印刷体数学公式识别关键问题研究

发布时间：2018-02-24 12:41

本文关键词： 公式识别粘连符号公式切分卷积神经网络深度学习　出处：《沈阳工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：印刷体数学公式识别是指将以图像方式输入的数学公式转化为可编辑的符号,从而实现公式的重用。目前,主流的OCR系统对普通文本的识别已达到较高水平,但在数学公式的识别方面还不理想,其中由于数学公式复杂的二维结构所导致的多种符号粘连以及数学符号种类、字体、大小的多样性是影响识别率的主要因素,需要更为有效的粘连符号切分和识别方法,从而提高数学公式整体的识别质量。论文首先对印刷体数学公式识别系统的构成及关键技术、识别中的难点进行介绍和讨论。其次,对数学公式粘连符号的切分方法进行了深入研究。针对普遍存在也更为复杂的斜体粘连问题,提出了基于优选路径评估的切分算法。该方法首先找到可能的粘连位置,利用特征因子对可能的粘连处切分线进行两步综合评估,选出性能良好的切分线,再针对不同粘连方向构建相应的组合折线切分路径,完成最终的图像切分。该方法提高了切分路径预测的准确性,有效地避免了切分对正常笔画的破坏。此外,应用深度学习理论中的卷积神经网络模型进行公式符号的识别,构建了识别公式字符的卷积神经网络,并通过实验优化网络参数。该卷积神经网络具有2个交替的卷积层与采样层,卷积层与采样窗口大小分别为5×5和2×2大小,选择线性矫正单元作为激活函数,并在网络的连接中使用了Dropout连接方式。通过大量的学习训练实现数学符号模式特征的自动提取并分类,从而解决现存方法中人工提取特征的不足,提高数学公式符号识别的准确性。为了验证方法的有效性,本文在Visual Studio 2010环境下,使用C++语言并结合OpenCV技术编程实现了基于优选评估的切分算法,用Keras框架搭建了面向公式识别的卷积神经网络。通过实验对比,本文所提出的切分方法准确率可达到90.14%,水平粘连符号切分准确率可达到85.60%。在识别测试中,神经网络对普通的公式字符集进行识别,识别率为97.46%,对经过切分处理前后的公式字符集进行识别,识别率分别为88.24%和97.29%。
[Abstract]:Print mathematical formula recognition is to convert the mathematical formula input by image into an editable symbol, so as to realize the reuse of the formula. At present, the mainstream OCR system has achieved a higher level of recognition of ordinary text. However, the recognition of mathematical formulas is not ideal, among which the diversity of mathematical symbols, typeface and size are the main factors that affect the recognition rate, which are caused by the complex two-dimensional structure of mathematical formulas, such as the adhesion of various symbols, the variety of mathematical symbols, the type of fonts and the size of mathematical symbols. In order to improve the recognition quality of mathematical formula, the paper first introduces and discusses the structure and key technology of printed mathematical formula recognition system, and the difficulties in recognition. In this paper, the segmentation method of mathematical formula adhesion symbol is deeply studied. Aiming at the problem of italic adhesion, a segmentation algorithm based on optimal path evaluation is proposed. The possible adhesion location is first found by this method. Using the characteristic factors to evaluate the possible splicing lines of adhesion in two steps, the segmentation lines with good performance are selected, and the corresponding combined broken line segmentation paths are constructed according to the different adhesion directions. The final image segmentation is completed. The method improves the accuracy of segmentation path prediction and effectively avoids the damage of segmentation to the normal stroke. In addition, the convolution neural network model in depth learning theory is used to recognize the formula symbols. A convolution neural network for recognizing formula characters is constructed, and the network parameters are optimized by experiments. The neural network has two alternating convolution layers and sampling layers. The size of the convolution layer and the sampling window are 5 脳 5 and 2 脳 2, respectively. The linear correction unit is chosen as the activation function, and the Dropout connection mode is used in the connection of the network. Through a lot of learning and training, the feature of mathematical symbol pattern can be automatically extracted and classified. In order to solve the problem of artificial feature extraction and improve the accuracy of mathematical formula symbol recognition, in order to verify the validity of the method, this paper is based on the Visual Studio 2010 environment. The segmentation algorithm based on optimal selection and evaluation is realized by using C language and OpenCV technology, and the convolution neural network oriented to formula recognition is built with Keras framework. The accuracy of the segmentation method proposed in this paper can reach 90.14, and the accuracy of horizontal adhesion symbol segmentation can reach 85.60. In the recognition test, the neural network can recognize the common formula character set. The recognition rate is 97.46 and the recognition rate of the formula character set before and after segmentation is 88.24% and 97.29 respectively.
【学位授予单位】：沈阳工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP183;TP391.4

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