【作者】 林桂芳；

【导师】 王科俊；

【作者基本信息】 哈尔滨工程大学 ， 模式识别与智能系统， 2004， 硕士

【摘要】 本课题研究数学表达式中符号的识别，因为在科技高度发展的现代，数学表达式是大多数科技文献的核心，对它的研究可以使数学表达式用于检索，提高文献的科技性；实现公式输入的自动化，以解决手动输入的低效率问题；随着计算机网络的发展，网上传递资料成为人们常用的方式，改变数学表达式图片的存在形式，可以节省空间，提高网络的传输速度等。 本文分析了国内外数学公式识别研究的现状，建立一个通用的数学公式识别系统是研究的难点，也是实际应用所需求的。在本系统中，首先对符号图像进行阈值的二值化处理；图像在生成的过程中容易引进噪声，对此进行了图像的平滑去噪；为了得到符号图像清晰的拓扑结构，采用了Hilditch算法进行符号图像的细化处理；由于数学表达式中符号大小的多样性不利于识别，所以对这些符号进行了大小的归一化。然后使用骨架链码法，根据结构分析后的符号的孔洞数及其位置、端点数、角点数等结构特征对数学表达式中常见到的103个符号进行实验初分类，可分成十个小的类，每个小类都对应着一个神经网络。再对符号的数字图像统计字符的9个网格特征和4个交叉点特征，即符号的13维特征向量作为特征值。提取特征值后用神经网络进行训练学习，在课题中采用的模板都是固定标准(大小、灰度级)的。最后用模板匹配的方法进行符号识别。由于计算机编码的限制，有些特殊符号识别的结果就采用其它符号替代的方式进行研究，通过大量实验，103个符号都能够被正确识别出来。更多还原

【Abstract】 This paper investigated the recognition of the symbols in mathematical expressions. With the development of science and technology nowadays, the researches on the mathematical expressions, which are composed of many rules of science and technology, can make the mathematical expressions be used in searches, and therefore improve the level of science and technology in literature. The automation of expressions input can solve the low efficiency which result from hand input. With the development of computer network, it become the common way to transfer information in network and to transform the pictures’ presence form of the mathematical expressions which can save the room and increase the transfer rate and so on.This paper introduced the research status quo of mathematics expression in the world, the difficulty in research is establish a system of mathematics expression recognition in common currency and it is required in practice application. In this system, we disposed the symbol image in binary system number to ascertain the threshold value at first. It will import noise in the process of image creation, so we adopted a method with the image to flatness the noise. We also thinned the symbol image with the Hilditch arithmetic to obtain the clear topology structure. Because of the diversity of symbol magnitude in mathematics expression, it is not easy to recognize the symbol, so we disposed thesesymbols into uniform size, then use the method of framework-chain cord and according to the symbol structure characters such as the number and the position of hole, the number of end point, the numbers of angle and so on, we classify those 103 symbols which are familiar in mathematical expressions into eight classes and ten sub-class, and each sub-class corresponds to a neural network. The 13-dimention eigenvectors, include the 9 gridding characters and 4 crossing characters belong to figure image of the symbol by statistical, as the eigenvalue of the symbol then train and study these picked eigenvalue with the neural network, save as template at last. In this paper, the templates are in fixed standard (the magnitude and the picture contrast), we can recognize the symbol with template marching. But some special characters were recognized and researched substituted by other symbols due to the restriction of the computer coding, thus all these 103 symbols can be recognized by experiment at last.更多还原