Abstract
Structural analysis helps in parsing the mathematical expressions. Various approaches for structural analysis have been reported in literature, but they mainly deal with online and printed expressions. In this work, two-dimensional, stochastic context-free grammar is used for the structural analysis of offline handwritten mathematical expressions in a document image. The spatial relation between characters in an expression has been incorporated so that the structural variability in handwritten expressions can be tackled.
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References
Alvaro, F., Benedi, J.M., et al.: Recognition of printed mathematical expressions using two-dimensional stochastic context-free grammars. In: 2011 International Conference on Document Analysis and Recognition (ICDAR), pp. 1225–1229. IEEE (2011)
Álvaro, F., Sánchez, J.A., Benedí, J.M.: Offline features for classifying handwritten math symbols with recurrent neural networks. In: 2014 22nd International Conference on Pattern Recognition (ICPR), pp. 2944–2949. IEEE (2014)
Álvaro, F., Sánchez, J.A., Benedí, J.M.: Recognition of on-line handwritten mathematical expressions using 2d stochastic context-free grammars and hidden Markov models. Pattern Recognit. Lett. 35, 58–67 (2014)
Anderson, R.H.: Two-dimensional mathematical notation. In: Syntactic Pattern Recognition, Applications, pp. 147–177. Springer (1977)
Chen, L.: A system for on-line recognition of handwritten mathematical expressions. Comput. Process. Chin. Orient. Lang. 6(1), 19–39 (1992)
Chou, P.A.: Recognition of equations using a two-dimensional stochastic context-free grammar. In: Visual Communications and Image Processing IV, vol. 1199, pp. 852–866. International Society for Optics and Photonics (1989)
Faure, C., Wang, Z.X.: Automatic perception of the structure of handwritten mathematical expressions. In: Computer Processing of Handwriting, pp. 337–361. World Scientific (1990)
Fitzgerald, J.A., Geiselbrechtinger, F., Kechadi, M.T.: Structural analysis of handwritten mathematical expressions through fuzzy parsing. ACST 6, 151–156 (2006)
Fukuda, R., Sou, I., Tamari, F.: A technique of mathematical expression structure analysis for the handwriting input system. In: Proceedings of the Fifth International Conference on Document Analysis and Recognition, 1999, ICDAR’99, pp. 131–134. IEEE (1999)
Garain, U., Chaudhuri, B.B.: Recognition of online handwritten mathematical expressions. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 34(6), 2366–2376 (2004)
Ha, J., Haralick, R.M., Phillips, I.T.: Understanding mathematical expressions from document images. In: Proceedings of the Third International Conference on Document Analysis and Recognition, 1995, vol. 2, pp. 956–959. IEEE (1995)
Inoue, K., Miyazaki, R., Suzuki, M.: Optical recognition of printed mathematical documents. In: Proceedings of the Third Asian Technology Conference on Mathematics, pp. 280–289 (1998)
Julca-Aguilar, F., Mouchère, H., Viard-Gaudin, C., Hirata, N.S.: Top-down online handwritten mathematical expression parsing with graph grammar. In: IberoAmerican Congress on Pattern Recognition, pp. 444–451. Springer (2015)
Kosmala, A., Rigoll, G.: On-line handwritten formula recognition using statistical methods. In: Proceedings of the Fourteenth International Conference on Pattern Recognition, 1998, vol. 2, pp. 1306–1308. IEEE (1998)
Lee, H.J., Wang, J.S.: Design of a mathematical expression understanding system. Pattern Recognit. Lett. 18(3), 289–298 (1997)
Liang, P., Narasimhan, M., Shilman, M., Viola, P.: Efficient geometric algorithms for parsing in two dimensions. In: Proceedings of the Eighth International Conference on Document Analysis and Recognition, 2005, pp. 1172–1177. IEEE (2005)
MacLean, S., Labahn, G.: A new approach for recognizing handwritten mathematics using relational grammars and fuzzy sets. Int. J. Doc. Anal. Recognit. (IJDAR) 16(2), 139–163 (2013)
Miller, E.G., Viola, P.A.: Ambiguity and constraint in mathematical expression recognition. In: AAAI/IAAI, pp. 784–791 (1998)
Mitra, J., Garain, U., Chaudhuri, B., HV, K.S., Pal, T.: Automatic understanding of structures in printed mathematical expressions. In: Proceedings of the Seventh International Conference on Document Analysis and Recognition, 2003, pp. 540–544. IEEE (2003)
Okamoto, M.: Recognition of mathematical expressions by using the layout structure of symbols. In: Proceedings of the 1st International Conference on Document Analysis and Recognition, 1991, pp. 242–250 (1991)
Okamoto, M., Miyazawa, A.: An experimental implementation of a document recognition system for papers containing mathematical expressions. In: Structured Document Image Analysis, pp. 36–53. Springer (1992)
Yamamoto, R., Sako, S., Nishimoto, T., Sagayama, S.: On-line recognition of handwritten mathematical expressions based on stroke-based stochastic context-free grammar. In: Tenth International Workshop on Frontiers in Handwriting Recognition. Suvisoft (2006)
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Aggarwal, R., Harit, G., Tiwari, A.K. (2020). Structural Analysis of Offline Handwritten Mathematical Expressions. In: Chaudhuri, B., Nakagawa, M., Khanna, P., Kumar, S. (eds) Proceedings of 3rd International Conference on Computer Vision and Image Processing. Advances in Intelligent Systems and Computing, vol 1024. Springer, Singapore. https://doi.org/10.1007/978-981-32-9291-8_18
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DOI: https://doi.org/10.1007/978-981-32-9291-8_18
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