手写体数学表达式识别的贝叶斯模型
A Bayesian model for recognizing handwritten mathematical expressions
摘要：
识别手写数学是一个具有挑战性的分类问题，需要同时识别包括输入的所有符号以及符号和子表达式之间的复杂二维关系。由于手写输入中存在的模糊性，希望始终保持完美的识别精度通常是不现实的。我们提出了一个系统，它捕获所有可识别的解释的输入，并组织他们在一个解析森林，从单独的解析树可以提取和报告。如果排名最高的解释不正确，则用户可以请求替代并选择他们期望的识别结果。树提取步骤使用一种新的概率树评分策略，其中贝叶斯网络是基于输入的结构构建的，并且每个联合变量分配对应于不同的解析树。然后按照概率递减的顺序报告解析树。两个准确性评估表明，由此产生的识别系统比以前的版本（使用非概率方法）和其他学术数学识别器更准确。
英文摘要：
Recognizing handwritten mathematics is a challenging classification problem, requiring simultaneous identification of all the symbols comprising an input as well as the complex two-dimensional relationships between symbols and subexpressions. Because of the ambiguity present in handwritten input, it is often unrealistic to hope for consistently perfect recognition accuracy. We present a system which captures all recognizable interpretations of the input and organizes them in a parse forest from which individual parse trees may be extracted and reported. If the top-ranked interpretation is incorrect, the user may request alternates and select the recognition result they desire. The tree extraction step uses a novel probabilistic tree scoring strategy in which a Bayesian network is constructed based on the structure of the input, and each joint variable assignment corresponds to a different parse tree. Parse trees are then reported in order of decreasing probability. Two accuracy evaluations demonstrate that the resulting recognition system is more accurate than previous versions (which used non-probabilistic methods) and other academic math recognizers.
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