediction using machine learning methods. Journal of Software: Evolution and Process 31(10):1–25. https://doi.org/10.1002/smr.2211

    Article  Google Scholar 

  5. Alvaro F (2015) Mathematical expression recognition based on probabilistic grammars [Departamento de Sistemas Inform’aticos y Computaci’on, Universitat Polit’ecnica de Val’encia]. 10.1.1.1031.2330

  6. Álvaro F, Sánchez JA (2010) Comparing several techniques for offline recognition of printed mathematical symbols. International Conference on Pattern Recognition 1953–1956. https://doi.org/10.1109/ICPR.2010.481

  7. Álvaro F, Sánchez JA, Benedí JM (2011) Recognition of printed mathematical expressions using two-dimensional stochastic context-free grammars. International Conference on Document Analysis and Recognition, 1225–1229. https://doi.org/10.1109/ICDAR.2011.247

  8. Álvaro F, Sánchez JA, Benedí JM (2012) Unbiased evaluation of handwritten mathematical expression recognition. International Conference on Frontiers in Handwriting Recognition 181–186. https://doi.org/10.1109/ICFHR.2012.287

  9. Álvaro F, Sánchez JA, Benedí JM (2013) An image-based measure for evaluation of mathematical expression recognition. Iberian Conference on Pattern Recognition and Image Analysis IbPRIA 2013: Pattern Recognition and Image Analysis. LNCS 7887:682–690. https://doi.org/10.1007/978-3-642-38628-2_81

    Article  Google Scholar 

  10. Álvaro F, Sánchez JA, Benedí JM (2014) Recognition of on-line handwritten mathematical expressions using 2D stochastic context-free grammars and hidden Markov models. Pattern Recogn Lett 35(1):58–67. https://doi.org/10.1016/j.patrec.2012.09.023

    Article  Google Scholar 

  11. Alvaro F, Sanchez JA, Benedi JM, Sánchez J-A, Benedí JM (2014) Offline features for classifying handwritten math symbols with recurrent neural networks. 22nd International Conference on Pattern Recognition, 2944–2949. https://doi.org/10.1109/ICPR.2014.507

  12. Álvaro F, Sánchez JA, Benedí JM (2016) An integrated grammar-based approach for mathematical expression recognition. Pattern Recogn 51:135–147. https://doi.org/10.1016/j.patcog.2015.09.013

    Article  ADS  Google Scholar 

  13. Aly W, Uchida S, Suzuki M (2008) Identifying subscripts and superscripts in mathematical documents. Math Comput Sci 2(2):195–209. https://doi.org/10.1007/s11786-008-0051-9

    Article  Google Scholar 

  14. Aly W, Uchida S, Fujiyoshi A, Suzuki M (2009) Statistical classification of spatial relationships among mathematical symbols. 2009 10th International Conference on Document Analysis and Recognition, i, 1350–1354. https://doi.org/10.1109/ICDAR.2009.90

  15. Anderson RH (1967) Syntax-directed recognition of hand-printed two-dimensional mathematics. Symposium on interactive systems for experimental applied mathematics: proceedings of the Association for Computing Machinery Inc. Symposium 436–459. https://doi.org/10.1145/2402536.2402585

  16. Arora S, Bhattacharjee D, Nasipuri M, Basu DK, Kundu M (2008) Combining multiple feature extraction techniques for Handwritten Devnagari Character recognition. Proceedings of IEEE Region 10 Colloquium and 3rd International Conference on Industrial and Information Systems, ICIIS 2008 1–6. https://doi.org/10.1109/ICIINFS.2008.4798415

  17. Ashiquzzaman A, Tushar AK, Rahman A (2017) Handwritten Arabic numeral recognition using deep learning neural networks. Proceedings of IEEE International Conference on Imaging, Vision and Pattern Recognition, IcIVPR 2017(2):1–4. https://doi.org/10.1109/ICIVPR.2017.7890866

    Article  Google Scholar 

  18. Awal AM, Mouchère H, Viard-Gaudin C (2009) Towards handwritten mathematical expression recognition. 2009, 10th International Conference on Document Analysis and Recognition 1046–1050. https://doi.org/10.1109/ICDAR.2009.71

  19. Awal A-MM, Mouchère H, Viard-Gaudin C (2010) The problem of handwritten mathematical expression recognition evaluation. 12th International Conference on Frontiers in Handwriting Recognition 646–651. https://doi.org/10.1109/ICFHR.2010.106

  20. Awal A-M, Mouchère H, Viard-Gaudin C (2010a) A hybrid classifier for handwritten mathematical expression recognition. Document Recognition and Retrieval XVII 7534:753410. https://doi.org/10.1117/12.840023

    Article  Google Scholar 

  21. Awal A-M, Mouchère H, Viard-Gaudin C (2010b) Improving online handwritten mathematical expressions recognition with contextual modeling. Twelveth International Conference on Frontiers in Handwriting Recognition 427–432. https://doi.org/10.1109/ICFHR.2010.73

  22. Awal AM, Mouchère H, Viard-Gaudin C (2014) A global learning approach for an online handwritten mathematical expression recognition system. Pattern Recogn Lett 35(1):68–77. https://doi.org/10.1016/j.patrec.2012.10.024

    Article  Google Scholar 

  23. Bage DD, Adhiya KP, Gharde SS (2010) a New Approach for Recognizing Offline Handwritten Mathematical Symbols using character geometry. International Journal of Innovative Research in Science, Engineering and Technology 2(7):2823–2830

    Google Scholar 

  24. Baker JB, Sexton AP, Sorge V (2010) Faithful mathematical formula recognition from PDF documents. 9th IAPR International Workshop on Document Analysis Systems 485–492. https://doi.org/10.1145/1815330.1815393

  25. Basu S, Das N, Sarkar R, Kundu M, Nasipuri M, Basu DK (2005) An MLP based approach for recognition of handwritten “Bangla” numerals. Proceedings of the 2nd Indian International Conference on Artificial Intelligence, IICAI 2005 407–417

  26. Belaid A, Haton JP (1984) a syntactic approach for handwritten mathematical formula recognition. IEEE Trans Pattern Anal Mach Intell PA(1):105–111. https://doi.org/10.1109/TPAMI.1984.4767483

    Article  Google Scholar 

  27. Bharambe M (2015) recognition of offline handwritten mathematical expressions. National Conference on Digital Image and Signal Proceeding 35–39

  28. Bott JN, Gabriele D, LaViola JJ (2011) Now or later: An initial exploration into user perception of mathematical expression recognition feedback. Proceedings - SBIM 2011: ACM SIGGRAPH / Eurographics Symposium on Sketch-Based Interfaces and Modeling, 1:125–132. https://doi.org/10.1145/2021164.2021187

  29. Brereton P, Kitchenham BA, Budgen D, Turner M, Khalil M (2007) Lessons from applying the systematic literature review process within the software engineering domain. J Syst Softw 80(4):571–583. https://doi.org/10.1016/j.jss.2006.07.009

    Article  Google Scholar 

  30. Bryant A, Charmaz K, Urquhart C (2012) The evolving nature of grounded theory method: The case of the information systems discipline. In: The SAGE Handbook of Grounded Theory https://doi.org/10.4135/9781848607941.n16

  31. Büyükbayrak H, Yanikoglu B (2007) Online handwritten mathematical expression recognition. Document recognition and retrieval XIV (International Society for Optics and Photonics), 6500, 65000

  32. Campanelli AS, Parreiras FS (2015) Agile methods tailoring - A systematic literature review. J Syst Softw 110:85–100. https://doi.org/10.1016/j.jss.2015.08.035

    Article  Google Scholar 

  33. Cao Y, **e Z, Li L (2019) Research on identification of handwritten mathematical formulas. International Conference on Applications and Techniques in Cyber Security and Intelligence,Springer, Cham., 1, 1494–1500.

  34. Celar S, Stojkic Z, Seremet Z, Marusic Z, Zelenika D (2015) Classification of test documents based on handwritten student ID’s characteristics. Procedia Engineering 100:782–790. https://doi.org/10.1016/j.proeng.2015.01.432

    Article  Google Scholar 

  35. Celik M, Yanikoglu B (2011) Probabilistic mathematical formula recognition using a 2D context-free graph grammar. International Conference on Document Analysis and Recognition 161–166. https://doi.org/10.1109/ICDAR.2011.41

  36. Chajri Y, Bouikhalene B (2016) Handwritten mathematical expressions recognition. International Journal of Signal Processing, Image Processing and Pattern Recognition 9(5):69–76. https://doi.org/10.14257/ijsip.2016.9.5.07

    Article  Google Scholar 

  37. Chan C (2020) Stroke extraction for offline handwritten mathematical expression recognition. IEEE Access 8:61565–61575. https://doi.org/10.1109/ACCESS.2020.2984627

    Article  Google Scholar 

  38. Chan K-F, Yeung DYD (2000a) An Efficient syntactic approach to structural analysis of on-line handwritten mathematical expressions. Pattern Recogn 33(3):375–384. https://doi.org/10.1016/S0031-3203(99)00067-9

    Article  ADS  Google Scholar 

  39. Chan KF, Yeung DY (2000b) Mathematical expression recognition: A survey. International Journal on Document Analysis and Recognition(IJDAR) 3(1):3–15. https://doi.org/10.1007/PL00013549

    Article  MathSciNet  Google Scholar 

  40. Chan K-F, Yeung D (2001a) Pencalc: A novel application of on-line mathematical expression recognition technology. Proceedings of Sixth International Conference on Document Analysis and Recognition. IEEE, 274–278

  41. Chan K-F, Yeung DY (2001b) Error detection, error correction and performance evaluation in on-line mathematical expression recognition. Pattern Recogn 34(8):1671–1684. https://doi.org/10.1016/S0031-3203(00)00102-3

    Article  ADS  Google Scholar 

  42. Chaudhuri BB, Garain U (2013) An approach for recognition and interpretation of mathematical expressions in printed document. Pattern Analysis & Applications 3(2):120–131

    Article  Google Scholar 

  43. Chen Y, Okada M (2001) Structural analysis and semantic understanding for offline mathematical expressions. Int J Pattern Recognit Artif Intell 15(EC06):967–987. https://doi.org/10.1142/S021800140100126X

    Article  Google Scholar 

  44. Chen X, Sun H, Tobe Y, Zhou Z, Sun X (2015) Coverless information hiding method based on the chinese mathematical expression. Proceedings of International Conference on Cloud Computing and Security, Springer Cham 9483:133–143. https://doi.org/10.1007/978-3-319-27051-7

    Article  Google Scholar 

  45. Choudhary A, Ahlawat S, Gupta H, Bhandari A, Dhall A, Kumar M (2021) Offline handwritten mathematical expression evaluator using convolutional neural network. International Conference on Innovative Computing and Communications, pp. 527–537

  46. Clark R, Kung Q, Van Wyk A (2013) System for the recognition of online handwritten mathematical expressions. Eurocon 2013:2029–2035. https://doi.org/10.1016/j.ympev.2006.04.014

    Article  CAS  Google Scholar 

  47. Code C, Asst EO, Naik B (2013) A shape-based layout descriptor for classifying spatial relationships in handwritten math. Proceedings of the 2013 ACM Symposium on Document Engineering pp 123–126

  48. Corbin J, Strauss A, Department of Social and Behavioral Sciences. University of California (2016) Grounded Theory Research: Procedures, Canons and Evaluative Criteria. Qual Sociol 19(6):418–427. https://doi.org/10.1515/zfsoz-1990-0602

    Article  Google Scholar 

  49. Da Silva W, Silva CE (2014) Mathematical models to describe thin-layer drying and to determine drying rate of whole bananas. J Saudi Soc Agric Sci 13(1):67–74 https://www.sciencedirect.com/science/article/pii/S1658077X13000040

    Google Scholar 

  50. Dagenais B, Ossher H, Bellamy RKE, Robillard MP, De Vries JP (2009) A qualitative study on project landscapes. Proceedings of the 2009 ICSE Workshop on Cooperative and Human Aspects on Software Engineering, CHASE. 2009:32–35. https://doi.org/10.1109/CHASE.2009.5071407

  51. Dai Nguyen H, Duc Le A, Nakagawa M (2016) Recognition of online handwritten math symbols using deep neural networks. IEICE Trans Inf Syst, 3110–3118. https://doi.org/10.1587/transinf.2016EDP7102

  52. Dai J, Sun Y, Su G, Ye S, Sun Y (2019) Recognizing offline handwritten mathematical expressions efficiently. 10th International Conference on E-Education, E-Business, E-Management and E-Learning, pp 198–204. https://doi.org/10.1145/3306500.3306543

  53. Davila K, Zanibbi R (2017) Layout and semantics: Combining representations for mathematical formula search. Proceedings of the 40th International ACM SIGIR Conference on Research and Development in Information Retrieval(SIGIR), pp 1165–1168. https://doi.org/10.1145/3077136.3080748

  54. Drsouza L, Mascarenhas M (2018) Offline handwritten mathematical expression recognition using convolutional neural network. International Conference on Information, Communication, Engineering and Technology, pp 1–3. https://doi.org/10.1109/ICICET.2018.8533789

  55. Eto Y, Suzuki M (2001) Mathematical formula recognition using virtual link network. Proceedings of Sixth International Conference on Document Analysis and Recognition, pp 762–767. https://doi.org/10.1109/icdar.2001.953891

  56. Fahmy H, Blostein D (1993) A graph grammar programming style for recognition of music notation. Mach Vis Appl 6(2–3):83–99. https://doi.org/10.1007/BF01211933

    Article  Google Scholar 

  57. Fang D, Zhang C (2020) Multi-feature Learning by Joint Training for Handwritten Formula Symbol Recognition. IEEE Access 8(2):48101–48109. https://doi.org/10.1109/ACCESS.2020.2979346

    Article  Google Scholar 

  58. Farulla GA, Armano T, Capietto A, Murru N, Rossini R (2016) Artificial neural networks and fuzzy logic for recognizing alphabet characters and mathematical symbols. International Conference on Computers Hel** People with Special Needs, 7–14. https://doi.org/10.1007/978-3-319-41264-1_1

  59. Feng X, Shiiba K, Okazaki Y, Okamoto M, Kondo H (2001) Java based on-line handwriting interface for mathematical expression and its character recognition performance character recognition. 85th Technology Research Meeting of JSISE (Japanese Society for Information and Systems in Education), 1–8

  60. Fitzgerald J, Geiselbrechtinger F, Kechadi M (2006) Structural analysis of handwritten mathematical expressions through fuzzy parsing. ACST 6:151–156

    Google Scholar 

  61. Fitzgerald JA, Geiselbrechtinger F, Kechadi T (2007) Mathpad: A fuzzy logic-based recognition system for handwritten mathematics. Ninth International Conference on Document Analysis and Recognition 2:694–698. https://doi.org/10.1109/ICDAR.2007.4377004

    Article  Google Scholar 

  62. Fontenele Marques Junior FDC, Pontes De Araujo T, Moura Sousa JV, Carvalho Da Costa NJ, Teixeira Melo R, Martins Pinto A, Andrade Saraiva A, F MJFC, Ara D, P T (2019) Recognition of simple handwritten polynomials using segmentation with fractional calculus and convolutional neural networks. 8th Brazilian Conference on Intelligent Systems. pp 245–250. https://doi.org/10.1109/BRACIS.2019.00051

  63. Garain U (2005) Automatic recognition of printed and handwritten mathematical expressions. Indian Institute of Statistics, Kolkata

    Google Scholar 

  64. Garain U (2009) Identification of mathematical expressions in document images. In: 10th International Conference on Document Analysis and Recognition, pp 1340–1344. https://doi.org/10.1109/ICDAR.2009.203

    Chapter  Google Scholar 

  65. Garain U, Chaudhuri B (2002) On development and statistical analysis of a corpus for printed and handwritten mathematical expressions Computer Science Preprint Archive Available at SSRN: Https://Ssrn.Com/Abstract=3125396 2002(7):689–699

    Google Scholar 

  66. Garain U, Chaudhuri BB (2005) A corpus for OCR research on mathematical expressions. Int J Doc Anal Recognit 7(4):241–259. https://doi.org/10.1007/s10032-004-0140-5

    Article  Google Scholar 

  67. Garain U, Chaudhuri B (2007) OCR of printed mathematical expressions. Springer, London, Digital Document Processing. https://doi.org/10.1109/isscc.1986.1156961

    Book  Google Scholar 

  68. Garst, P. (2004). Modeless gesture-driven editor for handwritten mathematical expressions (Patent No. US 2004/0054701 A1). In Mathsoft Engineering & Education Inc, 2004, U.S. Patent Application No. 10/378,386. (US 2004/0054701 A1). https://doi.org/10.4324/9781315853178

  69. Genoe R, Fitzgerald J, Kechadi T. (2006a) A purely online approach to mathematical expression recognition. International Workshop on Frontiers in Handwriting Recognition pp 1–6. iffinria-00104890f

  70. Genoe Ray, Fitzgerald JA, Kechadi T (2006b) An online fuzzy approach to the structural analysis of handwritten mathematical expressions. IEEE International Conference on Fuzzy Systems pp 244–250. https://doi.org/10.1109/FUZZY.2006.1681721

  71. Gharde SS (2012) Evaluation of classification and feature extraction techniques for simple mathematical equations. International Journal of Applied Information Systems 1(5):34–38

    Article  ADS  Google Scholar 

  72. Gharde SS, Baviskar PV, Adhiya KP (2013) Identification of handwritten simple mathematical equation based on SVM and projection histogram. ACM Symposium on Document Engineering 3(2):425–429

    Google Scholar 

  73. Glaser BG, Strauss AL, Strutzel E (1968) The discovery of grounded theory: Strategies for qualitative research. Nursing Research Journal 17(4):364

    Article  Google Scholar 

  74. Gong Y, Li S, Wang X, Wang X (2015) Real-time recognition method of understanding on-line handwritten mathematical expression. Computer Engineering and Applications Journal 7:43

    Google Scholar 

  75. Han F, Zhu S (2005) Bottom-up / Top-Down Image Parsing by Attribute Graph Grammar. Tenth IEEE International Conference on Computer Vision 1778–1785. https://doi.org/10.1109/ICCV.2005.50

  76. Hirata N, Honda W (2011) Automatic labeling of handwritten mathematical symbols via expression matching. Graph-Based Representations in Pattern Recognition. GbRPR 2011. Lecture Notes in Computer Science pp 295–304. https://doi.org/10.1177/107808747000500401

  77. Hirata NST, Julca-Aguilar NST, Julca-Aguilar F (2015) Matching based ground-truth annotation for online handwritten mathematical expressions. Pattern Recogn 48(3):837–848. https://doi.org/10.9790/7388-05621214

    Article  ADS  Google Scholar 

  78. Hong Z, You N, Tan J, Bi N (2019) Residual BiRNN based Seq2Seq model with transition probability matrix for online handwritten mathematical expression recognition. International Conference on Document Analysis and Recognition pp 635–640. https://doi.org/10.1109/ICDAR.2019.00107

  79. Hordri NF, Samar A, Yuhaniz SS, Shamsuddin SM (2017) A systematic literature review on features of deep learning in big data analytics. Proceedings of International Journal of Advances in Soft Computing and Its Applications 9(1):32–49

    Google Scholar 

  80. Hossain MB, Naznin F, Joarder YA, Zahidul Islam M, Uddin MJ (2018) Recognition and solution for handwritten equation using convolutional neural network. 2018 Joint 7th International Conference on Informatics, Electronics & Vision (ICIEV) and 2018 2nd International Conference on Imaging, Vision & Pattern Recognition pp 250–255. https://doi.org/10.1109/ICIEV.2018.8640991

  81. Hu L, Zanibbi R (2016) MST-based visual parsing of online handwritten mathematical expressions. 15th International Conference on Frontiers in Handwriting Recognition 337–342. https://doi.org/10.1109/ICFHR.2016.0070

  82. Hu L, Hart K, Pospesel R, Zanibbi R (2012) Baseline extraction-driven Parsing of handwritten mathematical expressions. 21st International Conference on Pattern Recognition pp 326–330

  83. Hu Y, Peng L, Tang Y (2014) On-line handwritten mathematical expression recognition method based on statistical and semantic analysis. 11th IAPR International Workshop on Document Analysis Systems pp 171–175. https://doi.org/10.1109/DAS.2014.47

  84. Huang BQ, Kechadi MM (2007) A structural analysis approach for online handwritten mathematical expressions. International Journal of Computer Science and Network Security 7(7):47–56. https://doi.org/10.1142/9789812837042_0014

    Article  Google Scholar 

  85. Huang BQ, Zhang YB, Kechadi MT (2007) Preprocessing Techniques for Online Handwriting Recognition. Seventh International Conference on Intelligent Systems Design and Applications pp 793–800. https://doi.org/10.1109/isda.2007.31

  86. Jain C, Zanibbi R (2017). Recognition of Online Handwritten Math Symbols using Density Features

  87. Jianyu X, Qian** W, Liurong H (2008) Recognition of mathematical expressions based on convex hull and fuzzy recognition. Computer Applications and Software 5:82

    Google Scholar 

  88. ** J, Han X, Wang Q (2003) Mathematical formulas extraction. In Proceedings of the International Conference on Document Analysis and Recognition, ICDAR (pp 1138–1141). https://doi.org/10.1109/ICDAR.2003.1227834

  89. Julca-Aguilar F, Mouchère H, Viard-Gaudin C (2015) Top-down online handwritten mathematical expression parsing with graph grammar. Proceedings of IberoAmerican Congress on Pattern Recognition. Springer, Cham. pp 144–151.

  90. Kacem A, Belaïd A, Ben Ahmed M (2001) Automatic extraction of printed mathematical formulas using fuzzy logic and propagation of context. Int J Doc Anal Recognit 4(2):97–108. https://doi.org/10.1007/s100320100064

    Article  Google Scholar 

  91. Kanahori T, Tabata K, Cong W, Tamari F, Suzuki M (2000) On-line recognition of mathematical expressions using automatic rewriting method. International Conference on Multimodal Interfaces pp 394–401. https://doi.org/10.1007/3-540-40063-x_52

  92. Khuong VTM, Phan M (2019) Interactive user interface for recognizing online handwritten mathematical expressions and correcting misrecognition. In: Proceedings of International Conference on Document Analysis and Recognition Workshops (ICDARW), IEEE, 2, pp 26–30

    Google Scholar 

  93. Khuong VTM, Huy U, Masaki N (2019) Generating synthetic handwritten mathematical expressions from a LaTeX Sequence or a MathML script. Proceedings of International Conference on Document Analysis and Recognition (ICDAR),IEEE, pp 922–927

  94. Khuong V-T-m, Member S, Phan K, Ung H (2021) Clustering of handwritten mathematical expressions for computer-assisted marking. IEICE Trans Inf Syst 2:275–284

    Article  Google Scholar 

  95. Kim K, Rhee TH, Lee JS, Kim JH (2009) Utilizing consistency context for handwritten mathematical expression recognition. International Conference on Document Analysis and Recognition 1051–1055. https://doi.org/10.1109/ICDAR.2009.140

  96. Kitchenham B, Pearl Brereton O, Budgen D, Turner M, Bailey J, Linkman S (2009) Systematic literature reviews in software engineering - A systematic literature review. Inf Softw Technol 51(1):7–15. https://doi.org/10.1016/j.infsof.2008.09.009

    Article  Google Scholar 

  97. Kosmala A, Rigoll G (2000) Online handwritten formula recognition with integrated correction recognition and execution. In: Proceedings 15th International Conference on Pattern Recognition. ICPR-2000 IEEE, pp 590–593

    Google Scholar 

  98. Sakshi, Kukreja V (2021) A retrospective study on handwritten mathematical symbols and expressions : Classification and recognition. Eng Appl Artif Intell 103:104292. https://doi.org/10.1016/j.engappai.2021.104292

    Article  Google Scholar 

  99. Kumar PP, Agarwal A, Bhagvati C (2018) Isolated structural error analysis of printed mathematical expressions. Pattern Anal Applic 21(4):1097–1107. https://doi.org/10.1007/s10044-017-0667-y

    Article  MathSciNet  Google Scholar 

  100. Kumar P, Shreekanth T, Shashank NS, Sneha S (2019) A simplified research for mathematical expression recognition and its conversion to speech. International Journal of Recent Technology and Engineering 8(2S8):1033–1038. https://doi.org/10.35940/ijrte.B1008.0882S819

    Article  Google Scholar 

  101. Kundu S, Paul S, Kumar Bera S, Abraham A, Sarkar R (2020) Text-line extraction from handwritten document images using GAN. Expert Syst Appl 140:112916. https://doi.org/10.1016/j.eswa.2019.112916

    Article  Google Scholar 

  102. Labahn SMG (2013) A new approach for recognizing handwritten mathematics using relational grammars and fuzzy sets. Int J Doc Anal Recognit 16(2):139–163. https://doi.org/10.1007/s10032-012-0184-x

    Article  Google Scholar 

  103. Lapointe A, Blostein D (2009) Issues in performance evaluation: A case study of math recognition. Proceedings of the International Conference on Document Analysis and Recognition, ICDAR pp 1355–1359. https://doi.org/10.1109/ICDAR.2009.247

  104. LaViola JJ, Zeleznik RC (2007) A practical approach for writer-dependent symbol recognition using a writer-independent symbol recognizer. IEEE Trans Pattern Anal Mach Intell 29(11):1917–1926. https://doi.org/10.1109/TPAMI.2007.1109

    Article  PubMed  Google Scholar 

  105. LaViola JJ, Leal A, Miller TS, Zeleznik RC (2008) Evaluation of techniques for visualizing mathematical expression recognition results. Proceedings of Graphics Interface pp 131–138

  106. Le A, Nakagawa M (2013) A tool for ground-truthing online handwritten mathematical expressions. 16th International Graphonomics Society Conference. https://doi.org/10.9790/487X-171214553

  107. Le AD, Nakagawa M (2015) Improving structure analysis for online handwritten mathematical expressions. 18th Meeting on Image Recogntion and Understanding, 1–2. %60

  108. Le AD, Nakagawa M (2016) A system for recognizing online handwritten mathematical expressions by using improved structural analysis. Int J Doc Anal Recognit 19(4):305–319. https://doi.org/10.1007/s10032-016-0272-4

    Article  Google Scholar 

  109. Le A, Nakagawa M (2017) Training an end-to-end system for handwritten mathematical expression recognition by generated patterns. 2017 14th IAPR International Conference on Document Analysis and Recognition 1:1056–1061. https://doi.org/10.1109/ICDAR.2017.175

  110. Le AD, Phan T Van, Nakagawa M (2014) A system for recognizing online handwritten mathematical expressions and improvement of structure analysis. 11th IAPR International Workshop on Document Analysis Systems pp 51–55. https://doi.org/10.1109/DAS.2014.52

  111. Le AD, Indurkhya B, Nakagawa M (2019a) Pattern generation strategies for improving recognition of Handwritten Mathematical Expressions. Pattern Recogn Lett 128:255–262. https://doi.org/10.1016/j.patrec.2019.09.002

    Article  ADS  Google Scholar 

  112. Le AD, Nguyen HD, Indurkhya B, Nakagawa M (2019b) Stroke order normalization for improving recognition of online handwritten mathematical expressions. Int J Doc Anal Recognit 22(1):29–39. https://doi.org/10.1007/s10032-019-00315-2

    Article  Google Scholar 

  113. Li C, Zeleznik R, Miller T, LaViola JJ (2008) Online recognition of handwritten mathematical expressions with support for matrices. Proceedings - International Conference on Pattern Recognition pp 1–4. https://doi.org/10.1109/icpr.2008.4761825

  114. Lin X, Gao L, Tang Z, Hu X, Lin X (2012) Identification of embedded mathematical formulas in PDF documents using SVM. Document Recognition and Retrieval XIX 8297:82970D. https://doi.org/10.1117/12.912445

    Article  Google Scholar 

  115. Liu C, Zuo L, Li X, Tian X (2016) An improved algorithm for identifying mathematical formulas in the images of PDF documents. Proceedings of 2015 IEEE International Conference on Progress in Informatics and Computing, PIC 2015 pp 252–256. https://doi.org/10.1109/PIC.2015.7489848

  116. Liu H, Yu C, Wu H (2021) Smart non-intrusive device recognition based on deep learning methods. In Smart Device Recognition (pp 229–258). Springer

  117. Lods A, Anquetil E, Mace S (2019) Fuzzy visibility graph for structural analysis of online handwritten mathematical expressions. International Conference on Document Analysis and Recognition pp 641–646. https://doi.org/10.1109/ICDAR.2019.00108

  118. MacLean S, Labahn G (2010) Recognizing handwritten mathematics via fuzzy parsing (Issue Tech.Rep.CS-2010-13)

  119. MacLean S, Labahn G (2015) A Bayesian model for recognizing handwritten mathematical expressions. Pattern Recogn 48(8):2433–2445. https://doi.org/10.1016/j.patcog.2015.02.017

    Article  ADS  Google Scholar 

  120. MacLean S, Labahn G, Labahn SMG, MacLean S, Labahn G (2013) A new approach for recognizing handwritten mathematics using relational grammars and fuzzy sets. Int J Doc Anal Recognit 16(2):139–163. https://doi.org/10.1007/s10032-012-0184-x

    Article  Google Scholar 

  121. Mahdavi M, Zanibbi R, Mouchere H, Viard-Gaudin C, Garain U (2019) ICDAR 2019 CROHME + TFD: Competition on recognition of handwritten mathematical expressions and typeset formula detection. International Conference on Document Analysis and Recognition pp 1533–1538. https://doi.org/10.1109/ICDAR.2019.00247

  122. Malon C, Uchida S, Suzuki M (2008) Mathematical symbol recognition with support vector machines. Pattern Recogn Lett 29(9):1326–1332. https://doi.org/10.1016/j.patrec.2008.02.005

    Article  ADS  Google Scholar 

  123. Medjkoune S, Mouchère H (2012) Using speech for handwritten mathematical expression recognition disambiguation. International Conference on Frontiers in Handwriting Recognition,IEEE pp 187–192. http://plc-solutions.blogspot.com/p/block-diagram-of-plc.html

  124. Medjkoune S, Mouchère H, Petitrenaud S (2013) Multimodal mathematical expressions recognition: Case of speech and handwriting. In: International Conference on Human-Computer Interaction. Springer, Berlin, Heidelberg, pp 77–86

    Google Scholar 

  125. Medjkoune S, Mouchere H, Petitrenaud S, Viard-Gaudin C (2017) Combining speech and handwriting modalities for mathematical expression recognition. IEEE Transactions on Human-Machine Systems 47(2):259–272. https://doi.org/10.1109/THMS.2017.2647850

    Article  Google Scholar 

  126. Memon J, Sami M, Khan RA (2019) Handwritten Optical Character Recognition (OCR): A Comprehensive Systematic Literature Review (SLR). http://arxiv.org/abs/2001.00139

  127. Mohan K, Lu C (2013) Recognition of online handwritten mathematical expressions. In: Standford University

  128. Mohan K, Lu C (2015) Recognition of online handwritten mathematical expressions using convolutional neural networks. In: Standford University

  129. Mouchère H, Viard-Gaudin C, Kim DH, Kim JH, Garain U (2011) CROHME2011: Competition on recognition of online handwritten mathematical expressions. Proceedings of the International Conference on Document Analysis and Recognition, ICDAR pp 1497–1500. https://doi.org/10.1109/ICDAR.2011.297

  130. Mouchère H, Viard-Gaudin C, Kim DH, Kim JH, Garain U (2012) ICFHR 2012 - Competition on Recognition of On-line Mathematical Expressions (CROHME 2012). Proceedings - International Workshop on Frontiers in Handwriting Recognition, IWFHR, Crohme pp 811–816. https://doi.org/10.1109/ICFHR.2012.215

  131. Mouchere H, Viard-Gaudin C, Zanibbi R, Garain U, Kim DH, Kim JH (2013) ICDAR 2013 CROHME: Third international competition on recognition of online handwritten mathematical expressions. 2013 12th International Conference on Document Analysis and Recognition pp 1428–1432. https://doi.org/10.1109/ICDAR.2013.288

  132. Mouchere H, Viard-Gaudin C, Zanibbi R, Garain U (2014) ICFHR 2014 Competition on Recognition of On-Line Handwritten Mathematical Expressions (CROHME 2014). 2014 14th International Conference on Frontiers in Handwriting Recognition pp 791–796. https://doi.org/10.1109/ICFHR.2014.138

  133. Mouchère H, Viard-Gaudin C, Zanibbi R, Garain U (2016) ICFHR2016 CROHME: Competition on recognition of online handwritten mathematical expressions. Proceedings of International Conference on Frontiers in Handwriting Recognition, ICFHR pp 607–612. https://doi.org/10.1109/ICFHR.2016.0116

  134. Muñoz FÁ (2010) Off-line Recognition of Printed Mathematical Expressions Using Stochastic Context-Free Grammars. Universidad Politecnica de Valencia

    Google Scholar 

  135. Nguyen CT, Khuong VTM, Nguyen HT, Nakagawa M (2020) CNN based spatial classification features for clustering offline handwritten mathematical expressions. Pattern Recogn Lett 131:113–120. https://doi.org/10.1016/j.patrec.2019.12.015

    Article  ADS  Google Scholar 

  136. Okamoto M, Imai H, Takagi K (2001) Performance evaluation of a robust method for mathematical expression recognition. Sixth International Conference on Document Analysis and Recognition pp 121–128. https://doi.org/10.1109/ICDAR.2001.953767

  137. Pacheco-Venegas ND, López G, Andrade-Aréchiga M (2015) Conceptualization, development and implementation of a web-based system for automatic evaluation of mathematical expressions. Computers and Education 88:15–28. https://doi.org/10.1016/j.compedu.2015.03.021

    Article  Google Scholar 

  138. Pattaniyil N, Zanibbi R (2014) Combining TF-IDF Text Retrieval with an Inverted Index over Symbol Pairs in Math Expressions: The Tangent Math Search Engine at {NTCIR 2014}. NTCIR Workshop 11 Meeting, 135–142

  139. Pfleeger SL (2005) The Role of Evidential Force in Empirical Software Engineering. IEEE Softw 22(1):66–73 https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1377126

    Article  Google Scholar 

  140. Phan K, Nguyen C, Le A (2015) An incremental recognition method for online handwritten mathematical expressions. 3rd IAPR Asian Conference on Pattern Recognition pp 171–175

  141. Phan KM, Le AD, Nakagawa M (2016) Semi-incremental recognition of online handwritten mathematical expressions. 15th International Conference on Frontiers in Handwriting Recognition 258–264. https://doi.org/10.1109/ICFHR.2016.0057

  142. Phan KM, Le AD, Indurkhya B, Nakagawa M (2018) Augmented incremental recognition of online handwritten mathematical expressions. International Journal on Document Analysis and Recognition (IJDAR) 21(4):253–268. https://doi.org/10.1007/s10032-018-0306-1

    Article  Google Scholar 

  143. Phong BH, Hoang TM, Le T-L (2021) Mathematical variable detection in scientific document images. International Journal of Computational Vision and Robotics 11(1):66–89

    Article  Google Scholar 

  144. Pillay A (2014) Intelligent combination of structural analysis algorithms: Application to mathematical expression recognition. Rochester Institute of Technology

  145. Plamondon RR, Srihari SN (2000) On-line and off-line handwriting recognition: A comprehensive survey. IEEE Trans Pattern Anal Mach Intell 22(1):63–84. https://doi.org/10.1109/34.824821

    Article  Google Scholar 

  146. Plötz T, Fink GA (2009) Markov models for offline handwriting recognition: A survey. Int J Doc Anal Recognit 12(4):269–298. https://doi.org/10.1007/s10032-009-0098-4

    Article  Google Scholar 

  147. Predovic G, Abdulkader A, Dresevic B, Viola P, (U.S. Patent No. 8, 009, 915. Washington, D. U. S. P. and T. O.  (2011) Recognition of mathematical expressions (Patent No. U.S. Patent No. 8,009,915. Washington, DC: U.S. Patent and Trademark Office.). https://patentimages.storage.googleapis.com/47/9b/41/6846dbfd8ea793/US8009915.pdf

  148. Průša D, Hlaváč V (2007) Mathematical formulae recognition using 2D grammars. 2017 Nineth International Conference on Document Analysis and Recognition 2:849–853. https://doi.org/10.1109/ICDAR.2007.4377035

  149. Qi X, Pan W, Yusup WY (2009) The study of structure analysis strategy in handwritten recognition of general mathematical expression. International Forum on Information Technology and Applications 2:101–107. https://doi.org/10.1109/IFITA.2009.169

    Article  Google Scholar 

  150. Quiniou S, Mouchère H, Saldarriaga SP, Viard-gaudin C, Morin E, Petitrenaud S, Medjkoune S (2011) HAMEX - A handwritten and audio dataset of mathematical expressions. Proceedings of the International Conference on Document Analysis and Recognition, ICDAR pp 452–456. https://doi.org/10.1109/ICDAR.2011.97

  151. Rahmi S, Nadia R, Hasibah B, Hidayat W (2017) The relation between self-efficacy toward math with the math communicatION. Infinity Journal 6(2):177–182. https://doi.org/10.22460/infinity.v6i2.p177-182

    Article  Google Scholar 

  152. Raman TV (1994) Aster: Audio system for technical readings. Inf Technol Disabil 1(4):1–11

    MathSciNet  Google Scholar 

  153. Ramteke RJ, Mehrotra SC (2006) Feature extraction based on moment invariants for handwriting recognition. IEEE Conference on Cybernetics and Intelligent Systems 2006:1–6. https://doi.org/10.1109/ICCIS.2006.252262

    Article  Google Scholar 

  154. Ramteke S, Patil D, Patil N (2012) Neural network approach to Mathematical Expression Recognition System. International Journal of Engineering Research & Technology (IJERT) 7(10):2278–0181

    Google Scholar 

  155. Reichenbach MS, Agarwal A, Zanibbi R (2014) Rendering expressions to improve accuracy of relevance assessment for math search. SIGIR 2014 - Proceedings of the 37th International ACM SIGIR Conference on Research and Development in Information Retrieval pp 851–854. https://doi.org/10.1145/2600428.2609457

  156. Ren H, Wang W, Liu C (2019) Recognizing online handwritten Chinese characters using RNNs with new computing architectures. Pattern Recogn 93:179–192. https://doi.org/10.1016/j.patcog.2019.04.015

    Article  ADS  Google Scholar 

  157. Rhee TH, Kim JH (2009) Efficient search strategy in structural analysis for handwritten mathematical expression recognition. Pattern Recogn 42(12):3192–3201. https://doi.org/10.1016/j.patcog.2008.10.036

    Article  ADS  Google Scholar 

  158. Rohatgi S, Zhong W, Zanibbi R, Wu J, Giles CL (2019) Query auto completion for math formula search 6–11. http://arxiv.org/abs/1912.04115

  159. Ruiz V, Linares I, Sanchez A, Velez J (2020) Off-line handwritten signature verification using compositional synthetic generation of signatures and Siamese Neural Networks. Neurocomputing 374:30–41. https://doi.org/10.1007/1-4020-0613-6_11008

    Article  Google Scholar 

  160. Sain K, Dasgupta A, Garain U (2010) EMERS: A tree matching-based performance evaluation of mathematical expression recognition systems. Int J Doc Anal Recognit 14(1):75–85. https://doi.org/10.1007/s10032-010-0121-9

    Article  Google Scholar 

  161. Savchenkov P, Savinov E, Mikhail T, Kiyan S, Esin A (2018) Neural Network Based Recognition of Mathematical Expressions (Patent No. 15 / 187 , 723). In United States Patent (15 / 187 , 723) Google Patents

  162. Shan G, Wang H, Liang W, Chen K (2021) Robust encoder-decoder learning framework towards offline handwritten mathematical expression recognition based on multi-scale deep neural network. SCIENCE CHINA Inf Sci 64(3):1–12

    Article  ADS  Google Scholar 

  163. Shi Y, Soong F (2008) A symbol graph-based handwritten math expression recognition. In: 19th International Conference on Pattern Recognition, pp 1–4

    Google Scholar 

  164. Shi Y, Li HY, Soong FK (2007) A unified framework for symbol segmentation and recognition of handwritten mathematical expressions. In: 9th International Conference on Document Analysis and Recognition, 2, pp 854–858. https://doi.org/10.1109/ICDAR.2007.4377036

    Chapter  Google Scholar 

  165. Shi Y, Soong F, Zhou J (2011) Symbol graph generation in handwritten mathematical expression recognition. In: US Patent No 7,885,456

  166. Shinde S, Waghulade R (2016) Handwritten mathematical expressions recognition using back propagation artificial neural network. Communications on Applied Electronics 4(7):1–6. https://doi.org/10.5120/cae2016652125

    Article  CAS  Google Scholar 

  167. Shinde S, Waghulade RB, Bormane DS (2018) A new neural network based algorithm for identifying handwritten mathematical equations. International Conference on Trends in Electronics and Informatics pp 204–209. https://doi.org/10.1109/ICOEI.2017.8300916

  168. Shuvo SN, Hasan F, Ahmed MU, Hossain SA, Abujar S (2021) MathNET: Using CNN Bangla Handwritten Digit, Mathematical Symbols, and Trigonometric Function Recognition. In: Soft Computing Techniques and Applications. Springer, pp 515–523

    Chapter  Google Scholar 

  169. Simistira F, Papavassiliou V, Katsouros V, Carayannis G (2012). A system for recognition of on-line handwritten mathematical expressions. International Conference on Frontiers in Handwriting Recognition, pp 193–198. https://doi.org/10.1109/ICFHR.2012.172

  170. Simistira F, Papavassiliou V, Katsouros V, Carayannis G (2014) Recognition of spatial relations in mathematical formulas. In: 14th International Conference on Frontiers in Handwriting Recognition pp 164–168. https://doi.org/10.1109/ICFHR.2014.35

    Chapter  Google Scholar 

  171. Simistira F, Katsouros V, Carayannis G (2015) Recognition of online handwritten mathematical formulas using probabilistic SVMs and stochastic context free grammars. Pattern Recogn Lett 53:85–92. https://doi.org/10.1016/j.patrec.2014.11.015

    Article  ADS  Google Scholar 

  172. So CMY (2005) An Analysis of mathematical expressions used in practice, technical report [University of Western Ontario]. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.367.529&rep=rep1&type=pdf

  173. Stria J, Pruša D, Hlavác V (2014) Combining structural and statistical approach to online recognition of handwritten mathematical formulas. Nineteenth Computer Vision Winter Workshop pp 103–109

  174. Suzuki T (2000) A new system for the real-time recognition of handwritten mathematical formulas. 15th International Conference on Pattern Recognition, 4 pp 515–518. https://doi.org/10.1109/icpr.2000.902970

  175. Suzuki M, Uchida S, Nomura A (2005) A ground-truthed mathematical character and symbol image database. Proceedings of Eighth International Conference on Document Analysis and Recognition (ICDAR) pp 1–5

  176. Takiguchi Y, Okada M, Miyake Y (2005) A fundamental study of output translation from layout recognition and semantic understanding system for mathematical formulae. Eighth International Conference on Document Analysis and Recognition pp 745–749. https://doi.org/10.1109/ICDAR.2005.10

  177. Tapia E (2005) Understanding mathematics: A system for the recognition of on-line handwritten mathematical expressions

  178. Tapia E. (2007) Handwritten Mathematical notation a survey on recognition of on-line handwritten mathematical. January, 17

  179. Tapia E, Rojas R (2003) Recognition of on-line handwritten mathematical formulas in the e-chalk system. Seventh International Conference on Document Analysis and Recognition 3:980–984. https://doi.org/10.1109/ICDAR.2003.1227805

    Article  Google Scholar 

  180. Tapia E, Rojas R (2004) Recognition of On-line Handwritten Mathematical Expressions Using a Minimum Spanning Tree Construction and Symbol Dominance. International Workshop on Graphics Recognition 3088:329–340. https://doi.org/10.1007/978-3-540-25977-0_30

    Article  Google Scholar 

  181. Tapia E, Rojas R (2007a) A survey on recognition of on line handwritten mathematical notation. In: Technical Report B-07-01 Freie Universität Berlin, Institut für Informatik Takustr. 9, 14195 Berlin, Germany

  182. Tapia E, Rojas R (2007b) MathFoR: The Mathematical Formula Recognition System. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.94.2663&rep=rep1&type=pdf

  183. Thimbleby W (2004) A better calculator: Processing handwritten mathematical expressions to solve problems

  184. Tian X-D, Li H-Y, Li X-F, Zhang L-P (2006) Research on symbol recognition for mathematical expressions. First International Conference on Innovative Computing, Information and Control pp 357–360. https://doi.org/10.1109/icicic.2006.506

  185. Toyozumi K, Yamada N, Kitasaka T (2004) A study of symbol segmentation method for handwritten mathematical formula recognition using mathematical structure information. Proceedings of the 17th International Conference on Pattern Recognition, 2, pp 630–633. https://doi.org/10.1109/ICPR.2004.1334327

  186. Tran GS, Huynh CK, Le TS, Phan TP, Bui KN (2018) Handwritten mathematical expression recognition using convolutional neural network. 3rd International Conference on Control, Robotics and Cybernetics pp 15–19. https://doi.org/10.1109/CRC.2018.00012

  187. Ung HQ, Vu KTM, Le AD, Nguyen CT, Nakagawa M (2018) Bag-of-features for clustering online handwritten mathematical expressions. International Conference on Pattern Recognition and Artificial Intelligence pp 127–132

  188. Veres O, Rishnyak I, Rishniak H (2019) Application of methods of machine learning for the recognition of mathematical expressions. CEUR Workshop Proceedings 2362:1–12

  189. Vuong BQ, Hui SC, He Y (2008) Progressive structural analysis for dynamic recognition of on-line handwritten mathematical expressions. Pattern Recogn Lett 29(5):647–655. https://doi.org/10.1016/j.patrec.2007.11.017

    Article  ADS  Google Scholar 

  190. Vuong B-QQ, He Y, Hui SC (2010) Towards a web-based progressive handwriting recognition environment for mathematical problem solving. Expert Syst Appl 37(1):886–893. https://doi.org/10.1016/j.eswa.2009.05.091

    Article  Google Scholar 

  191. Wang H, Shan G (2020) Recognizing handwritten mathematical expressions as LaTex sequences using a multiscale robust neural network. In Computer Vision and Pattern Recognition (Issue 37)

  192. Wang J, Du J, Zhang J, Wang ZR (2019) Multi-modal attention network for handwritten mathematical expression recognition. Proceedings of the International Conference on Document Analysis and Recognition, ICDAR pp 1181–1186. https://doi.org/10.1109/ICDAR.2019.00191

  193. Wang J, Du J, Zhang J (2020a) Stroke constrained attention network for online handwritten mathematical expression recognition. Pattern Recogn 119:1–29 http://arxiv.org/abs/2002.08670

    Google Scholar 

  194. Wang Z, Du J, Wang J (2020b) Writer-aware CNN for parsimonious HMM-based offline handwritten Chinese text recognition. Pattern Recogn 100(10702). https://doi.org/10.1016/j.patcog.2019.107102

  195. Wangperawong A (2018) Attending to Mathematical Language with Transformers

  196. Wen J, Li S, Lin Z, Hu Y, Huang C (2012) Systematic literature review of machine learning based software development effort estimation models. Inf Softw Technol 54(1):41–59. https://doi.org/10.1016/j.infsof.2011.09.002

    Article  Google Scholar 

  197. Wu W, Li F, Kong J, Hou L, Zhu B (2006) A bottom-up OCR system for mathematical formulas recognition. International Conference on Intelligent Computing pp 274–279. https://doi.org/10.1007/11816157_27

  198. Wu JW, Yin F, Zhang YM, Zhang XY, Liu CL (2020) Handwritten mathematical expression recognition via paired adversarial learning. Int J Comput Vis https://doi.org/10.1007/s11263-020-01291-5

  199. Wu J, Yin F, Zhang Y, Zhang X, Liu C (2021) Graph-to-Graph : Towards Accurate and Interpretable Online Handwritten Mathematical Expression Recognition. AAAI Conference on Artificial Intelligence 35:2925–2933

    Article  Google Scholar 

  200. **angwei Q, Abaydulla Y (2010) The study of mathematical expression recognition and the embedded system design. Journal of Software 5(1):44–53. https://doi.org/10.4304/jsw.5.1.44-53

    Article  Google Scholar 

  201. Yamamoto R, Sako S, Nishimoto T, Sagayama S (2006) On-line recognition of handwritten mathematical expressions based on stroke-based stochastic context-free grammar. Tenth International Workshop on Frontiers in Handwriting Recognition

  202. Yan L, Ratra P, Khanna H, Yan L (2019) Recognizing handwritten mathematical expressions. International Journal of Engineering Applied Science and Technology 4(3):1–7

    Google Scholar 

  203. Yogatama BW, Lee J, Harimurti S, Adiono T (2018) FPGA-based optical character recognition for handwritten mathematical expressions. International SoC Design Conference pp 125–126. https://doi.org/10.1109/ISOCC.2018.8649966

  204. Zanibbi R, Blostein D (2012) Recognition and retrieval of mathematical expressions. Int J Doc Anal Recognit 15(4):331–357. https://doi.org/10.1007/s10032-011-0174-4

    Article  Google Scholar 

  205. Zanibbi R, Yuan B (2011) Keyword and image-based retrieval of mathematical expressions. Document Recognition and Retrieval XVIII, 78740I. https://doi.org/10.1117/12.873312

  206. Zanibbi R, Blostein D, Cordy JR (2001a) Baseline structure analysis of handwritten mathematics notation. Sixth International Conference on Document Analysis and Recognition 768–773. https://doi.org/10.1109/ICDAR.2001.953892

  207. Zanibbi R, Novins K, Arvo J, Zanibbi K (2001b) Aiding manipulation of handwritten mathematical expressions through style-preserving morphs. Proceedings - Graphics Interface 127–134

  208. Zanibbi R, Blostein D, Cordy JR (2002) Recognizing mathematical expressions using tree transformation. IEEE Trans Pattern Anal Mach Intell 24(11):1455–1467. https://doi.org/10.1109/TPAMI.2002.1046157

    Article  Google Scholar 

  209. Zanibbi R, Mouchère H, Viard-Gaudin C (2013) Evaluating structural pattern recognition for handwritten math via primitive label graphs. Document Recognition and Retrieval XX 8658:865817. https://doi.org/10.1117/12.2008409

    Article  Google Scholar 

  210. Zanibbi R, Davila K, Kane A, Tompa FW (2016a) Multi-stage math formula search: Using appearance-based similarity metrics at scale. SIGIR 2016 - Proceedings of the 39th International ACM SIGIR Conference on Research and Development in Information Retrieval pp 145–154. https://doi.org/10.1145/2911451.2911512

  211. Zanibbi R, Hu L, Zanibbi R (2016b) Line-of-sight stroke graphs and Parzen shape context features for handwritten math formula representation and symbol segmentation. 15th International Conference on Frontiers in Handwriting Recognition pp 180–186. https://doi.org/10.1109/ICFHR.2016.0044

  212. Zhang T (2017) New Architectures for Handwritten Mathematical Expressions Recognition. Image Processing [Eess.IV]. Université de Nantes, 2017., English. f.

  213. Zhang J, Hong L (2008) A survey on recognition of on-line handwritten mathematical expression. Journal of Huaibei Coal Industry Teachers College (Natural Science Edition) 29(3)

  214. Zhang L, Blostein D, Zanibbi R (2005) Using fuzzy logic to analyze superscript and subscript relations in handwritten mathematical expressions. Eighth International Conference on Document Analysis and Recognition pp 972–976. https://doi.org/10.1109/ICDAR.2005.250

  215. Zhang T, Mouchere H, Viard-Gaudin C (2016) Online handwritten mathematical expressions recognition by merging multiple 1D interpretations. 15th International Conference on Frontiers in Handwriting Recognition pp 187–192. https://doi.org/10.1109/ICFHR.2016.0045

  216. Zhang J, Du J, Dai L (2017) A GRU-Based encoder-decoder approach with attention for online handwritten mathematical expression recognition. Fourteenth IAPR International Conference on Document Analysis and Recognition pp 902–907. https://doi.org/10.1109/ICDAR.2017.152

  217. Zhang J, Du J, Dai L (2018a) Track, Attend, and Parse (TAP): An End-to-End Framework for Online Handwritten Mathematical Expression Recognition. IEEE Transactions on Multimedia 21(1):221–233. https://doi.org/10.1109/TMM.2018.2844689

    Article  Google Scholar 

  218. Zhang T, Mouchère H, Viard-Gaudin C (2018b) A tree-BLSTM-based recognition system for online handwritten mathematical expressions. Neural Comput & Applic 2(1). https://doi.org/10.1007/s00521-018-3817-2

  219. Zhang W, Bai Z, Zhu Y (2019) An improved approach based on CNN-RNNs for mathematical expression recognition. 4th International Conference on Multimedia Systems and Signal Processing 57–61. https://doi.org/10.1145/3330393.3330410

  220. Zhelezniakov D, Cherneha A, Zaytsev V, Ignatova T, Radyvonenko O, Yakovchuk O (2020a) Evaluating new requirements to pen-centric intelligent user interface based on end-to-end mathematical expressions recognition. International Conference on Intelligent User Interfaces pp 212–220. https://doi.org/10.1145/3377325.3377482

  221. Zhelezniakov D, Zaytsev V, Radyvonenko O (2020b) Online handwritten mathematical expression recognition and applications: A survey. IEEE Access 24:1–24

    Google Scholar 

  222. Zhelezniakov D, Zaytsev V, Radyvonenko O (2021) Online handwritten mathematical expression recognition and applications : A survey 9

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vinay Kukreja.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest. The authors declare that no potential conflicts of interest (financial or non-financial).

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendix 1

Table 22 Studies categorized under Quality Assessment Labels

Appendix 2

Table 23 Quality Assessment Questions

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sakshi, Kukreja, V. Machine learning and non-machine learning methods in mathematical recognition systems: Two decades’ systematic literature review. Multimed Tools Appl 83, 27831–27900 (2024). https://doi.org/10.1007/s11042-023-16356-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-023-16356-z

Keywords

Navigation