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A dive in white and grey shades of ML and non-ML literature: a multivocal analysis of mathematical expressions

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Abstract

With the advent and advancement of machine learning and deep learning techniques, machine-based recognition systems for mathematical text have captivated the attention of the research community for the last four decades. Mathematical Expression Recognition systems have been identified based on terms of their techniques, approach, dataset, and accuracies. This study majorly targets a rigorous review of both the published form of literature and the least attended literature, i.e., grey literature. Apart from the digital libraries, the papers and other instances of information have been gathered from the grey sources like google patents, archives, technical reports, app stores, etc., culminating in 262 instances. After the heedful filtration imposed on both white and grey literature, the final pool of studies has been investigated for eight formulated research questions. The answers extracted have been analyzed, providing both quantitative and qualitative insights. The analysis and surveys have systematically summed up the potentials of both white and grey shades of literature present on MER and brought exciting extractions out of 155 formal white literature and 107 grey sources. The survey extracts and brings out the highlighting observations after analysis, which sublimates the fact that 52% of grey literature is composed of mobile applications and user interfaces, whereas the published 63% of white data is presently concentrated in 39 different conferences, and the prominent conference is ICDAR (#30). A list of challenges and open issues has been extracted for directing future research dimensions.

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Notes

  1. (www.textrelease.com).

  2. (www.emeraldinsight.com/toc/ijgl/1/4).

  3. (www.greynet.org).

References

  • Abirami M, Jaganathan S (2019) Handwritten mathematical recognition tool. In: Int Conf on Comput Intell in data Sci pp 1–4. https://doi.org/10.1109/ICCIDS.2019.8862155

  • Aguilar FDJ, Hirata NST (2012) ExpressMatch: a system for creating ground-truthed datasets of online mathematical expressions. In: IAPR Int workshop on document Anal Sys pp 155–159. https://doi.org/10.1109/DAS.2012.38

  • 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  MATH  Google Scholar 

  • Ahmad R, Naz S, Razzak I (2021) Efficient skew detection and correction in scanned document images through clustering of probabilistic hough transforms. Pattern Recogn Lett 152:93–99

    Article  Google Scholar 

  • Ali I, Mahjoub M (2018) Dynamic random forest for the recognition of arabic handwritten mathematical symbols with a novel set of features. Int Arab J Inf Technol 15(3A Special Issue):565–575

    Google Scholar 

  • Álvaro F (2013) A shape-based layout descriptor for classifying spatial relationships in handwritten math. In: ACM Symp on Doc Eng pp 123–126

  • Álvaro F, Sánchez JA (2010) Comparing several techniques for offline recognition of printed mathematical symbols. In: Int Conf on Pattern Recognit pp 1953–1956. https://doi.org/10.1109/ICPR.2010.481

  • Álvaro F, Sánchez JA, Benedí JM (2011) Recognition of printed mathematical expressions using two-dimensional stochastic context-free grammars. In: Proceedings of the Int Conf on Doc Anal and Recognit ICDAR, September 2011, pp 1225–1229. https://doi.org/10.1109/ICDAR.2011.247

  • Álvaro F, Sánchez JA, Benedí JM (2012) Unbiased evaluation of handwritten mathematical expression recognition. In: Int Conf on frontiers in handwriting Recognit pp 181–186. https://doi.org/10.1109/ICFHR.2012.287

  • Álvaro F, Sánchez JA, Benedí JM (2014a) 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 

  • Álvaro F, Sánchez JA, Benedí JM (2014b) Offline features for classifying handwritten math symbols with recurrent neural networks. In: 22nd Int Conf on pattern Recognit, Stockholm, Sweden, pp 2944–2949. https://doi.org/10.1109/ICPR.2014.507

  • 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  MATH  Google Scholar 

  • 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  MATH  Google Scholar 

  • Aly W, Uchida S, Fujiyoshi A, Suzuki M (2009) Statistical classification of spatial relationships among mathematical symbols. In: 2009 10th Int Conf on Doc Anal and Recognit vol 1, pp 1350–1354. https://doi.org/10.1109/ICDAR.2009.90

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

  • Asebriy Z, Bencharef O (2016) A semantic approach for mathematical expression retrieval. Int J Adv Comput Sci Appl 7(9):190–194

    Google Scholar 

  • Ashida K, Okamoto M. Imai H, Nakatsuka T (2006) Performance evaluation of a mathematical formula recognition system with a large scale of printed formula images. In: Second Int Conf on Doc image Anal for libr (DIAL’06), p 12

  • Awal AM, Mouchère H, Viard-Gaudin C (2009) Towards handwritten mathematical expression recognition. In: 2009, 10th Int Conf on Doct Anal and Recognit Barcelona, Spain, pp 1046–1050. https://doi.org/10.1109/ICDAR.2009.71

  • Awal A-M, Mouchère H, Viard-Gaudin C (2010a) A hybrid classifier for handwritten mathematical expression recognition. Doc Recognit Retr XVII 7534:753410. https://doi.org/10.1117/12.840023

    Article  Google Scholar 

  • Awal A-M, Mouchère H, Viard-Gaudin C (2010b) Improving online handwritten mathematical expressions recognition with contextual modeling. In: Twelveth Int Conf on Front in Handwrit Recognit Kolkata, India, pp 427–432. https://doi.org/10.1109/ICFHR.2010.73

  • Awal A-M, Mouchère H, Viard-Gaudin C (2010c) The problem of handwritten mathematical expression recognition evaluation. In: 12th Int Conf on Front in Handwrit Recognit Kolkata, India, pp 646–651. https://doi.org/10.1109/ICFHR.2010.106

  • 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 

  • Bage DD, Adhiya KP, Gharde SS (2010) A new approach for recognizing offline handwritten mathematical symbols using character geometry. Int J Innov Re Sci Eng Technol 2(7):2823–2830

    Google Scholar 

  • Baker JB, Sexton AP, Sorge V (2010) Faithful mathematical formula recognition from PDF documents. In: 9th IAPR Int workshop on Doc Anal Sys pp 485–492. https://doi.org/10.1145/1815330.1815393

  • Baumann, S. (1995) A simplified attributed graph grammar for high-level music recognition. In: Int Conf on Doc Anal and Recognit vol 2, pp 1080–1083. https://doi.org/10.1109/ICDAR.1995.602096

  • Belaid A, Haton JP (1984) A syntactic approach for handwritten mathematical formula recognition. IEEE Trans Pattern Anal Mach Intel. https://doi.org/10.1109/TPAMI.1984.4767483

    Article  Google Scholar 

  • Bender S, Haurilet M (2019) Learning fine-grained image representations for mathematical expression recognition. In: Int Conf on Doc Anal and Recognit. pp 56–61. https://doi.org/10.1109/ICDARW.2019.00015

  • Bharambe M (2015) Recognition of offline handwritten mathematical expressions. In: National Conf on Digit Image and Signal Proc pp 35–39

  • Blacketer L, Lewis H, Urrutxua H (2022) Identifying illumination conditions most suitable for attitude detection in light curves of simple geometries. Adv Space Res 69(3):1578–1587

    Article  Google Scholar 

  • Bott JN, LaViola Jr JJ (2010) A pen-based tool for visualizing vector mathematics. In: EUROGRAPHICS Symp on sketch-Based interfaces and Model pp 103–110

  • Carbune V, Gonnet P, Deselaers T, Rowley HA, Daryin A, Calvo M, Wang L-L, Keysers D, Feuz S, Gervais P (2020) Fast multi-language LSTM-based online handwriting recognition. Int J Doc Anal Recognit (IJDAR) 23(2):89–102

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Celik M, Yanikoglu B (2011) Probabilistic mathematical formula recognition using a 2D context-free graph grammar. In: Int Cof on Doc Anal and Recognit Beijing China, pp 161–166. https://doi.org/10.1109/ICDAR.2011.41

  • Chajri Y, Bouikhalene B (2016) Handwritten mathematical expressions recognition. Int J Signal Process Image Process Pattern Recognit 9(5):69–76. https://doi.org/10.14257/ijsip.2016.9.5.07

    Article  Google Scholar 

  • Chajri Y, Maarir A, Bouikhalene B (2016) a comparative study of handwritten mathematical symbols recognition. In: Thirteenth Int Conf on Comput Graphics, Imaging and visualization, pp 448–451. https://doi.org/10.1109/CGiV.2016.92

  • 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 

  • Chan KF, Yeung DY (1998) Elastic structural matching for online handwritten alphanumeric character recognition. In: Fourteenth Int Conf on Pattern Recognit vol 2, pp 1508–1511. https://doi.org/10.1109/ICPR.1998.711993

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

    Article  Google Scholar 

  • Chan KF, Yeung DY (2000b) Mathematical expression recognition: a survey. Int J Doc Anal Recognit (IJDAR) 3(1):3–15. https://doi.org/10.1007/PL00013549

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Chan K, Yeung D (2001b) PenCalc: novel application of on-line mathematical expression recognition technology. In: Sixth Int Conf on Doc Anal and Recognit pp 774–778.

  • Chatbri H, Kameyama K, Kwan P (2015) Towards a segmentation and recognition-free approach for content-based document image retrieval of handwritten queries. In: 3rd IAPR Asian Conf on pattern Recognit pp 146–150. https://doi.org/10.1109/ACPR.2015.7486483

  • Cheema S, LaViola Jr JJ (2012) PhysicsBook : a sketch-based interface for animating physics diagrams. In: ACM Int Conf on Intel user Interfaces pp 51–60. https://doi.org/10.1145/2166966.2166977

  • 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 

  • Chou PA (1989) Recognition of equations using a two-dimensional stochastic context-free grammar. Visual Commun Image Process IV 119:852–865. https://doi.org/10.1117/12.970095

    Article  Google Scholar 

  • Claeys C, Foulon V, De Winter S, Spinewine A (2013) Initiatives promoting seamless care in medication management: an international review of the grey literature. Int J Clin Pharm 35(6):1040–1052

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Code C, Asst EO, Naik B, Álvaro F (2013) A shape-based layout descriptor for classifying spatial relationships in handwritten math. In: Proceedings of the 2013 ACM symposium on document engineering, pp 123–126

  • Conn VS, Valentine JC, Cooper HM, Rantz MJ (2003) Grey literature in meta-analyses. Nurs Res 52(4):256–261

    Article  Google Scholar 

  • Cossairt T (2019) Setpad : a sketch-based tool for exploring discrete math set problems. In: Eurographics workshop on sketch-based Interfaces and Model pp 1–89. https://doi.org/10.2312/SBM/SBM12/047-056

  • Dai J, Sun Y, Su G, Ye S, Sun Y (2019) Recognizing offline handwritten mathematical expressions efficiently. In: 10th Int Conf on E-educ, E-bus, E-manage and E-learn pp 198–204. https://doi.org/10.1145/3306500.3306543

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

    Article  Google Scholar 

  • Davila K, Agarwal A, Gaborski R, Zanibbi R, Ludi S (2013) Accessmath: indexing and retrieving video segments containing math expressions based on visual similarity. In: IEEE western New York image processing workshop, pp 14–17. https://doi.org/10.1109/WNYIPW.2013.6890981

  • Davila K, Ludi S, Zanibbi R (2014) Using off-line features and synthetic data for on-line handwritten math symbol recognition. In: Fourteenth Int Conf on Front in Handwrit Recognit Hersonissos, Greece, pp 323–328. https://doi.org/10.1109/ICFHR.2014.61

  • De Angelis G, Lonetti F (2021) About the assessment of grey literature in software engineering. In: Eval and Assess in Softw Eng pp 373–378

  • Deepu V, Madhvanath S, Ramakrishnan AG (2004) Principal component analysis for online handwritten character recognition. In: Seventeenth Int Conf on pattern Recognit pp 327–330. https://doi.org/10.1109/ICPR.2004.1334196

  • Deufemia V, Risi M, Tortora G (2014) Sketched symbol recognition using latent-dynamic conditional random fields and distance-based clustering. Pattern Recognit 47(3):1159–1171. https://doi.org/10.1016/j.patcog.2013.09.016

    Article  Google Scholar 

  • Drsouza L, Mascarenhas M (2018) Offline handwritten mathematical expression recognition using convolutional neural network. In: Int Conf on Information, Communicat, Eng and Technol pp 1–3. https://doi.org/10.1109/ICICET.2018.8533789

  • Dutta K, Krishnan P, Mathew M, Jawahar CV (2018) Improving CNN-RNN hybrid networks for handwriting recognition. In: 2018 16th Int Conf on Front in Handwrit Recognit (ICFHR), pp 80–85

  • Elik MC (2010) Handwriten mathematical expression recognition using, pp 1–66. Accessed 10 May 2022 http://research.sabanciuniv.edu/19058

  • Eto Y, Suzuki M (2001) Mathematical formula recognition using virtual link network. In: Proceedings of sixth Int Conf on Doc Anal and Recognit pp 762–767. https://doi.org/10.1109/icdar.2001.953891

  • 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 

  • 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. In: 85th Technol Res meeting of JSISE (Japanese Society for Information and Systems in Education), pp 1–8

  • Fitzgerald JA, Geiselbrechtinger F, Kechadi T (2007) Mathpad: a fuzzy logic-based recognition system for handwritten mathematics. In: Ninth Int Conf on Doc Anal and Recognit Curitiba, Brazil, vol 2, pp 694–698 https://doi.org/10.1109/ICDAR.2004377004

  • Floyd RG, Cooley KM, Arnett JE, Fagan TK, Mercer SH, Hingle C (2011) An overview and analysis of journal operations, journal publication patterns, and journal impact in school psychology and related fields. J Sch Psychol 49(6):617–647

    Article  Google Scholar 

  • Francisco Das Chagas Fontenele Marques, Thelmo Pontes de Araujo, Jose Vigno Moura Sousa, Nator Junior Carvalho Da Costa, Rodrigo Teixeira de Melo, Alano Martins Pinto, Arata Andrade Saraiva et al (2019) Recognition of simple handwritten polynomials using segmentation with fractional calculus and convolutional neural networks. In: 8th Brazilian conference on intelligent systems, pp 245–250. https://doi.org/10.1109/BRACIS.2019.00051

  • Fu Y, Liu T, Gao M, Zhou A (2020) EDSL: an encoder-decoder architecture with symbol-level features for printed mathematical expression recognition. Comput Vision and Pattern Recognit pp 1–14. http://arxiv.org/abs/2007.02517

  • Fujimoto M (2003) Infty editor—a mathematics typesetting tool with a handwriting interface and a graphical front-end to OpenXM servers s (Computer Algebra : Algorithms, Implementations and Applications)

  • Galafassi S, Nizzetto L, Volta P (2019) Plastic sources: a survey across scientific and grey literature for their inventory and relative contribution to microplastics pollution in natural environments, with an emphasis on surface water. Sci Total Environ 693:133499

    Article  Google Scholar 

  • Garain U (2009) Identification of mathematical expressions in document images. In: 10th Int Conf on Doc Anal and Recognit, pp 1340–1344. https://doi.org/10.1109/ICDAR.2009.203

  • Garain U, Chaudhuri BB (2003). On machine understanding of online handwritten mathematical expressions. In: Seventh Int Conf on Doc Anal and Recognit Edinburgh, UK, pp 349–353. https://doi.org/10.1109/ICDAR.2003.1227687

  • Garain U, Chaudhuri B (2004) Recognition of online handwritten mathematical expressions. IEEE Trans Syst Man Cybern 34(6):2366–2376. https://doi.org/10.1109/TSMCB.2004.836817

    Article  Google Scholar 

  • Garousi V, Felderer M (2019) Guidelines for including grey literature and conducting multivocal literature reviews in software engineering. Inf Softw Technol 106:101–121

    Article  Google Scholar 

  • Genoe R, Kechadi T (2010a) Fuzzy spatial analysis techniques for mathematical expression recognition. In: Artificial intelligence and soft computing. ICAISC 2010a. Lecture notes in computer science, vol 6113, pp 80–87. https://doi.org/10.1007/978-3-642-13208-7_11

  • Genoe R, Kechadi T (2010b) A real-time recognition system for handwritten mathematics backtracking and relationship discovery. In: Int Conf on Front in Handwrit Recognit pp 399–404. https://doi.org/10.1109/ICFHR.2010.69

  • Genoe R, Fitzgerald J, Kechadi T (2006a). A purely online approach to mathematical expression recognition. In: Int workshop on Front in Handwrit Recognit pp 1–6. https://hal.inria.fr/inria-00104890/document

  • Genoe R, Fitzgerald JA, Kechadi T (2006b) An online fuzzy approach to the structural analysis of handwritten mathematical expressions. In: IEEE Int Conf on fuzzy Sys, Vancouver, BC, Canada. , pp 244–250. https://doi.org/10.1109/FUZZY.2006.1681721

  • Genoe R, Fitzgerald JJA, Kechadi T, Genoe R, Fitzgerald JJA, Kechadi T, Online, A.P, Genoe R, Fitzgerald JJA, Kechadi T (2006c) A purely online approach to mathematical expression recognition. In: Tenth Int workshop on Front in Handwrit Recognit pp 1–6

  • Gharde SS, Baviskar PV, Adhiya KP (2013) Identification of handwritten simple mathematical equation based on SVM and projection histogram. Int J of Soft Comput and Eng 3(2):425–429

  • Ghoshal R, Banerjee A (2020) SVM and MLP based segmentation and recognition of text from scene images through an effective binarization scheme. In: Comput Intell in pattern Recognit Springer, Singapore, pp 237–246

  • Godin K, Stapleton J, Kirkpatrick SI, Hanning RM, Leatherdale ST (2015) Applying systematic review search methods to the grey literature: a case study examining guidelines for school-based breakfast programs in Canada. Syst Rev 4(1):1–10

    Article  Google Scholar 

  • Golubitsky O, Watt SM (2010) Distance-based classification of handwritten symbols. Int J Doc Anal Recognit 13(2):133–146. https://doi.org/10.1007/s10032-009-0107-7

    Article  Google Scholar 

  • Golubitsky O, Mazalov V, Watt SM (2010) Toward affine recognition of handwritten mathematical characters. In: Nineth IAPR Int workshop on Doc Anal Sys pp 35–42. https://doi.org/10.1145/1815330.1815335

  • Guan SK, Moh M, Moh TS (2019) Context-based multi-stage offline handwritten mathematical symbol recognition using deep learning. In Int Conf on high Perform Comput and Simulat HPCS 2019, pp 185–192. https://doi.org/10.1109/HPCS48598.2019.9188180

  • Gul S, Shah TA, Ahmad S, Gulzar F, Shabir T (2020) Is grey literature really grey or a hidden glory to showcase the sleeping beauty. Collect Curation. https://doi.org/10.1108/cc-10-2019-0036

    Article  Google Scholar 

  • Guo Y, Huang L, Liu C, Jiang X (2007). An automatic mathematical expression understanding system. In: Ninth Int Conf on Doc Anal and Recognit pp 719–723. https://doi.org/10.1109/ICDAR.2007.4377009

  • He W, Luo Y, Yin F, Hu H, Han J, Ding E, Liu CL (2016). context-aware mathematical expression recognition: an end-to-end framework and a benchmark. In: 23rd Int Conf on Pattern Recognit pp 3246–3251. https://doi.org/10.1109/ICPR.2016.7900135

  • Hirata N, Honda W (2011a) Automatic labeling of handwritten mathematical symbols via expression matching. In: Graph-based Represent in Pattern Recognit GbRPR 2011a. lecture notes in Comput Sci pp 295–304. https://doi.org/10.1177/107808747000500401

  • Hirata NST, Honda WY (2011b) Automatic labeling of handwritten mathematical symbols via expression matching. graph-based Represent in Pattern Recognit. In: GbRPR 2011b. Lecture notes in Comput Sci vol 6658, pp 295–304. https://doi.org/10.1007/978-3-642-20844-7_30

  • Hong Z, You N, Tan J, Bi N (2019) Residual BiRNN based Seq2Seq model with transition probability matrix for online handwritten mathematical expression recognition. In: Int Conf on Doc Anal and Recognit pp 635–640. https://doi.org/10.1109/ICDAR.2019.00107

  • Hossain MB, Naznin F, Joarder YA, Zahidul Islam M, Uddin MJ, Hossain B, Naznin F, Joarder YA, Islam Z, Uddin J (2018). Recognition and solution for handwritten equation using convolutional neural network. In: 2018 joint 7th Int Conf on Informa Electronics & Vis (ICIEV) and 2018 2nd Int Conf on Imaging, Vis & Pattern Recognit pp 250–255. https://doi.org/10.1109/ICIEV.2018.8640991

  • Hu L, Zanibbi R (2011) HMM-based recognition of online handwritten mathematical symbols using segmental K-means initialization and a modified pen-up/down feature. In: Int Conf on Doc Anal and Recognit Beijing, China, pp 457–462. https://doi.org/10.1109/ICDAR.2011.98

  • Hu L, Zanibbi R (2013) Segmenting handwritten math symbols using adaboost and multi-scale shape context features. In: 12th Int Conf on Doc Anal and Recognit Washington, DC, USA, pp 1180–1184. https://doi.org/10.1109/ICDAR.2013.239

  • Hu L, Zanibbi R (2016) MST-based visual parsing of online handwritten mathematical expressions. In: 15th Int Conf on Front in Handwrit Recognit pp 337–342. https://doi.org/10.1109/ICFHR.2016.0070

  • Hu L, Hart K, Pospesel R, Zanibbi R (2012) Baseline extraction-driven parsing of handwritten mathematical expressions. In: 21st Int conf on Pattern Recognit pp 326–330

  • Hu Y, Peng L, Tang Y (2014) On-line handwritten mathematical expression recognition method based on statistical and semantic analysis. In: 11th IAPR Int workshop on Doc Anal Sys pp 171–175. https://doi.org/10.1109/DAS.2014.47

  • Huang BQ, Kechadi MM (2007) A structural analysis approach for online handwritten mathematical expressions. Int J Comput Sci Netw Secur 7(7):47–56. https://doi.org/10.1142/9789812837042_0014

    Article  Google Scholar 

  • Huang BQ, Zhang YB, Kechadi MT (2007) Preprocessing techniques for online handwriting recognition. In: Seventh international conference on intelligent systems design and applications, pp 793–800. https://doi.org/10.1109/isda.2007.31

  • Hunsinger J, Lang M (2000) A single-stage top-down probabilistic approach towards understanding spoken and handwritten mathematical formulas. In: Sixth Int Conf on spoken language process vol 4, pp 386–389.

  • Islam MNA, Khan SK (2019) HishabNet: detection, localization and calculation of handwritten bengali mathematical expressions. http://arxiv.org/abs/1909.00823

  • Jain C, Zanibbi R (2017) Recognition of Online Handwritten Math Symbols using Density Features. Report, Rochester Inst of Technol 1:1–4

  • Jakjoud W, Lazrek A (2011) Segmentation method of offline mathematical symbols. In: Int Conf on multimedia Comput and Sys—proceed. https://doi.org/10.1109/ICMCS.2011.5945634

  • Jeyaraman MM, Al-Yousif N, Robson RC, Copstein L, Balijepalli C, Hofer K, Fazeli MS, Ansari MT, Tricco AC, Rabbani R et al (2020) Inter-rater reliability and validity of risk of bias instrument for non-randomized studies of exposures: a study protocol. Syst Rev 9(1):1–12

    Article  Google Scholar 

  • Jiang Y, Tian F, Wang H, Zhang X, Wang X, Dai G (2010) Intelligent understanding of handwritten geometry theorem proving. In: 15th Int Conf on Intell user Interf Hong Kong, China, pp 119–128. https://doi.org/10.1145/1719970.1719988

  • Jimenez D,  Nguyen L (2013) Recognition of Handwritten Mathematical Symbols with PHOG.Report, Stanf University 1:1–5

  • Jin J, Jiang H, Wang KAI, Wang Q (2004) Automatic performance evaluation of mathematical expression recognition. In: Third Int Conf on machine Learn and Cybern pp 26–29

  • Jjn J, Han ZHI, Wang Q (2002) Typeset mathematical expression analysis. In: Int Conf on machine Learn and Cybern vol 2, pp 1038–1043. https://doi.org/10.1109/ICMLC.2002.1174541

  • Julca-Aguilar F, Hirata NST, Viard-Gaudin C, Mouchere H, Medjkoune S (2014) Mathematical symbol hypothesis recognition with rejection option. In: 2014 14th Int Conf on Front in Handwrit Recognit 2014-December, pp 500–505. https://doi.org/10.1109/ICFHR.2014.90

  • Julca-Aguilar F, Mouchère H, Viard-Gaudin C, Mouchere H, Christian V-G, Hirata NST, Mouchère H, Viard-Gaudin C (2015) Top-down online handwritten mathematical expression parsing with graph grammar. In: IberoAmerican congress on Pattern Recognit vol 2, pp 444–451. https://doi.org/10.1007/978-3-319-25751-8_53

  • Julca-Aguilar F, Hirata NS, Mouchère H,  Viard-Gaudin C (2016) Subexpression and dominant symbol histograms for spatial relation classification in mathematical expressions. In IEEE 23rd Int Conference on Pattern Recognit (ICPR) (pp. 3446–3451).

  • Julca-Aguilar F, Mouchère H, Viard-Gaudin C, Hirata NST (2020) A general framework for the recognition of online handwritten graphics. Int J Doc Anal Recognit 23:143–160. https://doi.org/10.1007/s10032-019-00349-6

    Article  Google Scholar 

  • 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 

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

  • Kang B,  LaViola J (2012) Logicpad: A pen-based application for visualization and verification of boolean algebra. In Proceedings of the 2012 ACM Int Conf on Intell User Interfaces (pp. 265–268). https://doi.org/10.1145/2166966.2167014

  • Kasuya Y, Yamana H (2007) MathBox : interactive pen-based interface for inputting mathematical expressions. In: Int Conf on Intell user Interfaces, pp 274–277

  • Keele S (2007) Guidelines for performing systematic literature reviews in software engineering.Technical Report, Keele University, Vol. 5, pp: 1–65

  • Keramatian K, Chakrabarty T, Saraf G, Pinto JV, Yatham LN (2021) Grey matter abnormalities in first-episode mania: a systematic review and meta-analysis of voxel-based morphometry studies. Bipolar Disord 23(3):228–240

    Article  Google Scholar 

  • Khuman YLK, Devi HM, Singh NA (2021) Entropy-based skew detection and correction for printed meitei/meetei script ocr system. Mater Today: Proc 37:2666–2669

    Google Scholar 

  • Khuong V, 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 

  • Kim DH, Kim JH (2010) Top-down down search with bottom-up bottom p evidence for recognizing handwritten mathematical expressions expression korea advanced institute of science and technology. In: 12th international conference on frontiers in handwriting recognition, pp 507–512. https://doi.org/10.1109/ICFHR.2010.84

  • Kim K, Rhee TH, Lee JS, Kim JH (2009) Utilizing consistency context for handwritten mathematical expression recognition. In: International conference on document analysis and recognition, Barcelona, Spain, pp 1051–1055. https://doi.org/10.1109/ICDAR.2009.140

  • Kosmala A, Rigoll G, Brakensiek A (2000) Online handwritten formula recognition with integrated correction recognition and execution. In: Proceedings 15th international conference on pattern recognition. ICPR-2000 IEEE., vol. 15, pp 590–593. https://doi.org/10.1109/icpr.2000.906143

  • Ks SB, Bhat V, Krishnan AS (2018) SolveIt : an application for automated recognition and processing of handwritten mathematical equations. In: 4th international conference for convergence in technology, pp 1–8. https://doi.org/10.1109/I2CT42659.2018.9058273

  • Kukreja V, Sakshi (2022) Machine learning models for mathematical symbol recognition: a stem to stern literature analysis. Multimed Tools Appl. https://doi.org/10.1007/s11042-022-12644-2

    Article  Google Scholar 

  • Kulkarni RV, Vasambekar PN (2010) An overview of segmentation techniques for handwritten connected digits. In: International conference on signal and image processing, pp 479–482. https://doi.org/10.1109/ICSIP.2010.5697522

  • Kumar PP, Agarwal A, Bhagvati C (2012) A structure based approach for mathematical expression retrieval. In: International workshop on multi-disciplinary trends in artificial intelligence. Springer, Berlin, pp 23–34

    Google Scholar 

  • Kumar PP, Agarwal A, Bhagvati C (2014) A string matching based algorithm for performance evaluation of mathematical expression recognition. Sadhana 39:63–79. https://doi.org/10.1007/s12046-013-0221-6

    Article  MATH  Google Scholar 

  • Labahn G, Lank E, MacLean S, Marzouk M, Tausky D (2008) Mathbrush: a system for doing math on pen-based devices. In: Eighth IAPR international workshop on document analysis systems, pp 599–606. https://doi.org/10.1109/DAS.2008.21

  • Lavanya K, Bajaj S, Tank P, Jain S (2017) Handwritten digit recognition using hoeffding tree, decision tree and random forests—a comparative approach. In: International conference on computational intelligence in data science, pp 1–6. https://doi.org/10.1109/ICCIDS.2017.8272641

  • 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  Google Scholar 

  • Lavirotte S, Pottier L (1998) Mathematical formula recognition using graph grammar. Doc Recognit V 3305:44–52. https://doi.org/10.1117/12.304644

    Article  Google Scholar 

  • Le AD (2020) Recognizing handwritten mathematical expressions via paired dual loss attention network and printed mathematical expressions. In: IEEE/CVF conference on computer vision and pattern recognition, pp 566–567. https://doi.org/10.1109/CVPRW50498.2020.00291

  • Le A, Nakagawa M (2013) A tool for ground-truthing online handwritten mathematical expressions. In: 16th international graphonomics society conference. https://doi.org/10.9790/487X-171214553

  • Le AD, Nakagawa M (2015) Improving structure analysis for online handwritten mathematical expressions. In: 18th meeting on image recogntion and understanding, 1–2. %60

  • Le AD, Nakagawa M (2016a) 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 

  • Le AD, Nakagawa M (2016b) Comparison of parsing algorithms for recognizing online handwritten mathematical expressions. In: 15th international conference on frontiers in handwriting recognition, pp 390–394. https://doi.org/10.1109/ICFHR.2016.0079

  • Le AD, Nakagawa M (2017a) Speedup of parsing for recognition of online handwritten mathematical expressions. In: International conference on document analysis and recognition, pp 896–901. https://doi.org/10.1109/ICDAR.2017.151

  • Le AD, Nakagawa M (2017b) Training an end-to-end system for handwritten mathematical expression recognition by generated patterns. In: 2017b 14th IAPR international conference on document analysis and recognition, Kyoto, Japan, vol 1, pp 1056–1061. https://doi.org/10.1109/ICDAR.2017.175

  • Le AD, Phan Van T, Nakagawa M (2014) A system for recognizing online handwritten mathematical expressions and improvement of structure analysis. In: 11th IAPR international workshop on document analysis systems, pp 51–55. https://doi.org/10.1109/DAS.2014.52

  • Le AD, Nguyen HD, Nakagawa M (2016) Modified X-Y cut for re-ordering strokes of online handwritten mathematical expressions. In: 12th IAPR international workshop on document analysis systems, pp 233–238. https://doi.org/10.1109/DAS.2016.19

  • Le AD, Indurkhya B, Nakagawa M (2019a) Pattern generation strategies for improving recognition of handwritten mathematical expressions. Pattern Recognit Lett 128:255–262. https://doi.org/10.1016/j.patrec.2019.09.002

    Article  Google Scholar 

  • 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 

  • Lee W, de Silva R, Peterson EJ, Calfee RC, Stahovich TF (2008) Newton’s Pen: a pen-based tutoring system for statics. Comput Graph 32(5):511–524

    Article  Google Scholar 

  • Lee J, Yogatama BW, Christian H (2018) Optical character recognition for handwritten mathematical expressions in educational humanoid robots. In: IEEE 8th international conference on system engineering and technology, Bandung, Indonesia, pp 178–183. https://doi.org/10.1109/ICSEngT.2018.8606374

  • Lefebvre C, Manheimer E, Glanville, J (2008) Searching for studies. Cochrane handbook for systematic reviews of interventions: Cochrane book series, pp: 95–15

  • Li Z, Tian X (2010) An improved analysis approach of overbrace/underbrace structure in printed mathematical expressions. In: 2010 international conference on innovative computing and communication and 2010 Asia-pacific conference on information technology and ocean engineering, Macao, China, pp 58–61. https://doi.org/10.1109/CICC-ITOE.2010.22

  • Li C, Miller TS, Zeleznik RC, LaViola Jr JJ (2008) AlgoSketch : algorithm sketching and interactive computation. In: EUROGRAPHICS workshop on sketch-based interfaces and modeling, pp 175–181. https://doi.org/10.2312/SBM/SBM08/175-182

  • Li Z, Jin L, Lai S, Zhu Y (2020) Improving attention-based handwritten mathematical expression recognition with scale augmentation and drop attention. In: 17th international conference on frontiers in handwriting recognition, pp 175–180. https://doi.org/10.1109/ICFHR2020.2020.00041

  • Lin X, Gao L, Tang Z, Hu X, Lin X (2012) Identification of embedded mathematical formulas in PDF documents using SVM. Doc Recognit Retr XIX 8297:82970D. https://doi.org/10.1117/12.912445

    Article  Google Scholar 

  • Lin Y, Wang C, Zeng J (2016) A case study on mathematical expression recognition to GPU. J Supercomput 73(8):3333–3343. https://doi.org/10.1007/s11227-016-1819-3

    Article  Google Scholar 

  • Lin J, Wang X, Wang Z, Beyette D, Liu JC (2019) Prediction of mathematical expression declarations based on spatial , semantic , and syntactic analysis. In: ACM symposium on document engineering, vol 15, pp 1–10. https://doi.org/10.1145/3342558.3345399

  • Littin RH (1995) Mathematical expression recognition: parsing pen/tablet input in real-time using LR techniques. University of Waikato, Hamilton

    Google Scholar 

  • Lods A, Anquetil E, Mace S (2019) Fuzzy visibility graph for structural analysis of online handwritten mathematical expressions. In: International conference on document analysis and recognition, Sydney, NSW, Australia, pp 641–646. https://doi.org/10.1109/ICDAR.2019.00108

  • Lyu P, Bai X, Yao C, Zhu Z, Huang T, Liu W (2017) Auto-encoder guided GAN for chinese calligraphy synthesis. In: International conference on document analysis and recognition, vol 1, pp 1095–1100. https://doi.org/10.1109/ICDAR.2017.181

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

  • 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  MATH  Google Scholar 

  • 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  MATH  Google Scholar 

  • Madhvanath S, Vijayasenan D, Murugan T (2004) LipiTk : a generic toolkit for online handwriting recognition. SIGGRAPH ’07: ACM SIGGRAPH 2007, pp 13–18

  • Madisetty S, Maurya KK, Aizawa A, Desarkar MS (2020) A neural approach for detecting inline mathematical expressions from scientific documents. Expert Syst. https://doi.org/10.1111/exsy.12576

    Article  Google Scholar 

  • Mahdavi M, Condon M, Davila K, Zanibbi R (2019a) LPGA: line-of-sight parsing with graph-based attention for math formula recognition. In: International conference on document analysis and recognition, pp 647–654. https://doi.org/10.1109/ICDAR.2019.00109

  • Mahdavi M, Zanibbi R, Mouchere H, Viard-Gaudin C, Garain U (2019b) ICDAR 2019 CROHME + TFD: competition on recognition of handwritten mathematical expressions and typeset formula detection. In: International conference on document analysis and recognition, Sydney, NSW,Australia, pp 1533–1538. https://doi.org/10.1109/ICDAR.2019.00247

  • 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  Google Scholar 

  • Medjkoune S, Mouchère H (2014) Text alignment from bimodal mathematical expression sources. In: 2014 14th international conference on Frontiers in handwriting recognition, pp 205–209

  • Medjkoune S, Mouchère H, Petitrenaud S, Viard-gaudin C (2011) Handwritten and audio information fusion for mathematical symbol recognition. In: International conference on document analysis and recognition, pp 379–383. https://doi.org/10.1109/ICDAR.2011.84

  • Medjkoune S, Mouchère H, Mouchere H, Petitrenaud S, Viard-gaudin C (2012) Using speech for handwritten mathematical expression recognition disambiguation. In: International conference on frontiers in handwriting recognition, IEEE, Bari, Italy, pp 187–192. https://doi.org/10.1016/j.engappai.2014.06.008

  • Medjkoune S, Mouchere H, Petitrenaud S, Viard-Gaudin C, Mouch H, Petitrenaud S, Viard-Gaudin C (2017) Combining speech and handwriting modalities for mathematical expression recognition. IEEE Trans Human-Mach Syst 47(2):259–272. https://doi.org/10.1109/THMS.2017.2647850

    Article  Google Scholar 

  • Mohan K, Lu C (2013a) Recognition of online handwritten mathematical expressions, project final report. Standford University, Stanford. https://doi.org/10.1109/EUROCON.2013.6625259

    Book  Google Scholar 

  • Mohan K, Lu C (2013b) Recognition of online handwritten mathematical expressions. Standford University, Standford

    Google Scholar 

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

    Google Scholar 

  • Mollah AF, Basu S, Das N, Sarkar R, Nasipuri M, Kundu M (2009) A fast skew correction technique for camera captured business card images. In: Annual IEEE India conference, pp 4–7

  • Mori K (2013) A system for real-time recognition of handwritten mathematical formulas. In: 15th international conference on pattern recognition, pp 515–518. https://doi.org/10.1109/ICDAR.2001.953948

  • Mouchère H, Viard-Gaudin C, Kim DH, Kim JH, Garain U (2011) CROHME2011: competition on recognition of online handwritten mathematical expressions. In: Proceedings of the international conference on document analysis and recognition, ICDAR, Beijing, China, pp 1497–1500. https://doi.org/10.1109/ICDAR.2011.297

  • Mouchère H, Zanibbi R, Garain U, Viard-Gaudin C (2014) Advancing the state-of-the-art for handwritten math recognition: the CROHME competitions, 2011–2014. Int J Doc Anal Recognit 19(2):173–189. https://doi.org/10.1007/s10032-016-0263-5

    Article  Google Scholar 

  • Muñoz FÁ (2010) Off-line recognition of printed mathematical expressions using stochastic context-free grammars. Universidad Politecnica de Valencia, Valencia

    Google Scholar 

  • Naik S, Metkewar P (2015) Recognizing offline handwritten mathematical expressions (ME) based on a predictive approach of segmentation using K-NN classification. Int J Technol 3:345–354

    Article  Google Scholar 

  • Naik SA, Metkewar PS, Mapari SA (2017) Recognition of ambiguous mathematical characters within mathematical expressions. In: Second international conference on electrical, computer and communication technologies, pp 1–4. https://doi.org/10.1109/ICECCT.2017.8117840

  • Nazemi A, Tavakolian N, Fitzpatrick D, Suen, CY (2019) Offline handwritten mathematical symbol recognition utilising deep learning. https://doi.org/10.48550/arXiv.1910.07395

  • Nghiem MQ, Yoko G, Matsubayashi Y, Aizawa A(2011) Towards Mathematical Expression Understanding, Report, National Institute of Informatics, pp: 1–8

  • Nguyen DH, Le Duc A, Nakagawa M (2015) Deep neural networks for recognizing online handwritten mathematical symbols. In: Third IAPR Asian conference on pattern recognition deep, pp 121–125. https://doi.org/10.1109/ACPR.2015.7486478

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Nwokoma FO, Odii JN, Ayogu II, Ogbonna JC (2021) Camera-based OCR scene text detection issues: a review. World J Adv Res Rev 12(3):484–489

    Article  Google Scholar 

  • Ogawa RT, Malen B (1991) Towards rigor in reviews of multivocal literatures: Applying the exploratory case study method. Rev Educ Res 61(3): 265–286.

  • Okamoto M (1991) Recognition of mathematical expressions by using the layout structure of symbols. In: First international conference document analysis and recognition, vol 2, pp 242–250

  • Okamoto M, Imai H, Takagi K (2001) Performance evaluation of a robust method for mathematical expression recognition. In: Sixth international conference on document analysis and recognition, pp 121–128. https://doi.org/10.1109/ICDAR.2001.953767

  • Pandita R, Singh S (2011) Grey Literature: A Valuable Untapped Stockpile of Information. J of the Young Librarians Association 5:1–9. Available at SSRN:https://ssrn.com/abstract=3476007

  • Perwej Y, Chaturvedi A (2012) Machine recognition of hand written characters using neural networks. Int J Comput Appl 14(2):1–5. https://doi.org/10.5120/1819-2380

    Article  Google Scholar 

  • Petersen BK, Larma ML, Mundhenk TN, Santiago CP, Kim SK, Kim JT (2019) Deep symbolic regression: Recovering mathematical expressions from data via risk-seekingpolicy gradients. https://doi.org/10.48550/arXiv.1912.04871

  • Phan KM, Nguyen CT, Le A D, Nakagawa M (2015a) An incremental recognition method for online handwritten mathematical expressions. In: 3rd IAPR Asian conference on pattern recognition, Kuala Lumpur, Malaysia, pp 171–175. https://doi.org/10.1109/ACPR.2015.7486488

  • Phan K, Nguyen C, Le A (2015b) An incremental recognition method for online handwritten mathematical expressions. In: 3rd IAPR Asian conference on pattern recognition, pp 171–175

  • Phan KM, Le AD, Nakagawa M (2016) Semi-incremental recognition of online handwritten mathematical expressions. In: 15th international conference on frontiers in handwriting recognition, Shenzhen, China, pp 258–264. https://doi.org/10.1109/ICFHR.2016.0057

  • Phan KM, Le AD, Indurkhya B, Nakagawa M (2018) Augmented incremental recognition of online handwritten mathematical expressions. Int J Doc Anal Recognit (IJDAR) 21(4):253–268. https://doi.org/10.1007/s10032-018-0306-1

    Article  Google Scholar 

  • Phong BH, Dat LT, Yen NT, Hoang TM, Le T-L (2020a) A deep learning based system for mathematical expression detection and recognition in document images. In: 12th international conference on knowledge and systems engineering, pp 85–90. https://doi.org/10.1109/KSE50997.2020.9287693

  • Phong BH, Hoang TM, Le T-L (2020b) A hybrid method for mathematical expression detection in scientific document images. IEEE Access 8:83663–83684. https://doi.org/10.1109/ACCESS.2020.2992067

    Article  Google Scholar 

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

    Google Scholar 

  • 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 

  • Pollanen M, Wisniewski T, Yu X (2007) Xpress: a novice interface for the real-timecommunication of mathematical expressions. In Proceedings of MathUI (Vol. 8)

  • Průša D, Hlaváč V (2007) Mathematical formulae recognition using 2D grammars. In: 2017 nineth international conference on document analysis and recognition, vol 2, pp 849–853. https://doi.org/10.1109/ICDAR.2007.4377035

  • Qi X, Pan W, Yusup WY (2009) The study of structure analysis strategy in handwritten recognition of general mathematical expression. Int Forum Inf Technol Appl 2:101–107. https://doi.org/10.1109/IFITA.2009.169

    Article  Google Scholar 

  • Raggett D, Batsalle D (1998) Adding math to Web pages with EzMath. Comput Netw ISDN Syst 30(1–7):679–681

    Article  MATH  Google Scholar 

  • Ramadhan I, Purnama B, Al Faraby S (2016) Convolutional neural networks applied to handwritten mathematical symbols classification. In IEEE 4th international conference on information and communication technology, pp 1–4.https://doi.org/10.1109/ICoICT.2016.7571941

  • Ramsay JO (2000) Functional components of variation in handwriting. J Am Stat Assoc 95(449):9–15. https://doi.org/10.1080/01621459.2000.10473894

    Article  Google Scholar 

  • Ramteke RJ, Mehrotra SC (2006) Feature extraction based on moment invariants for handwriting recognition. In: 2006 IEEE conference on cybernetics and intelligent systems, pp 1–6. https://doi.org/10.1109/ICCIS.2006.252262

  • Reddy GS, Sarma B, Naik RK, Prasanna SRM, Mahanta C (2012) Assamese online handwritten digit recognition system using hidden Markov models. In: ACM international conference proceeding series, pp 108–113. https://doi.org/10.1145/2432553.2432573

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

    Article  MATH  Google Scholar 

  • 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 

  • Sakhawat Z, Ali S, Hongzhi L (2018) Handwritten digits recognition based on deep learning4J. In: ACM international conference proceeding series, Espoo, Finland, pp 21–25. https://doi.org/10.1145/3268866.3268888

  • 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 

  • Sakshi, Kukreja V (2022) Segmentation and contour detection for handwritten mathematical expressions using OpenCV. In: 2022 international conference on decision aid sciences and applications (DASA), pp 305–310.

  • Sakshi, Sharma C, Kukreja V (2021a) The survey on handwritten mathematical expressions recognition. In: Cyber intelligence and information retrieval: proceedings of CIIR 2021a, vol 291, p 129

  • Sakshi, Kukreja V, Ahuja S (2021b) Recognition and classification of mathematical expressions using machine learning and deep learning methods. In: 9th international conference on reliability, infocom technologies and optimization, pp 1–5. https://doi.org/10.1109/icrito51393.2021.9596161

  • Sakshi, Lodhi S, Kukreja V (2022a) Deep neural network for recognition of enlarged mathematical corpus. In: 2022a international conference on decision aid sciences and applications (DASA), pp 411–415

  • Sakshi, Sharma C, Kukreja V (2022b) CNN-based handwritten mathematical symbol recognition model. Cyber intelligence and information retrieval. Springer, Singapore, pp 407–416

    Chapter  Google Scholar 

  • Saroui BS, Sorge V (2015) Trajectory recovery and stroke reconstruction of handwritten mathematical symbols. In: International conference on document analysis and recognition, pp 1051–1055. https://doi.org/10.1109/ICDAR.2015.7333922

  • 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

  • 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. Sci China Inf Sci 64(3):1–12. https://doi.org/10.1007/s11432-018-9824-9

    Article  Google Scholar 

  • Shi Y, Soong FK (2008) A symbol graph based handwritten math expression recognition. In: 19th international conference on pattern recognition, pp 1–4. https://doi.org/10.1109/ICPR.2008.4761542

  • 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, vol 2, pp 854–858. https://doi.org/10.1109/ICDAR.2007.4377036

  • Shi Y, Soong F, Zhou J (2011) Symbol graph generation in handwritten mathematical expression recognition. In: U.S. Patent No. 7,885,456. https://doi.org/10.1109/ICPR.2008.4761542

  • Shinde S, Waghulade R (2016) Handwritten mathematical expressions recognition using back propagation artificial neural network. Commun Appl Electron 4(7):1–6. https://doi.org/10.5120/cae2016652125

    Article  Google Scholar 

  • Shinde S, Waghulade RB (2017) An improved algorithm for recognizing mathematical equations by using machine learning approach and hybrid feature extraction technique. In: IEEE international conference on electrical, instrumentation and communication engineering, pp 1–7. https://doi.org/10.1109/ICEICE.2017.8191926

  • Shinde S, Waghulade RB, Bormane DS (2018) A new neural network based algorithm for identifying handwritten mathematical equations. In: International conference on trends in electronics and informatics, Tirunelveli, India, pp 204–209. https://doi.org/10.1109/ICOEI.2017.8300916

  • 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, vol 1248. Springer, Singapore, pp 515–523. https://doi.org/10.1007/978-981-15-7394-1_47

    Chapter  Google Scholar 

  • Simistira F, Papavassiliou V, Katsouros V, Carayannis G (2012) A system for recognition of on-line handwritten mathematical expressions. In: International conference on frontiers in handwriting recognition, pp 193–198. https://doi.org/10.1109/ICFHR.2012.172

  • 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, Hersonissos, Greece, pp 164–168. https://doi.org/10.1109/ICFHR.2014.35

  • 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  Google Scholar 

  • Sindhu VS, Sant Y, Malhotra R, Sreedevi I (2022) The HWDI dataset of camera captured warped hindi text document images. In: 2022 12th international conference on cloud computing, data science & engineering (confluence), pp 295–299

  • Singh H, Sharma RK, Singh VP (2021) Online handwriting recognition systems for Indic and non-Indic scripts: a review. Artif Intell Rev 54(2):1525–1579

    Article  Google Scholar 

  • Smithies S (1999) Freehand formula entry system: a thesis submitted for the degree of master of science at the University of Otago, Dunedin, New Zealand. University of Otago, Dunedin

    Google Scholar 

  • Soldani J, Tamburri DA, Van Den Heuvel WJ (2018) The pains and gains of microservices: a systematic grey literature review. J Syst Softw 146:215–232. https://doi.org/10.1016/j.jss.2018.09.082

    Article  Google Scholar 

  • Stria J, Pruša D, Hlavác V (2014) Combining structural and statistical approach to online recognition of handwritten mathematical formulas. In: Nineteenth computer vision winter workshop, pp 103–109

  • Sucan IA (2006) A search engine for mathematical formulae. In: Artificial intelligence and symbolic computation. AISC 2006. Lecture notes in computer science, p 2140. https://doi.org/10.1007/11856290_21

  • Sueiras J, Ruiz V, Sanchez A, Velez JF (2018) Offline continuous handwriting recognition using sequence to sequence neural networks. Neurocomputing 289:119–128

    Article  Google Scholar 

  • Suzuki T (2000) A new system for the real-time recognition of handwritten mathematical formulas. In: 15th international conference on pattern recognition, vol 4, pp 515–518. https://doi.org/10.1109/icpr.2000.902970

  • Suzuki M, Kanahori T, Ohtake N (2004) Integrated OCR software for mathematical. In: International conference on computers for handicapped persons, pp 648–655

  • Takiguchi Y, Okada M, Miyake Y (2005) A fundamental study of output translation from layout recognition and semantic understanding system for mathematical formulae. In: Eighth international conference on document analysis and recognition, pp 745–749. https://doi.org/10.1109/ICDAR.2005.10

  • Tan CL, Cao R, Shen P (2001) Wavelet applications in segmentation of handwriting in archival documents. In: Wavelet analysis and its applications. WAA 2001. Lecture notes in computer science, vol 2251, pp 176–187. https://doi.org/10.1007/3-540-45333-4_23

  • Tapia E (2004) JMathNotes: a java-based editor for on-line handwritten mathematical expressions. In: Fourth interuational conference on document analysis and recognition, ICDAR, pp 357–361

  • Tapia E (2005) Understanding mathematics: A system for the recognition of on-line handwritten mathematical expressions, Doctoral dissertation, Public university in Berlin, Germany

  • Tapia E (2007) Handwritten Mathematical Notation A Survey on Recognition of On-LineHandwritten Mathematical. Technical Report, Public university in Berlin, Germany. pp:1–17

  • Tapia E, Berlin D (2005) Recognition of on-line handwritten mathematical expressions in the E-chalk system—an extension. In: Eighth international conference on document analysis and recognition, vol 2, pp 1206–1210. https://doi.org/10.1109/ICDAR.2005.197

  • Tapia E, Rojas R (2003) Recognition of on-line handwritten mathematical formulas in the e-chalk system. In: Seventh international conference on document analysis and recognition, , Georgia, USA, vol 3, pp 980–984. https://doi.org/10.1109/ICDAR.2003.1227805

  • Tapia E, Rojas R (2004) Recognition of on-line handwritten mathematical expressions using a minimum spanning tree construction and symbol dominance. In: International workshop on graphics recognition, vol 3088, pp 329–340. https://doi.org/10.1007/978-3-540-25977-0_30

  • Taranta EM, Vargas AN, Compton SP, Laviola JJ Jr (2016) A dynamic pen-based interface for writing and editing complex mathematical expressions with math boxes. ACM Trans Interact Intell Syst (TiiS) 6(2):1–25. https://doi.org/10.1145/2946795

    Article  Google Scholar 

  • Thimbleby W (2004) A better calculator: Processing handwritten mathematical expressions to solve problems.Swansea University,UK. pp: 1-81 (Thesis)

  • Tian XD, Zuo LN, Yang F, Ha MH (2007) An improved method based on gabor feature for mathematical symbol recognition. In: 2007 international conference on machine learning and cybernetics, vol 3, pp 1678–1682. https://doi.org/10.1109/ICMLC.2007.4370417

  • Toyozumi K, Yamada N (2004) A study of symbol segmentation method for handwritten mathematical. In: Proceedings of the 17th international conference on pattern recognition, 2004. ICPR 2004, vol 2, pp 2–5

  • Toyozumi K, Yamada N, Kitasaka T, Mori K, Mase K (2004) A study of symbol segmentation method for handwritten mathematical formula recognition using mathematical structure information. In: Proceedings of the 17th international conference on pattern recognition, vol 2, pp 630–633. https://doi.org/10.1109/ICPR.2004.1334327

  • Toyozumi K, Suzuki T, Mori K, Suenaga Y (2006) An on-line handwritten mathematical equation recognition system that can process matrix expressions by referring to the relative positions of matrix elements. Syst Comput Jpn 37(14):1278–1285. https://doi.org/10.1002/scj.10684

    Article  Google Scholar 

  • Tran GS, Huynh CK, Le TS, Phan TP, Bui KN (2018) Handwritten mathematical expression recognition using convolutional neural network. In: 3rd international conference on control, robotics and cybernetics, pp 15–19. https://doi.org/10.1109/CRC.2018.00012

  • Tree-Based Structure Recognition Evaluation for Math Expressions: Techniques and Case Study (2019)

  • Truong T, Nguyen CT, Phan KM, Nakagawa M (2020) Improvement of end-to-end offline handwritten mathematical expression recognition by weakly supervised learning. In: 17th international conference on frontiers in handwriting recognition, pp 181–186. https://doi.org/10.1109/ICFHR2020.2020.00042

  • Ung HQ, Khuong VTM, Le AD, Nguyen CT, Nakagawa M (2018a). Bag-of-features for clustering online handwritten mathematical expressions. In: Int Conf on Pattern Recognit and Artificial Intelligence, pp 127–132

  • Ung HQ, Khuong VTM, Le AD, Nguyen CT, Nakagawa M (2018b) Bag-of-features for clustering online handwritten mathematical expressions. In: Int Conf on Pattern Recognit and Artificial Intell pp 127–132

  • Viard-gaudin C, Zhang T, Mouchère H, Viard-gaudin C (2016) Using BLSTM for interpretation of 2-D languages: case of handwritten mathematical expressions. Document Numerique 19:135–157. https://doi.org/10.3166/DN.19.2-3.135-157

    Article  Google Scholar 

  • Vinod HC, Niranjan SK (2020) Camera captured document de-warping and de-skewing. J Comput Theor Nanosci 17(9):4398–4403. https://doi.org/10.1166/jctn.2020.9085

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Vuong B-Q, 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 

  • Wang X (2017) A font setting based Bayesian Model to extract mathematical expression in PDF on a font setting based bayesian model to extract mathematical expression in PDF files. https://doi.org/10.1109/ICDAR.2017.129

  • Wang Z, Lin J (2019) Extraction of math expressions from PDF documents based on unsupervised modeling of fonts, pp 381–386. https://doi.org/10.1109/ICDAR.2019.00068

  • Wang X, Liu J-C (2017) A font setting based bayesian model to extract mathematical expression in PDF files. In: 14th IAPR Int Conf on Doc Analy and Recognit vol 1, pp 759–764

  • Wang H, Shan G (2020) Recognizing handwritten mathematical expressions as LaTex sequences using a multiscale robust neural network. https://doi.org/10.48550/arXiv.2003.00817

  • Wang C, Mouchère H, Viard-Gaudin C, Jin L (2016a) Combined segmentation and recognition of online handwritten diagrams with high order Markov random field. In: Int Conf on Front in Handwrit Recognit pp 252–257. https://doi.org/10.1109/ICFHR.2016.0056

  • Wang H, Wang Y, Lu L, Liu J, Li S, Zhang Y (2016b) An improved algorithm for symbol segmentation of mathematical formula images. In: 16th Int Sympos on Communicat and Informat Technol ISCIT 2016, pp 461–464. https://doi.org/10.1109/ISCIT.2016.7751674

  • Wang X, Wang Z, Liu J-C (2019) Bigram label regularization to reduce over- segmentation on inline math expression detection. In: Int Conf on Doc Analy and Recognit pp 387–392. https://doi.org/10.1109/ICDAR.2019.00069

  • Wang J, Du J, Zhang J (2020) Stroke constrained attention network for online handwritten mathematical expression recognition. Pattern Recognit 119:1–29. https://doi.org/10.48550/arXiv.2002.08670

    Article  Google Scholar 

  • Watt SM, Xie X (2005) Prototype pruning by feature extraction for handwritten mathematical symbol recognition. Technical Report. Department of Computer Science, University of Western Ontario, Canada pp:1–14

  • Wigington C, Tensmeyer C, Davis B, Barrett W, Price B, Cohen S (2018) Start, follow, read: End-to-end full-page handwriting recognition. In: Proceedings of the european conference on computer vision (ECCV), pp 367–383

  • Wolfram S et al (1999) The MATHEMATICA®book, version 4. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Wu W, Li F, Kong J, Hou L, Zhu B (2006) A bottom-up OCR system for mathematical formulas recognition. In: Int Conf on Intell Comput pp 274–279. https://doi.org/10.1007/11816157_27

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Wu J, Yin F, Zhang Y, Zhang X, Liu C (2021) Graph-to-graph: towards accurate and interpretable online handwritten mathematical expression recognition. AAAI Conf Artif Intell 35:2925–2933

    Google Scholar 

  • Xiangwei Q, Abaydulla Y (2010) The study of mathematical expression recognition and the embedded system design. J Softw 5(1):44–53. https://doi.org/10.4304/jsw.5.1.44-53

    Article  Google Scholar 

  • Xinyan C, Hongli Y, Xin W (2013) Handwritten mathematical symbol recognition based on niche genetic algorithm. In: Third Int Conf on Intell Sys Design and Eng Applicat ISDEA 2013, pp 803–806. https://doi.org/10.1109/ISDEA.2012.191

  • Xue-Dong T, Hai-Yan L, Xin-Fu L, Li-Ping Z (2006). Research on symbol recognition for mathematical expressions. In: First Int Conf on Innovat Comput Inform and Cont vol 3, pp 357–360. https://doi.org/10.1109/icicic.2006.506

  • Yamamoto R, Sako S, Nishimoto T, Sagayama S (2006) On-line recognition of handwritten mathematical expressions based on stroke-based stochastic context-free grammar. In: Tenth Int workshop on Front in Handwrit Recognit

  • Yan L (2019) Recognizing handwritten mathematical expressions. Int J Eng Appl Sci Technol 4(3):201–206

    Google Scholar 

  • Yan L, Ratra P, Khanna H, Yan L (2019) Recognizing handwritten mathematical expressions. Int J Eng Appl Sci Technol 4(3):201–206

    Google Scholar 

  • Yan Z, Zhang X, Gao L, Yuan K, Tang Z (2020) ConvMath: a convolutional sequence network for mathematical expression recognition. In 2020 25th Int Conf on Pattern Recognit (ICPR) (pp. 4566-4572). IEE

  • Yang X, Sang F, Wang T, Pei X, Wang H, Hou T (2021) Research on the influence of camera velocity on image blur and a method to improve object detection precision. In: 2021 Int Conf on cyber-physical Soc Intell (ICCSI), pp 1–6

  • Yeo JBW (2004) Using LiveMath as an interactive computer tool for exploring algebra and calculus. In: 9th Asian Technol Conf in mathematics, pp 13–17

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

  • 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 

  • Zanibbi R, Yuan B (2011) Keyword and image-based retrieval of mathematical expressions. Doc Recognit Retr XVII I:78740I. https://doi.org/10.1117/12.873312

    Article  Google Scholar 

  • 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 

  • Zanibbi R, Blostein D, Cordy JR (2001) Baseline structure analysis of handwritten mathematics notation. In: Sixth Int Conf on Doc Analys and Recognit pp 768–773. https://doi.org/10.1109/ICDAR.2001.953892

  • Zanibbi R, Hu L, Zanibbi R (2016) Line-of-sight stroke graphs and Parzen shape context features for handwritten math formula representation and symbol segmentation. In: 15th Int Conf on Front in Handwrit Recognit pp 180–186. https://doi.org/10.1109/ICFHR.2016.0044

  • Zeleznik R, Miller T, Li C (2007) Designing UI techniques for handwritten mathematics. In: EUROGRAPHICS workshop on sketch-based interfaces and modeling, pp 91–98. https://doi.org/10.2312/SBM/SBM07/091-098

  • Zhang J, Hong L (2008) A survey on recognition of on-line handwritten mathematical expression. J Huaibei Coal Ind Teach Coll (natural Science Edition). https://doi.org/10.17169/refubium-23077

    Article  Google Scholar 

  • Zhang L, Blostein D, Zanibbi R (2005) Using fuzzy logic to analyze superscript and subscript relations in handwritten mathematical expressions. In: Eighth Int Conf on Doc Analys and Recognit pp 972–976. https://doi.org/10.1109/ICDAR.2005.250

  • Zhang DY, Tian XD, Li XF (2010) An improved method for segmentation of touching symbols in printed mathematical expressions. In: IEEE Int Conf on Adva Comput cont vol 2, pp 251–253. https://doi.org/10.1109/ICACC.2010.5486679

  • Zhang T, Mouchere H, Viard-Gaudin C (2016) Online handwritten mathematical expressions recognition by merging multiple 1D interpretations. In: 15th Int Conf on Front in Handwrit Recognit pp 187–192. https://doi.org/10.1109/ICFHR.2016.0045

  • Zhang J, Du J, Dai L (2017a) Track, attend, and parse (TAP): an end-to-end framework for online handwritten mathematical expression recognition. IEEE Trans Multimed 21(1):221–233. https://doi.org/10.1109/TMM.2018.2844689

    Article  Google Scholar 

  • Zhang J, Du J, Dai L (2017b) A GRU-based encoder-decoder approach with attention for online handwritten mathematical expression recognition. In: Fourteenth IAPR Int Conf on Doc Analy and Recognit pp 902–907. https://doi.org/10.1109/ICDAR.2017.152

  • Zhang J, Du J, Zhang S, Liu D, Hu Y, Hu J, Wei S, Dai L (2017c) Watch, attend and parse: An end-to-end neural network based approach to handwritten mathematical expression recognition. Pattern Recognit Lett 71:196–206. https://doi.org/10.1016/j.patcog.2017.06.017

    Article  Google Scholar 

  • Zhang T, Mouchere H, Viard-Gaudin C (2017d) Tree-Based BLSTM for mathematical expression recognition. In: 14th IAPR Int Conf on Doc Analy and Recognit vol 1, pp 914–919. https://doi.org/10.1109/ICDAR.2017.154

  • Zhang J, Du J, Dai L (2018a) Multi-scale attention with dense encoder for handwritten mathematical expression recognition. In: 24th Int Conf on Pattern Recognit pp 2245–2250. https://doi.org/10.1109/ICPR.2018.8546031

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

    Article  Google Scholar 

  • Zhang XY, Yin F, Zhang YM, Liu CL, Bengio Y (2018c) Drawing and recognizing chinese characters with recurrent neural network. IEEE Trans Pattern Anal Mach Intell 40(4):849–862. https://doi.org/10.1109/TPAMI.2017.2695539

    Article  Google Scholar 

  • Zhang W, Bai Z, Zhu Y (2019) An improved approach based on CNN-RNNs for mathematical expression recognition. In: 4th Int Conf on Multimedia Syst and Signal Process pp 57–61. https://doi.org/10.1145/3330393.3330410

  • Zhang J, Du J, Yang Y, Song Y, Dai L (2020) SRD: a tree structure based decoder for online handwritten mathematical expression recognition. IEEE Trans Multimed. https://doi.org/10.1109/TMM.2020.3011316

    Article  Google Scholar 

  • Zhao W, Gao L, Yan Z, Peng S, Du L (2021) Handwritten mathematical expression recognition with bidirectionally trained transformer. Springer, Cham

    Book  Google Scholar 

  • Zhelezniakov D, Zaytsev V, Radyvonenko O (2019) Acceleration of online recognition of 2D sequences using deep bidirectional LSTM and dynamic programming. In: Adv in Comput Intell IWANN 2019. Lecture notes in computer science, vol. 11507, pp. 1–13. https://doi.org/10.1007/978-3-030-20518-8

  • Zhelezniakov D, Cherneha A, Zaytsev V, Ignatova T, Radyvonenko O, Yakovchuk O (2020) Evaluating new requirements to pen-centric intelligent user interface based on end-to-end mathematical expressions recognition. In: Int Conf on Intell user Interfaces, Sydney, NSW, Australia, pp 212–220. https://doi.org/10.1145/3377325.3377482

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Appendices

Appendix

Appendix 1: Acronyms

Abbreviation

Full form

2D

Two Dimensional

3D

Three Dimensional

AI

Artificial Intelligence

AJAX

Asynchronous Java-script and XML

ANN

Artificial Neural Network

ASCII

American Standard Code for Information Interchange

BLSTM

Bidirectional Long Short-Term Memory

BPN

Back Propogation Neural Network

CAS

Computer Algebra System

CNN

Convolutional Neural Network

CRF

Conditional Random Field

CROHME

Competition On Recognition Online Handwritten Mathematical Expression

CYK

Cocke–Younger–Kasami

DCG

Definite Clause Grammar

DL

Deep Learning

DNN

Deep Neural Network

DRACULAE

Diagram Recognition Application for Computer Understanding of Large Algebraic Expressions

EM

Elastic Matching

EPS

Encapsulated Postscript

ERR RATE

Error Rate

EXP RATE

Expression Recognition Rate

FEES

Freehand Formula Entry System

FFN

Feedforward Neural Network

FOSA

Fuzzy Order Structural Analysis

GG

Graph Grammar

GIF

Graphical Interchange Format

GL

Grey Literature

GLR

Grey Literature Review

HME

Handwritten Mathematical Expression

HMM

Hidden Markov Methods

ICDAR

International Conference On Document Analysis And Recognition

ICFHR

International Conference On Frontiers In Handwriting Recognition

IJDAR

International Journal Document Analysis and Recognition

IML

Information Markup Language

KNN

K- Neural Network

LSTM

Long Short-Term Memory

ME

Mathematical Expression

MER

Mathematical Expression Recognition

ML

Machine Learning

MLR

Multivocal Literature Review

NLP

Natural Language Processing

NN

Neural Network

OCR

Optical Character Recognition

PC

Personal Computer

PNG

Portable Network Graphics

RBF

Radial Basis Function

RECOG RATE

Recognition Rate

RNN

Recurrent Neural Network

RQ

Research Question

SCFG

Stochastic Context Free Grammar

SEG RATE

Segmentation Rate

SLR

Systematic Literature Review

SVG

Scalable Vector Graphics

SVM

Support Vector Machine

SVM-DAG

Directed Acyclic Graph

SYM RECOG

Symbol Recognition

TBG

Tree Based Grammar

WMF

Windows Media Player

XHTML

Extended Hyper Text Markup Language

XM

Exiended Module

XML

Extensible Markup Language

Appendix 2: Bibliometric details of substages

Sub stages

References

Preprocessing

Celik and Yanikoglu (2011), Le et al. (2019a), Thimbleby (2004), Lin et al. (2012, 2016, 2019), Wang and Liu (2017), Zhang et al. (2017a, b, c, d), Phong et al. (2020b), MacLean et al. (2013), Bage et al. (2010), Shinde et al. (2018), Genoe et al. (2006c), Kumar et al. (2012), Shi et al. (2007), Zhelezniakov et al. (2019), Davila et al. (2013), Guo et al. (2007), Chan and Yeung (2000a), Shinde and Waghulade (2017), Wang et al. (2016b), Celar et al. (2015), Álvaro and Sánchez (2010), Le and Nakagawa (2016b), He et al. (2016), Guan et al. (2019), Ramadhan et al. (2016), Wang and Lin (2019), Chajri and Bouikhalene (2016), Shinde and Waghulade (2016), Abirami and Jaganathan (2019), Islam and Khan (2019), Hu and Zanibbi (2011), Mahdavi et al. (2019b), Gharde et al. (2013), Pillay (2014), Bender and Haurilet (2019), Fang and Zhang (2020), Lee et al. (2018), Okamoto et al. (2001), Huang et al. (2007), Watt and Xie (2005), Hossain et al. (2018), Naik et al. (2017), Jimenez and Nguyen (2013), Bharambe (2015), Dai Nguyen et al. (2016), Drsouza and Mascarenhas (2018), Tapia and Berlin (2005), Tapia and Rojas (2003), Álvaro et al. (2011), Le (2020), Naik and Metkewar (2015), Dai et al. (2019), Xue-Dong et al. (2006), Hu and Zanibbi (2013), Phan et al. (2016), Ks et al. (2018), Chan (2020), Clark et al. (2013), Vuong et al. (2010), Saroui and Sorge (2015), Davila et al. (2014)

Segmentation

Le et al. (2014), Le et al. (2016), Wang et al. (2016a, b, 2019), Aly et al. (2008), Kulkarni and Vasambekar (2010), Le et al. (2019a), Kanahori et al. (2000), Celik and Yanikoglu (2011), MacLean and Labahn (2015), Thimbleby (2004), Lin et al. (2012, 2016), Phong et al. (2020a), Wang and Liu (2017), Julca-Aguilar et al. (2020), Awal et al. (2014), Zhang et al. (2010, 2016, 2017a, b, c, d, 2018b, 2020), Awal et al. (2010a), Phong et al. (2020b), Madisetty et al. (2020), MacLean et al. (2013), Bage et al. (2010), Shinde et al. (2018), Suzuki (2000), Hunsinger and Lang (2000), Huang and Kechadi (2007), Shi and Soong (2008), Le and Nakagawa (2016a), Le and Nakagawa (2013), Zhelezniakov et al. (2019), Davila et al. (2013), Mouchère et al. (2014), Guo et al. (2007), Chan and Yeung (2000a, (2001a), Shinde and Waghulade (2017), Li and Tian (2010), Phan et al. (2015b), Álvaro et al. (2016), Toyozumi et al. (2006), Phan et al. (2018), Ung et al. (2018a), Hu et al. (2012), Medjkoune et al. (2017), Stria et al. (2014), Álvaro and Sánchez (2010), Golubitsky and Watt (2010), Fu et al. (2020), Rhee and Kim (2009), Aguilar and Hirata (2012), Elik (2010), Tran et al. (2018), Shinde and Waghulade (2016), Abirami and Jaganathan (2019), Gharde et al. (2013), Truong et al. (2020), Le and Nakagawa (2015), Pillay (2014), Feng et al. (2001), Bender and Haurilet (2019), Zanibbi et al. (2016), Hu and Zanibbi (2016), Hu et al. (2014), Yamamoto et al. (2006), Lee et al. (2018), Okamoto et al. (2001), Hossain et al. (2018), Bharambe (2015), Tapia and Berlin (2005), Álvaro et al. (2014a), Tapia and Rojas (2004), Mohan and Lu (2015), Tapia and Rojas (2003), Simistira et al. (2015), Álvaro et al. (2011), Fontenele Marques Junior et al. (2019), Zanibbi et al. (2002), Naik and Metkewar (2015), Dai et al. (2019), Xue-Dong et al. (2006), Shan et al. (2021), Jakjoud and Lazrek (2011), Phan et al. (2016), Ks et al. (2018), Ahmed et al. (2004), Xiangwei and Abaydulla (2010), Julca-Aguilar et al. (2015), Kim and Kim (2010), Chatbri et al. (2015), Awal et al. (2009), Tree-Based Structure Recognition Evaluation for Math Expressions: Techniques and Case Study, (2019), Jjn et al. (2002), Álvaro et al. (2012), Tapia (2005), Medjkoune et al. (2012)

Symbol Recognition

Le et al. (2014), Baker et al. (2010), Aly et al. (2009), MacLean and Labahn (2010), Shuvo et al. (2021), Clark et al. (2013), Kanahori et al. (2000), LaViola and Zeleznik (2007), Celik and Yanikoglu (2011), Le et al. (2016), Thimbleby (2004), Lin et al. (2016), Phong et al. (2020a), Sain et al. (2010), Awal et al. (2014), Zhang et al. (2016, 2017b, c); Awal et al. (2010a), Phong et al. (2020b), MacLean et al. (2013), Shinde et al. (2018), Suzuki (2000), Genoe et al. (2006c), Genoe and Kechadi (2010b), Kumar et al. (2014), Huang and Kechadi (2007), Shi and Soong (2008), Mori (2013), Simistira et al. (2012), Le and Nakagawa (2016a), Guo et al. (2007), Chan and Yeung (2000a, (2001a), Phan et al. (2015b), Álvaro et al. (2016), Toyozumi et al. (2006), Phan et al. (2018), Hirata and Honda (2011b), Wang et al. (2016a), Stria et al. (2014), Álvaro and Sánchez (2010), He et al. (2016), Ramadhan et al. (2016), Zeleznik et al. (2007), Golubitsky and Watt (2010), Rhee and Kim (2009), Wang and Lin (2019), Genoe and Kechadi (2010a), Elik (2010), Tran et al. (2018), Chajri and Bouikhalene (2016), Abirami and Jaganathan (2019), Garain (2009), Awal et al. (2010b), Le and Nakagawa (2015), Pillay (2014), Feng et al. (2001), Fitzgerald et al. (2007), Hu and Zanibbi (2016), Hu et al. (2014), Yamamoto et al. (2006), Okamoto et al. (2001), Vuong et al. (2008), Drsouza and Mascarenhas (2018), Mohan and Lu (2013b), Tapia and Berlin (2005),,Álvaro et al. (2014a), Tapia and Rojas (2004), Mohan and Lu (2015), Tapia and Rojas (2003), Álvaro et al. (2011), Fontenele Marques Junior et al. (2019), Dai et al. (2019), Xue-Dong et al. (2006), Hong et al. (2019), Shan et al. (2021), Jakjoud and Lazrek (2011), Phan et al. (2016), Ahmed et al. (2004), Le and Nakagawa (2017a), Chen and Okada (2001), Clark et al. (2013), Medjkoune and Mouchère (2014), Xiangwei and Abaydulla (2010), Vuong et al. (2010), Awal et al. (2009), Tree-Based Structure Recognition Evaluation for Math Expressions: Techniques and Case Study, (2019), Jjn et al. (2002), Álvaro et al. (2012), Tapia (2005), Viard-gaudin et al. (2016), Medjkoune et al. (2012)

Stroke Recognition

Genoe et al. (2006c), Le et al. (2019b), Genoe and Kechadi (2010b), Suzuki (2000), Le and Nakagawa (2013), Zhang et al. (2010), Toyozumi et al. (2006), Wang et al. (2016a, 2020), Zeleznik et al. (2007), Elik (2010), Tapia and Berlin (2005), Hong et al. (2019), Chan (2020), Shi et al. (2011), Medjkoune and Mouchère (2014), Vuong et al. (2010), Saroui and Sorge (2015), Viard-gaudin et al. (2016)

Structural Analysis

Le et al. (2014), Wu et al. (2021), Kanahori et al. (2000), Celik and Yanikoglu (2011), MacLean and Labahn (2015), Aly et al. (2009), Qi et al. (2009), Nghiem et al. (2011), Eto and Suzuki (2001), Thimbleby (2004), Lin et al. (2016), Phong et al. (2020a), Taranta et al. (2016), Awal et al. (2014), Sain et al. (2010), Zhang et al. (2005, 2016, 2017b, c, 2018b), Awal et al. (2010a), Phong et al. (2020b), MacLean et al. (2013), Suzuki (2000), Genoe and Kechadi (2010b), Hunsinger and Lang (2000), Mouchère et al. (2011), Mori (2013), Průša and Hlaváč (2007), Wang et al. (2019), Kumar et al. (2014), Huang and Kechadi (2007), Mori (2013), Simistira et al. (2012), Le and Nakagawa (2016a), Shi et al. (2007), Mouchère et al. (2014), Guo et al. (2007), Chan and Yeung (2000a, (2001a, Li and Tian (2010), Phan et al. (2015b), Álvaro et al. (2016), Toyozumi et al. (2006), Phan et al. (2018), Hirata and Honda (2011b), Jin et al. (2004), Medjkoune et al. (2017), Stria et al. (2014), Álvaro and Sánchez (2010), Yan et al. (2020), Rhee and Kim (2009), Aguilar and Hirata (2012), Wang and Lin (2019), Genoe and Kechadi (2010a), Tran et al. (2018), Chajri and Bouikhalene (2016), Garain (2009), Awal et al. (2010b), Le and Nakagawa (2015), Pillay (2014), Feng et al. (2001), Fitzgerald et al. (2007), Hu and Zanibbi (2016), Hu et al. (2014), Yamamoto et al. (2006), Okamoto et al. (2001), Vuong et al. (2008), Bharambe (2015), Mohan and Lu (2013b), Tapia and Berlin (2005), Álvaro et al. (2014a), Tapia and Rojas (2004), Tapia and Rojas (2003), Simistira et al. (2015), Álvaro et al. (2011), Le (2020), Zanibbi et al. (2002), Dai et al. (2019), Xue-Dong et al. (2006), Jakjoud and Lazrek (2011), Phan et al. (2016), Ahmed et al. (2004), Le and Nakagawa (2017a), Chen and Okada (2001), Medjkoune and Mouchère (2014), Xiangwei and Abaydulla (2010), Julca-Aguilar et al. (2015), Vuong et al. (2010), Awal et al. (2009), Álvaro et al. (2012), Tapia (2005), Medjkoune et al. (2012)

Feature Extraction

Awal et al. (2014), Zhang et al. (2016, 2017b, d, 2019), Madisetty et al. (2020), Bage et al. (2010), Shinde et al. (2018), Huang and Kechadi (2007), Davila et al. (2013), Phan et al. (2015b), Álvaro et al. (2016), Genoe et al. (2006b), Kacem et al. (2001), Toyozumi et al. (2006), Jin et al. (2004), Ramteke and Mehrotra (2006), Ung et al. (2018a), Celar et al. (2015), Li et al. (2020), Nguyen et al. (2020b), Wang et al. (2016a), Medjkoune et al. (2017), Álvaro and Sánchez (2010), He et al. (2016), Yan et al. (2020), Wang and Lin (2019), Genoe and Kechadi (2010a), Lods et al. (2019), Medjkoune et al. (2011), Wu et al. (2020), Chajri and Bouikhalene (2016), Shinde and Waghulade (2016), Hu and Zanibbi (2011), Lin et al. (2012), Gharde et al. (2013), Zanibbi and Yuan (2011), Bender and Haurilet (2019), Malon et al. (2008), Hu and Zanibbi (2016), Fang and Zhang (2020), Álvaro et al. (2014b), Lin et al. (2019), Huang et al. (2007), Watt and Xie (2005), Naik et al. (2017), Jimenez and Nguyen (2013), Bharambe (2015), Dai Nguyen et al. (2016), Drsouza and Mascarenhas (2018), Jain and Zanibbi (2017), Mohan and Lu (2013b), Mohan and Lu (2015), Tapia and Rojas (2003), Simistira et al. (2015), Simistira et al. (2014), Wang and Shan (2020), Le (2020), Naik and Metkewar (2015), Xue-Dong et al. (2006), Shan et al. (2021), Hu and Zanibbi (2013), Chen and Okada (2001), Julca-aguilar et al. (2016), Clark et al. (2013), Julca-Aguilar et al. (2015), Vuong et al. (2010), Le and Nakagawa (2017b), Viard-gaudin et al. (2016), Davila et al. (2014), Kim et al. (2009), Asebriy and Bencharef (2016)

Classification

Khuong et al. (2021), MacLean and Labahn (2015), Wang and Liu (2017), Julca-Aguilar et al. (2020), Awal et al. (2014), Zhang et al. (2016, 2017b, c, 2020), Phong et al. (2020b), Bage et al. (2010), Shinde et al. (2018), Álvaro (2013), Hunsinger and Lang (2000), Zhelezniakov et al. (2019), Mouchère et al. (2014), Shinde and Waghulade (2017), Álvaro et al. (2016), Genoe et al. (2006b), Jin et al. (2004), Ung et al. (2018a), Hu et al. (2012), Celar et al. (2015), Álvaro and Sánchez (2010), He et al. (2016), Guan et al. (2019), Yan et al. (2020), Ramadhan et al. (2016), Golubitsky and Watt (2010), Lods et al. (2019), Medjkoune et al. (2011), Shinde and Waghulade (2016), Abirami and Jaganathan (2019), Islam and Khan (2019), Hu and Zanibbi (2011), Lin et al. (2012), Gharde et al. (2013), Nguyen et al. (2020a), Bender and Haurilet (2019), Malon et al. (2008), Hu and Zanibbi (2016), Álvaro et al. (2014b), Lee et al. (2018), Huang et al. (2007), Hossain et al. (2018), Naik et al. (2017), Bharambe (2015), Dai Nguyen et al. (2016), Mohan and Lu (2013b), Mohan and Lu (2015), Simistira et al. (2015), Simistira et al. (2014), Wang and Shan (2020), Le (2020), Naik and Metkewar (2015), Xue-Dong et al. (2006), Hu and Zanibbi (2013), Ks et al. (2018), Le and Nakagawa (2017a), Clark et al. (2013), Kim and Kim (2010), Le and Nakagawa (2017b), Tree-Based Structure Recognition Evaluation for Math Expressions: Techniques and Case Study (2019), Tapia (2005), Davila et al. (2014)

Appendix 3: Data extraction attributes

Data extraction attributes

Title of the Paper

Segmentation

Year of Publication

Stroke Recognition

Category ML/Non-ML

Symbol Recognition

Publication Channel

Expression Recognition

Recognition Technique

Dataset

Type of Literature

Dataset Details

Preprocessing

Accuracy Metrics

Appendix 4: Grey literature sources

GL type

References

GL type

References

Command-string based

Application based

G-L-1

Raggett and Batsalle (1998)

G-L-29

https://apps.apple.com/in/app/mathbrush/id578957934

G-L-2

http://www.xthink.com/MathJournal.html.)

G-L-30

https://www.onenote.com/hrd

G-L-3

Fujimoto (2003)

G-L-31

https://www.galaxy.store/snot

G-L-4

Pollanen et al. (2007)

G-L-32

https://www.nebo.app

G-L-5

Suzuki et al. (2004)

G-L-33

https://www.myscript.com/calculator

G-L-6

Zanibbi et al. (2002)

G-L-34

Zhelezniakov et al. (2020)

G-L-7

Sucan (2006)

G-L-35

https://apps.apple.com/in/app/microsoft-maths-solver-hw-app/id1483962204

https://play.google.com/store/apps/details?id=com.microsoft.mat

Template based

G-L-36

https://apps.apple.com/in/app/photomath/id919087726

G-L-8

www.Inftyproject.org)

G-L-37

https://apps.apple.com/in/app/mathway/id467329677

G-L-9

Wolfram et al. (1999)

G-L-38

https://apps.apple.com/in/app/snapcalc-math-problem-solver/id1267331464

G-L-10

www.maplesoft.com)

G-L-39

https://apps.apple.com/in/app/photostudy-live-study-help/id797535508

G-L-11

Yeo (2004)

G-L-40

https://apps.apple.com/in/app/fastmath-take-photo-solve/id1438642238

G-L-12

source:www.desswci.com/en/products/mathtype/

G-L-41

https://play.google.com/store/apps/details?id=com.maplesoft.companion

Pen-based

G-L-42

https://play.google.com/store/apps/details?id=com.tinkutara.mathchat

G-L-13

Smithies (1999)

G-L-43

https://play.google.com/store/apps/details?id=com.ridzi.equationeditorandsymbol

G-L-14

Labahn et al. (2008)

G-L-44

https://play.google.com/store/apps/details?id=com.infologic.mathmagiclite

G-L-15

Tapia and Rojas (2003)

G-L-45

https://play.google.com/store/apps/details?id=com.math.photo.scanner.equation.formula.calculator

G-L-16

Fitzgerald et al. (2007)

G-L-46

https://play.google.com/store/apps/details?id=com.myscript.calculator

G-L-17

Kasuya and Yamana (2007)

G-L-47

https://play.google.com/store/apps/details?id=mobi.camera.calculator

G-L-18

Madhvanath et al. (2004)

G-L-48

https://play.google.com/store/apps/details?id=com.diotek.diopencalculator

G-L-19

Tapia (2004)

G-L-49

https://play.google.com/store/apps/details?id=com.lichtcode.calculatortouch

G-L-20

https://docs.microsoft.com/en-us/archive/msdn-magazine/2004/december/tablet-pc-supporting-digital-ink-in-your-windows-applications

G-L-50

https://play.google.com/store/apps/details?id=com.usman.scan_calculator

G-L-21

Li et al. (2008)

G-L-51

https://apps.apple.com/in/app/camera-math-homework-help/id1532857459

G-L-22

Chan and Yeung (2001b)

G-L-52

https://apps.apple.com/in/app/photomath/id919087726

G-L-23

Lee et al. (2008)

G-L-53

https://apps.apple.com/in/app/cymath-math-problem-solver/id1083328891

G-L-24

Jiang et al. (2010)

G-L-54

https://play.google.com/store/apps/details?id=air.mathonboard

G-L-25

Bott and LaViola (2010)

G-L-55

https://apps.apple.com/in/app/mathpix-snip/id1445642260

G-L-26

Kang and LaViola (2012)

Patents

G-L-27

Cheema and LaViola (2012)

G-L-56

https://patents.google.com/patent/US20200286402A1/en?oq=US20200286402A1

G-L-28

Cossairt (2019)

G-L-57

https://patents.google.com/patent/US5655136A/en?oq=US5655136A

Workshop, forums and symposiums

G-L-58

https://patents.google.com/patent/CN110751137A/en?oq=CN110751137A

G-L-70

Álvaro (2013)

G-L-59

https://patents.google.com/patent/EP1239406B1/en?oq=EP20020004377

G-L-71

Lin et al. (2019)

G-L-60

https://patents.google.com/patent/CN105512692B

G-L-72

Hu et al. (2014)

G-L-61

https://patents.google.com/patent/US7447360B2

G-L-73

Tree-Based Structure Recognition Evaluation for Math Expressions: Techniques and Case Study (2019)

G-L-62

https://patents.google.com/patent/US20170364744A1/

G-L-74

Le et al. (2014)

G-L-63

https://patents.google.com/patent/EP1239406B1/

G-L-75

Davila et al. (2013)

G-L-64

https://patents.google.com/patent/WO2003071393A2/

G-L-76

Le and Nakagawa (2016a)

G-L-65

https://patents.google.com/patent/US7885456B2

G-L-77

Yamamoto et al. (2006)

G-L-66

https://patents.google.com/patent/US5627914A/

G-L-78

Genoe et al. (2006c)

G-L-67

https://patents.google.com/patent/US8077975B2

G-L-79

Gharde et al. (2013)

G-L-68

https://patents.google.com/patent/US7561738B2/

G-L-80

Stria et al. (2014)

G-L-69

https://patents.google.com/patent/US20040054701A1/

G-L-81

Zeleznik et al. (2007)

Preprints

G-L-82

Baker et al. (2010)

G-L-100

Wang et al. (2020)

G-L-83

Golubitsky et al. (2010)

G-L-101

Islam and Khan (2019)

G-L-84

Le et al. (2016)

G-L-102

Fu et al. (2020)

G-L-85

Wang et al. (2016b)

G-L-103

Yan et al. (2020)

G-L-86

Zhelezniakov et al. (2019)

Dissertations

G-L-87

Aguilar and Hirata (2012)

G-L-104

Pillay (2014)

G-L-88

Hirata and Honda (2011a)

G-L-105

Tapia (2005)

G-L-89

Tapia and Rojas (2004)

G-L-106

Thimbleby (2004)

G-L-90

Kumar et al. (2012)

G-L-107

Elik (2010)

G-L-91

Nghiem et al. (2011)

  

Technical reports

G-L-92

Mohan and Lu (2013b)

G-L-96

Pillay (2014)

G-L-93

Jimenez and Nguyen (2013)

G-L-97

Jain and Zanibbi (2017)

G-L-94

Mohan and Lu (2015)

G-L-98

Viard-gaudin et al. (2016)

G-L-95

MacLean and Labahn (2010)

G-L-99

Feng et al. (2001)

Appendix 5: Accuracy metric frequency analysis

Accuracy metric

Count

Accuracy metric

Count

Accuracy metric

Count

Accuracy metric

Count

Recognition rate

46

Recall

12

Structure Recognition Rate

4

Bleu

2

Accuracy

45

Symbol Recognition Rate

9

Complexity

3

Confidence Values

1

Expression recognition rate

35

F Score

7

Correction Rate

2

Learning Rates

1

Segmentation rate

26

Classification Rate

5

Formula Recognition Rate

2

Distance Score Rate

1

Error rate

20

Relational Tree

5

Purity

2

P Value

1

Precision

15

Stroke Recognition Rate

5

Standard Deviation

2

T Value

1

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Sakshi, Kukreja, V. A dive in white and grey shades of ML and non-ML literature: a multivocal analysis of mathematical expressions. Artif Intell Rev 56, 7047–7135 (2023). https://doi.org/10.1007/s10462-022-10330-1

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