ce qui permet de choisir une solution qui optimise un critère global pour aboutir à la meilleure interprétation globale Ces solutions utilisent de l'information contextuelle, notamment des connaissances syntaxiques, pour guider les processus de segmentation et de reconnaissance, en empêchant de produire des solutions potentiellement invalides comme par exemple, [a + b). L'information contextuelle est généralement modélisée par une grammaire qui peut se limiter à produire des chaines (string grammar, Les travaux plus récents combinent ces trois tâches en produisant plusieurs alternatives concurrentes, 2006. ,
Classification of On-Line Mathematical Symbols with Hybrid Features and Recurrent Neural Networks, 2013 12th International Conference on Document Analysis and Recognition, pp.1012-1016, 2013. ,
DOI : 10.1109/ICDAR.2013.203
Offline Features for Classifying Handwritten Math Symbols with Recurrent Neural Networks, 2014 22nd International Conference on Pattern Recognition, pp.2944-2949 ,
DOI : 10.1109/ICPR.2014.507
Recognition of on-line handwritten mathematical expressions using 2D stochastic context-free grammars and hidden Markov models, Pattern Recognition Letters, vol.35, issue.32, pp.58-67, 2014. ,
DOI : 10.1016/j.patrec.2012.09.023
An integrated grammar-based approach for mathematical expression recognition, Pattern Recognition, vol.51, issue.40, pp.135-147, 2016. ,
DOI : 10.1016/j.patcog.2015.09.013
Statistical Classification of Spatial Relationships among Mathematical Symbols, 2009 10th International Conference on Document Analysis and Recognition, pp.1350-1354, 2009. ,
DOI : 10.1109/ICDAR.2009.90
Syntax-directed recognition of hand-printed two-dimensional mathematics, Symposium on Interactive Systems for Experimental Applied Mathematics: Proceedings of the Association for Computing Machinery Inc. Symposium, pp.436-459, 1967. ,
Two-Dimensional Mathematical Notation, Syntactic Pattern Recognition, Applications, pp.147-177, 1977. ,
DOI : 10.1007/978-3-642-66438-0_7
A global learning approach for an online handwritten mathematical expression recognition system, Pattern Recognition Letters, vol.35, issue.64, pp.68-77, 2014. ,
DOI : 10.1016/j.patrec.2012.10.024
URL : https://hal.archives-ouvertes.fr/hal-00756637
Exploiting the past and the future in protein secondary structure prediction, Bioinformatics, vol.15, issue.11, pp.937-946, 1999. ,
DOI : 10.1093/bioinformatics/15.11.937
Learning long-term dependencies with gradient descent is difficult, IEEE Transactions on Neural Networks, vol.5, issue.2, pp.157-166, 1994. ,
DOI : 10.1109/72.279181
Neural networks for pattern recognition, p.42, 1995. ,
Recognition of mathematical notation. Handbook of character recognition and document image analysis, pp.557-582, 1997. ,
Framewise and CTC training of Neural Networks for handwriting recognition, 2015 13th International Conference on Document Analysis and Recognition (ICDAR), pp.81-85, 2015. ,
DOI : 10.1109/ICDAR.2015.7333730
Scan, Attend and Read: End-to-End Handwritten Paragraph Recognition with MDLSTM Attention, 2017 14th IAPR International Conference on Document Analysis and Recognition (ICDAR), p.93, 2016. ,
DOI : 10.1109/ICDAR.2017.174
Connectionist speech recognition: a hybrid approach, p.51, 2012. ,
DOI : 10.1007/978-1-4615-3210-1
Probabilistic Mathematical Formula Recognition Using a 2D Context-Free Graph Grammar, 2011 International Conference on Document Analysis and Recognition, pp.161-166, 2011. ,
DOI : 10.1109/ICDAR.2011.41
Mathematical expression recognition: a survey, International Journal on Document Analysis and Recognition, vol.3, issue.1, pp.3-15, 2000. ,
DOI : 10.1007/PL00013549
A method for the structural analysis of two-dimensional mathematical expressions, Information Sciences, vol.2, issue.3, pp.253-272, 1970. ,
DOI : 10.1016/S0020-0255(70)80052-4
Recognition of Equations Using a Two-Dimensional Stochastic Context-Free Grammar, Visual Communications and Image Processing IV, pp.852-863, 1989. ,
DOI : 10.1117/12.970095
Introduction to algorithms, p.78, 2009. ,
Unifying Math Ontologies: A Tale of Two Standards, Calculemus/MKM, pp.263-278, 2009. ,
DOI : 10.1007/11826095_4
Computational geometry: Algorithms and applications, p.79 ,
What you get is what you see: A visual markup decompiler. arXiv preprint, pp.32-39 ,
OpenMath, ACM SIGSAM Bulletin, vol.34, issue.2, pp.2-5, 2000. ,
DOI : 10.1145/362001.362008
Rnnlib: A recurrent neural network library for sequence learning problems, 2013. ,
Framewise phoneme classification with bidirectional LSTM networks, Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005., pp.2047-2052, 2005. ,
DOI : 10.1109/IJCNN.2005.1556215
URL : http://www6.in.tum.de/pub/Main/Publications/Graves2005a.pdf
Offline Arabic Handwriting Recognition with Multidimensional Recurrent Neural Networks, Advances in neural information processing systems, pp.545-552, 2009. ,
DOI : 10.1007/978-1-4471-4072-6_12
A novel connectionist system for unconstrained handwriting recognition. Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.87, issue.5, pp.31855-868, 2009. ,
Hybrid speech recognition with Deep Bidirectional LSTM, 2013 IEEE Workshop on Automatic Speech Recognition and Understanding, pp.273-278 ,
DOI : 10.1109/ASRU.2013.6707742
Supervised sequence labelling with recurrent neural networks, pp.67-93, 2012. ,
DOI : 10.1007/978-3-642-24797-2
Automatic Labeling of Handwritten Mathematical Symbols via Expression Matching, International Workshop on Graph-Based Representations in Pattern Recognition, pp.295-304, 2011. ,
DOI : 10.1016/j.imavis.2008.04.004
Long Short-Term Memory, Neural Computation, vol.4, issue.8, pp.1735-1780, 1997. ,
DOI : 10.1016/0893-6080(88)90007-X
Gradient flow in recurrent nets: the difficulty of learning long-term dependencies, p.129, 2001. ,
Features and Algorithms for Visual Parsing of Handwritten Mathematical Expressions, pp.78-82 ,
Segmenting Handwritten Math Symbols Using AdaBoost and Multi-scale Shape Context Features, 2013 12th International Conference on Document Analysis and Recognition, pp.1180-1184, 2013. ,
DOI : 10.1109/ICDAR.2013.239
Artificial neural networks: a tutorial, Computer, vol.29, issue.3, pp.31-44, 1996. ,
DOI : 10.1109/2.485891
Recognition of Online Handwritten Mathematical Expressions using Contextual Information, pp.32-35, 2016. ,
URL : https://hal.archives-ouvertes.fr/tel-01326354
Segmentation and recognition of symbols within handwritten mathematical expressions, 1995 International Conference on Acoustics, Speech, and Signal Processing, pp.2439-2442, 1995. ,
DOI : 10.1109/ICASSP.1995.479986
On-line handwritten formula recognition using statistical methods, Proceedings. Fourteenth International Conference on Pattern Recognition (Cat. No.98EX170), pp.1306-1308, 1998. ,
DOI : 10.1109/ICPR.1998.711941
Visual languages for knowledge representation, Proc. of 11th Workshop on Knowledge Acquisition, Modeling and Management (KAW'98) Banff, p.15, 1998. ,
A time-delay neural network architecture for isolated word recognition, Neural Networks, vol.3, issue.1, pp.23-43, 1990. ,
DOI : 10.1016/0893-6080(90)90044-L
A soft-decision approach for symbol segmentation within handwritten mathematical expressions, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings, p.96, 1996. ,
DOI : 10.1109/ICASSP.1996.550766
Learning Long-Term Dependencies in NARX Recurrent Neural Networks, IEEE Transactions on Neural Networks, vol.7, issue.6, pp.1329-1338, 1996. ,
DOI : 10.1201/9781420049176.ch6
Improving MDLSTM for Offline Arabic Handwriting Recognition Using Dropout at Different Positions, International Conference on Artificial Neural Networks, pp.431-438, 2016. ,
DOI : 10.1162/neco.1997.9.8.1735
Recognition of Handwritten Arabic Words with Dropout Applied in MDLSTM, International Conference Image Analysis and Recognition, pp.746-752, 2016. ,
DOI : 10.1007/978-3-319-23117-4_32
A new approach for recognizing handwritten mathematics using relational grammars and fuzzy sets, International Journal on Document Analysis and Recognition (IJDAR), vol.24, issue.11, pp.139-163, 2013. ,
DOI : 10.1109/ICDAR.2005.250
A Survey of Visual Language Specification and Recognition, Visual language theory, pp.5-85, 1998. ,
DOI : 10.1007/978-1-4612-1676-6_2
Computer input/output of mathematical expressions, Proceedings of the second ACM symposium on Symbolic and algebraic manipulation , SYMSAC '71, pp.78-89, 1971. ,
DOI : 10.1145/800204.806270
Recognition of handwritten mathematical expressions, pp.32-127, 1999. ,
Segmentation-free handwritten Chinese text recognition with LSTM-RNN, 2015 13th International Conference on Document Analysis and Recognition (ICDAR), pp.171-175, 2015. ,
DOI : 10.1109/ICDAR.2015.7333746
Icfhr 2014 competition on recognition of on-line handwritten mathematical expressions, Frontiers in Handwriting Recognition (ICFHR), 2014 14th International Conference on, pp.791-796, 2014. ,
Advancing the state of the art for handwritten math recognition: the crohme competitions, International Journal on Document Analysis and Recognition (IJDAR), vol.19, issue.28, pp.2011-2014173, 2016. ,
Induction of multiscale temporal structure, Advances in neural information processing systems, pp.275-282, 1992. ,
Mathematical Expression Recognition based on Probabilistic Grammars, pp.78-98, 2015. ,
Evaluation: from precision, recall and f-measure to roc, informedness, markedness and correlation, p.31, 2011. ,
The utility driven dynamic error propagation network, p.45, 1987. ,
Learning internal representations by error propagation, p.44, 1985. ,
Learning Complex, Extended Sequences Using the Principle of History Compression, Neural Computation, vol.4, issue.2, pp.234-242, 1992. ,
DOI : 10.1080/09540098908915631
On supervised learning from sequential data with applications for speech recognition. Daktaro disertacija, Nara Institute of Science and Technology, p.45, 1999. ,
Bidirectional recurrent neural networks, IEEE Transactions on Signal Processing, vol.45, issue.11, pp.2673-2681, 1997. ,
DOI : 10.1109/78.650093
URL : https://maxwell.ict.griffith.edu.au/spl/publications/papers/ieeesp97_schuster.pdf
A handwriting-based equation editor, Graphics Interface, pp.84-91, 1999. ,
Improved Semantic Representations From Tree-Structured Long Short-Term Memory Networks, Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 1: Long Papers), pp.49-50 ,
DOI : 10.3115/v1/P15-1150
URL : https://doi.org/10.3115/v1/p15-1150
Understanding mathematics: A system for the recognition of on-line handwritten mathematical expressions, pp.17-127, 2005. ,
Recognition of On-line Handwritten Mathematical Expressions Using a Minimum Spanning Tree Construction and Symbol Dominance, International Workshop on Graphics Recognition, pp.329-340, 2003. ,
DOI : 10.1007/978-3-540-25977-0_30
A survey on recognition of on-line handwritten mathematical notation, p.32, 2007. ,
A study of symbol segmentation method for handwritten mathematical formula recognition using mathematical structure information, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004., pp.630-633, 2004. ,
DOI : 10.1109/ICPR.2004.1334327
A global parser for context-free phrase structure grammars, Communications of the ACM, vol.11, issue.4, pp.240-247, 1968. ,
DOI : 10.1145/362991.363001
Generalization of backpropagation with application to a recurrent gas market model, Neural Networks, vol.1, issue.4, pp.339-356, 1988. ,
DOI : 10.1016/0893-6080(88)90007-X
Backpropagation through time: what it does and how to do it, Proceedings of the IEEE, pp.1550-1560, 1990. ,
DOI : 10.1109/5.58337
Gradient-based learning algorithms for recurrent networks and their computational complexity. Backpropagation: Theory, architectures, and applications, pp.433-486, 1995. ,
Online symbol segmentation and recognition in handwritten mathematical expressions ICASSP-97, Acoustics, Speech, and Signal Processing IEEE International Conference on, pp.3377-3380, 1997. ,
Symbol segmentation and recognition for understanding handwritten mathematical expressions, Progress in handwriting recognition. Citeseer, p.78, 1997. ,
A soft-decision approach for structural analysis of handwritten mathematical expressions, 1995 International Conference on Acoustics, Speech, and Signal Processing, pp.2459-2462, 1995. ,
DOI : 10.1109/ICASSP.1995.480046
On-line recognition of handwritten mathematical expressions based on stroke-based stochastic context-free grammar, tenth International Workshop on Frontiers in Handwriting Recognition. Suvisoft, pp.32-127, 2006. ,
URL : https://hal.archives-ouvertes.fr/inria-00104743
A unified framework for symbol segmentation and recognition of handwritten mathematical expressions, Document Analysis and Recognition Ninth International Conference on, pp.854-858, 2007. ,
Recognition and retrieval of mathematical expressions, International Journal on Document Analysis and Recognition (IJDAR), vol.8, issue.11, pp.331-357, 2012. ,
DOI : 10.1007/s00530-002-0070-3
Recognizing mathematical expressions using tree transformation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.11, pp.1455-1467, 2002. ,
DOI : 10.1109/TPAMI.2002.1046157
Evaluating structural pattern recognition for handwritten math via primitive label graphs, Document Recognition and Retrieval XX, pp.865817-865817, 2013. ,
DOI : 10.1117/12.2008409
URL : https://hal.archives-ouvertes.fr/hal-00852866
Watch, attend and parse: An end-to-end neural network based approach to handwritten mathematical expression recognition, Pattern Recognition, vol.71, p.37, 2017. ,
DOI : 10.1016/j.patcog.2017.06.017
Using fuzzy logic to analyze superscript and subscript relations in handwritten mathematical expressions, Eighth International Conference on Document Analysis and Recognition (ICDAR'05), pp.972-976, 2005. ,
DOI : 10.1109/ICDAR.2005.250
DAG-Structured Long Short-Term Memory for Semantic Compositionality, Proceedings of the 2016 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pp.917-926 ,
DOI : 10.18653/v1/N16-1106
Long short-term memory over recursive structures, ICML, pp.1604-1612 ,
A Tree-BLSTM based Recogniton System for Online Handwritten Mathematical Expression, International Journal on Document Analysis and Recognition, issue.1, p.2017 ,
Using BLSTM for interpretation of 2-D languages. Document numérique, pp.135-157 ,
URL : https://hal.archives-ouvertes.fr/hal-01576302
Tree-Based BLSTM for Mathematical Expression Recognition, 2017 14th IAPR International Conference on Document Analysis and Recognition (ICDAR) ,
DOI : 10.1109/ICDAR.2017.154
URL : https://hal.archives-ouvertes.fr/hal-01576305
Online Handwritten Mathematical Expressions Recognition by Merging Multiple 1D Interpretations, 2016 15th International Conference on Frontiers in Handwriting Recognition (ICFHR), pp.187-192 ,
DOI : 10.1109/ICFHR.2016.0045
URL : https://hal.archives-ouvertes.fr/hal-01374392
Using BLSTM for Interpretation of 2D Languages -Case of Handwritten Mathematical Expressions. l'Ecrit et le Document (CIFED), 2016 Colloque International Francophone sur, pp.217-232, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01576302
On-line Handwritten Isolated Symbol Recognition using Bidirectional Long Short-term, BLSTM) Networks. Information and Communication Technologies, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01576309