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Handwritten Mathematical Symbol Recognition for Computer Algebra Applications Xiaofang Xie, Stephen M. Watt Dept. of Computer Science, University of Western Ontario ECCAD 2005 Motivation Provide computer algebra applications a nice pen-based interface Attract more users to Maple, Mathematica. Handwriting recognition is the key to PDA Make mathematics easier input and edited

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Math Editor Limitations: cannot cover all math symbols Slow comparing with hand writing

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Literature Overview Pattern Matching: feature matching, element matching, elastic matching Neural Network Hidden Markov Model On-line vs. Off-line recognition

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Literature Overview(cont.)

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Recognizer Architecture Data Collection Preprocessing Feature Extraction Hidden M. Model Grouping Vector Quantization Elastic Matching Combined Classifier Context Info

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Preprocessing Resampling Deslanting Smoothing Size Normalization Selectively Chop Head / Tail

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Feature Extraction Number of Strokes; Pendown; Pen Pressure Position of end points; Distance to initial. Writing Angle; SgnX; End points directions Point Density; Aspect Ratio Number of Cusps Number of Intersections Number of Loops Velocity; Acceleration

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Feature Extraction (Cont.)

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Design Hidden Markov Model Decompose symbols into basic elements

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Design Hidden Markov Model(Cont.) Multiple Path Hidden Markov Model

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Allomorph Analysis Variance makes recognition hard Contribute to design Hmm

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Combine Classifiers Classifiers complement each other Analyze the recognition results Detect Correlated Errors Develop Combination Scheme

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Context Information Solve Ambiguity Build Dictionary

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Partial Results ExperimentNo.of PrototypesRecog. Rate(%) P1:T1,2,3, P1,2:T1,2,3, P1,2,3:T1,2,3, P1,2,3,4:T1,2,3, Recog. Results on 227 mathematical symbols. P represents prototype, T represents test data.

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Partial Results(Cont.) ExperimentNo.of Prototypes Candidate Prototypes Percentage Pruned(%) Recog. Rate(%) P1:T P1,2:T P1-3:T P1-4:T Using features to prune prototypes.

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