基于RBF神经网络的手绘电气草图识别研究
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摘要
CAD技术由于其简单快捷、存储方便等诸多优点使得它在众多领域的设计中有着不可替代的作用,它能够大大提高设计质量、缩短设计周期、共享设备资源和增强数据处理能力。但是它主要应用于设计的后期阶段,对于设计过程中的灵感捕捉,思维探索帮助不大,不能满足设计早期阶段的需要。但纸上草图也有它自身的缺陷,缺少“设计记忆”,对设计方案难以存储、整理、搜索和重用,尤其缺少有效的互动交互性能。因此研究能够将纸笔的手绘草图和计算机结合起来的设计工具是设计师们所希望的,具有十分重要的意义。电路图设计在CAD技术中是一个非常重要的领域。
本文针对CAD技术的缺陷,对手绘电气草图在线识别技术进行了深入研究。并对手绘电气草图在线识别的关键部分做了探讨和实验。本文工作主要如下：
1.研究了面向RBF神经网络分类器的手绘电气草图两级特征的选择和提取方法,定义了手绘电气草图的结构特征和关系特征,并将其应用到手绘电气草图的特征提取当中。特征的提取和选择是手绘电气草图识别中最关键的部分,特征提取的好坏将直接影响识别效果。本文采用最佳逼近能力的RBF神经网络对手绘电气草图进行在线识别。所以选择类间距离大,而类内方差小的特征能够取得很好的识别效果。本文对手绘电气符号的结构进行仔细观察分析,发现了面向RBF神经网络分类器的手绘电气草图的不变性可分性特点即手绘电气草图由一些基本笔划顺次构成且这些基本笔划之间存在着一定的约束关系；并将顺次构成手绘电气草图的基本笔划特征定义为结构特征,将构成手绘电气草图的这些基本笔划之间的约束关系定义为关系特征。将结构特征作为分类识别系统中的一级特征,专门预留0或1开头的两位十进制数作为其编码；将关系特征作为分类识别系统中的二级特征,专门预留2或3开头的两位十进制数作为其编码。并相应给出结构特征和关系特征的提取算法。
2.改进了RBF神经网络的中心学习方法。常用的RBF神经网络聚类算法的中心学习一般使用K均值算法,这种方法对初始聚类中心敏感,使得算法结果不够精确,甚至无法收敛。本文提出的改进学习方法能够克服上述提到的缺点,并能充分利用了训练样本信息,有效降低了孤立点对聚类效果的影响和提高聚类效率。
3.提出了一种用RBF神经网络组成的特殊的两级串联的分类系统。在模式识别中分类器的设计也是非常关键的技术。本文通过对多级分类器集成技术的分析,提出了一种用RBF神经网络组成的特殊的两级串联的分类系统。两级分类器均采用RBF神经网络。第一级分类器用作预分类,第二级分类器用作细分类。预分类采用一个RBF神经网络,用一级特征作为预分类的输入特征向量；细分类采用三个RBF神经网络,用二级特征作为细分类的输入特征向量。并通过实验验证了这种分类系统的有效性。
Due to the advantage of simple, fast and conveniently storage, CAD technology plays an irreplaceable role in various fields designing. It can greatly enhance the qual-ity of design, reduce the design cycle, share device resources and strengthen data han-dling capacity. But CAD technology is mainly applied in early stages of design and has no role in catching inspiration and thinking exploration. It can't meet the needs of early stage designing. But paper sketches have their own disadvantage too. It lack of "designed memory"; hard to storage, arrange, search and reuse, especially lack of valid capability of interaction and alternation. For this reason, to study a sort of design tool that can combine paper-and-pencil hand-drawn sketch with computer is the hope of designers and is of great significance. Electric circuit diagram design is an impor-tant field of CAD technology.
The thesis pointed against the defects of CAD technology to study thoroughly on-line recognition of hand-drawn electronic component symbol and make research and experiments on the key component of on-line hand-drawn electronic component symbol. The main part works as follows:
1. A two levels hand-drawn electronic component symbol feature selection and extraction method that aimed at RBF(Radial Basis Function) neural networks is stud-ied in this thesis. Structural feature and relationship feature of hand-drawn electronic component symbol are defined in this thesis. Moreover, the definitions are applied in the feature extraction of hand-drawn electronic component symbol. Feature extraction and selection is the most crucial element in recognition of hand-drawn electronic component symbol, which affects directly recognition effect. This thesis used RBF neural networks which have the best approximation capability to recognize on-line hand-drawn electronic component symbol. So selecting feature which has large in-tra-class distance and small inter-class variance can achieve high recognition per-formance. Through observing and analyzing carefully the structure of hand-drawn electronic component symbol, the thesis found the invariable and separable traits of hand-drawn electronic component symbol, who aimed at RBF neural networks classi-fier. The traits are hand-drawn electronic component symbol is made up of some basic strokes sequentially and the basic strokes exist some constraint relation. The thesis used the term "structural feature"to define the basic strokes and used the term "rela- tionship feature" to define the constraint relation. In addition, the thesis used archi-tectural feature as the first level feature of the system of classification and recognition, then used relationship feature as the second level feature of the system of classifica-tion and recognition. Moreover, the thesis set aside binary decimal digit that started with 0 or 1 for structure feature and set aside binary decimal digit that started with 2 or 3 for relationship feature.
2. The method of learned RBF neural networks'center of radial function is im-proved in this thesis. Common method of learned RBF neural networks'basic func-tion center is k-means algorithm. K-means algorithm is sensitive to initial clustering center, that caused the results of the algorithm are not accurate enough even can't converge. The improved method of learning center can overcome the shortcoming mentioned above, take full advantage of training sample, decreased effectively the effects of isolated point and clustering accuracy, and improved the clustering effi-ciency.
3. A specific classification system that has two levels in series classifiers which is made up of RBF neural networks is proposed in this thesis. In pattern recognition, the design of classifier is a key technology too. By analyzing multistage classifiers inte-grated technology, the thesis proposed a specific classification system that has two levels in series classifier which is made up of RBF neural networks. The two levels classifiers both used RBF neural networks. The first level classifier is used to pre-classify and the second classifier is used to fine-classify. Pre-classification used one RBF neural networks and used the first level feature as his input feature vector. Fine-classification used three RBF neural networks and used the second level feature as his input feature vector. Then a recognition system is designed to verify the validity of those methods.
本文针对CAD技术的缺陷,对手绘电气草图在线识别技术进行了深入研究。并对手绘电气草图在线识别的关键部分做了探讨和实验。本文工作主要如下：
1.研究了面向RBF神经网络分类器的手绘电气草图两级特征的选择和提取方法,定义了手绘电气草图的结构特征和关系特征,并将其应用到手绘电气草图的特征提取当中。特征的提取和选择是手绘电气草图识别中最关键的部分,特征提取的好坏将直接影响识别效果。本文采用最佳逼近能力的RBF神经网络对手绘电气草图进行在线识别。所以选择类间距离大,而类内方差小的特征能够取得很好的识别效果。本文对手绘电气符号的结构进行仔细观察分析,发现了面向RBF神经网络分类器的手绘电气草图的不变性可分性特点即手绘电气草图由一些基本笔划顺次构成且这些基本笔划之间存在着一定的约束关系；并将顺次构成手绘电气草图的基本笔划特征定义为结构特征,将构成手绘电气草图的这些基本笔划之间的约束关系定义为关系特征。将结构特征作为分类识别系统中的一级特征,专门预留0或1开头的两位十进制数作为其编码；将关系特征作为分类识别系统中的二级特征,专门预留2或3开头的两位十进制数作为其编码。并相应给出结构特征和关系特征的提取算法。
2.改进了RBF神经网络的中心学习方法。常用的RBF神经网络聚类算法的中心学习一般使用K均值算法,这种方法对初始聚类中心敏感,使得算法结果不够精确,甚至无法收敛。本文提出的改进学习方法能够克服上述提到的缺点,并能充分利用了训练样本信息,有效降低了孤立点对聚类效果的影响和提高聚类效率。
3.提出了一种用RBF神经网络组成的特殊的两级串联的分类系统。在模式识别中分类器的设计也是非常关键的技术。本文通过对多级分类器集成技术的分析,提出了一种用RBF神经网络组成的特殊的两级串联的分类系统。两级分类器均采用RBF神经网络。第一级分类器用作预分类,第二级分类器用作细分类。预分类采用一个RBF神经网络,用一级特征作为预分类的输入特征向量；细分类采用三个RBF神经网络,用二级特征作为细分类的输入特征向量。并通过实验验证了这种分类系统的有效性。
Due to the advantage of simple, fast and conveniently storage, CAD technology plays an irreplaceable role in various fields designing. It can greatly enhance the qual-ity of design, reduce the design cycle, share device resources and strengthen data han-dling capacity. But CAD technology is mainly applied in early stages of design and has no role in catching inspiration and thinking exploration. It can't meet the needs of early stage designing. But paper sketches have their own disadvantage too. It lack of "designed memory"; hard to storage, arrange, search and reuse, especially lack of valid capability of interaction and alternation. For this reason, to study a sort of design tool that can combine paper-and-pencil hand-drawn sketch with computer is the hope of designers and is of great significance. Electric circuit diagram design is an impor-tant field of CAD technology.
The thesis pointed against the defects of CAD technology to study thoroughly on-line recognition of hand-drawn electronic component symbol and make research and experiments on the key component of on-line hand-drawn electronic component symbol. The main part works as follows:
1. A two levels hand-drawn electronic component symbol feature selection and extraction method that aimed at RBF(Radial Basis Function) neural networks is stud-ied in this thesis. Structural feature and relationship feature of hand-drawn electronic component symbol are defined in this thesis. Moreover, the definitions are applied in the feature extraction of hand-drawn electronic component symbol. Feature extraction and selection is the most crucial element in recognition of hand-drawn electronic component symbol, which affects directly recognition effect. This thesis used RBF neural networks which have the best approximation capability to recognize on-line hand-drawn electronic component symbol. So selecting feature which has large in-tra-class distance and small inter-class variance can achieve high recognition per-formance. Through observing and analyzing carefully the structure of hand-drawn electronic component symbol, the thesis found the invariable and separable traits of hand-drawn electronic component symbol, who aimed at RBF neural networks classi-fier. The traits are hand-drawn electronic component symbol is made up of some basic strokes sequentially and the basic strokes exist some constraint relation. The thesis used the term "structural feature"to define the basic strokes and used the term "rela- tionship feature" to define the constraint relation. In addition, the thesis used archi-tectural feature as the first level feature of the system of classification and recognition, then used relationship feature as the second level feature of the system of classifica-tion and recognition. Moreover, the thesis set aside binary decimal digit that started with 0 or 1 for structure feature and set aside binary decimal digit that started with 2 or 3 for relationship feature.
2. The method of learned RBF neural networks'center of radial function is im-proved in this thesis. Common method of learned RBF neural networks'basic func-tion center is k-means algorithm. K-means algorithm is sensitive to initial clustering center, that caused the results of the algorithm are not accurate enough even can't converge. The improved method of learning center can overcome the shortcoming mentioned above, take full advantage of training sample, decreased effectively the effects of isolated point and clustering accuracy, and improved the clustering effi-ciency.
3. A specific classification system that has two levels in series classifiers which is made up of RBF neural networks is proposed in this thesis. In pattern recognition, the design of classifier is a key technology too. By analyzing multistage classifiers inte-grated technology, the thesis proposed a specific classification system that has two levels in series classifier which is made up of RBF neural networks. The two levels classifiers both used RBF neural networks. The first level classifier is used to pre-classify and the second classifier is used to fine-classify. Pre-classification used one RBF neural networks and used the first level feature as his input feature vector. Fine-classification used three RBF neural networks and used the second level feature as his input feature vector. Then a recognition system is designed to verify the validity of those methods.
引文
[1]吴孔银,王立涛,汪洪峰,赵钢,柯烈强.手绘草图识别技术及其建模方法研究[J].成组技术与生产现代化.2007,24(4)：25-29.
[2]J. A. Landay and B.A.Myers. Interactive Sketching for the Early Stages of User Interface De-sign[J], Proc. of Human Factors in Computing Systems CHI95, Denvef, CO,1995:43—50.
[3]Mierosoft Presspass. Digital lnk.Breakthrough technology in tablet PC:Brings the Power of The Pen to the desktop[OL]. http://www.microsoft.com/presspass/features/2002/
[4]Microsoft Presspass. With launch of tablet PCs, Pen-based computing is a reality[OL]. http://www.microsoft.com/Press-pass/features/2002/
[5]孙正兴,冯桂焕,周若鸿等.基于草图的人机交互技术研究发展[J].计算机辅助设计与图形学学报.2005,17(9)：1890-1896
[6]李建新,廖士中.一个基于支持向量机的草图识别系统[D].天津：天津大学计算机应用技术.2006.
[7]常新立,徐东平.手绘几何图形的识别研究[D].武汉：武汉理工大学.2009
[8]Rubine D. Specifying gestures by example[J]. Computer Graphics,1991,21(4):329-327.
[9]Witkin A. P.. Scale space filtering:Anew approach to multi-scale description [J]. Image Under-standing.1984:183-192.
[10]Sezgin T. M.. Feature point detection and curve approximation for early processing of free-hand sketches [D]. Master thesis of MIT.2001
[11]Gross M. D.. The Electronic Cocktail Napkin-A Computational Environment for Working with Design Diagrams[J]. Design Studies.1996,17:53-59.
[12]Revankar S.& Yegnanarayanna B.. Machine Recognition and correction of Freehand Geo-metric Line Sketches [C]. Proc. of IEEE International conference on Systems, Man, and Cy-berneties.1991,1:87-92.
[13]Takayuki D.K., Ajay A & Van V.. Recognizing Multi-stroke Geometric Shapes:An Experi-mental Evaluation[C]. Proc. of 6th Annual ACM Symposium on User Interface Software and Technology.1993:121-128.
[14]孙正兴,彭彬彬,丛兰兰,等.在线草图识别中的用户适应性研究[J].计算机辅助设计与图形学学报,2004,16(9)：1207-1215
[15]Sun Z X, Zhang B, Qiu Q H. Freehand Sketchy Graphic Input System:SketchGIS[C]. The Second International Conference on Machine Learning and Cybernetics.2003:3232-3237.
[16]Tian Feng, Qin Yan-Yan et al. Analysis and design on PIBG Toolkit:A pen-based user inter-face toolkit[J]. Chinese Journal of Computer,2005,28(6):1036-1042
[17]姜映映,田丰,王旭刚,戴国忠.基于模板匹配和SVM的草图符号自适应识别方法.计算机学报.2009,32(2)：252-260.
[18]Mitsuo Ishii,et al.. An experimental input system of hand-drawn logic circuit diagram[C]. Proc.of 16thDA Conf,1979.
[19]俞斌,林行刚,吴佑寿.基于BAG的矢量化方法及其在手画逻辑电路图识别中的应用[J].电子学报.1990,18(4)：76-81.
[20]李宏,薛冰,杨英科,左少平,谢虹.一个具有自动输入功能的电路CAD系统[J].造船技术.1998,7：32-38.
[21]刘玉军,付左权,黄国庆,陈耀辉,刘达广.手绘模拟电路图识别技术研究[J].系统工程理论与实践.1999,9：92-99.
[22]王国余,李正明,花世群.手写电气元件符号的识别算法.江南大学学报(自然科学版)[J].2003,2(1)：53-55.
[23]王国余,李正明,王继生.基于神经网络的手写电气元件符号识别系统.江苏理工大学学报(自然科学版)[J].2001,22(2)：82-85.
[24]Leslie Gennari, et al. Combining geometry and domain knowledge to interpret hand-drawn diagrams[J]. Computers & graphics,2005,29:547-562.
[25]周建新,戴永,王求真.基于智能像卡输入的手绘电气符号特征提取方法研究[J].工程图形学报,2006,27(4)：19-23.
[26]莫建平,陈平.电路原理图纸识别系统研究与实现[J].微计算机信息.2006,22(4-2)：283-286.
[27]徐俊文,廖达雄,王淑侠,张小亮.在线手绘电路图的识别研究[J].科学技术与工程.2007,7(6)：1089-1094.
[28]Guihuan Feng, Christian Viard-Gaudin and Zhengxing Sun. On-line hand-drawn electric cir-cuit diagram recognition using 2D dynamic programming[J]. Pattern Recognition.2009, 42(12):3215-3223.
[29]G Boccignoe, A. Chianese, etc.. Recovering Dynamic Information from Static Handwriting[J]. Pattern Recognition,1993,26:409-419.
[30]D.S.Doermann and A. Rosenfeld. Recovery of Temporal Information from Static Images of Handwriting[J]. International Journal on Computer Vision.1995,15:143-164.
[31]余楚中.联机手写汉字识别中的笔画分类以及笔画识别[J]．重庆大学学报(自然科学版).1998,21(2)：131-134.
[32]黄襄念,程萍,杨波等人.自然手写汉字预处理子系统[J].重庆大学学报(自然科学版).2000,23(4)：33-36.
[33]李翠芸,裴继红.联机手绘图形识别的自适应HMM方法[D].西安：西安电子科技大学.2003.
[34]F.Nouboud and R.Plamondon, On-line Recognition of Handprinted Characters:Survey and Beta Tests[J]. Pattern Recognition.1990,25(9):1031-1044.
[35]R.Plamondon, D.Lopresti, etc., on-line Handwriting Recognition[J]. Encyclopedia of Electri-cal and Electronics Eng.,7.GWebster, eds., Wiley, New York,1999,15:123-146.
[36]张宏林.Visual C++数字图像模式识别技术及工程实践(第2版)[M].北京：人民邮电出版社.2008.159.
[37]Sergios Theodoridis, Konstantinos Koutroumbas.模式识别(第三版)[M].北京：电子工业出版社.2008.138.
[38]Wang Hui, Bell D., Murtagh F.. Axiomatic approach to feature subset selection based on relevance[C]. IEEE Transactions on Pattern Analysis Machine Intelligence.1999,21(3): 271-277.
[39]Narendra P.M., Fukunaga K.. A branch and bound algorithm for feature subset selection[J]. IEEE Transactions on Computers,1977,26(9):917-922.
[40]Dumain S., Platt J., Heckerman D., Sahami M.. Inductive learning algorithm and representa-tions for text categorization[M]. Bethesda:Proceedings of the CIKM-98,7th ACM Interna-tional Conference on Information and Knowledge Management,1998:148-155.
[41]孙晓楠.基于RBF神经网络的DNA序列分类方法[D].吉林：吉林大学电子科学与工程学院.2008.
[42]Park J, Sandberg I W. Universal Approximation Using Radial Basis Function Networks[J]. Neural Computation,1991,5(3):245-257.
[43]Bianchini M, Frasconi P, Cori M. Learning Without Local Minima in Radial Basis Function Networks[J]. IEEE Trans on Neural Networks,1995,6(3):749-756.
[44]Manolis Wallace, Nicolas, Tsapatsoulis, Stefanos Kollias. Intelligent initialization of resource allocating RBF networks[J]. Neural Networks.2005,18(2):117-122.
[45]韩立群.人工神经网络理论、设计及应用[M].北京：化学工业出版社,2007：164-176.
[46]高隽.人工神经网络原理及仿真实例[M].北京：机械工业出版社,2007：56-63.
[47]曾敏.一种基于RBF神经网络的命令集语音识别系统研究[D].南宁：广西大学.2007
[48]文秀琼.一种基于RBF神经网络的车牌识别技术的研究[D].南宁：广西大学.2008
[49]张小亮,孙根正.手绘流程图的在线识别研究[D].西安：西北工业大学航空宇航制造工程.2007.
[50]俞庆英,吴建国.联机手写汉字识别系统的研究与实现[D].安徽：安徽大学计算机应用技术,2005.
[51]宋卫东.解析几何[B].北京：高等教育出版社,2003.
[52]王淑侠,廖达雄.支持概念设计的手绘图在线识别研究[D].西安：西北工业大学航空宇航制造工程.2006.
[53]王淑侠,高满屯,齐乐华.基于二次曲线的在线手绘图识别[J].西北工业大学学报,2007,25(1)：37-40.
[54]刘妹琴,廖晓昕.RBF神经网络的一种鲁棒学习算法[J].华中理工大学学报,2000,28(2)：8-10.
[55]Suen C Y, Legault R, Nadal C, Cheriet M, Lam L. Building a new generation of handwriting recognition system[J]. Pattern Recognition Letters,1993,14(4):303-315.
[56]Huang Y S, Suen C Y, Combination of multiple classifiers with measurement values[C]. Pro-ceedings of the third Internal Conference of Document Analysis and recognition,1993: 598-601.
[57]金连文,徐秉铮.基于多级神经网络结构的手写体汉字识别[J].通信学报,1997,18(5)：21-27.
[58]Mark W K. On the multistage bayes classifier[J]. Pattern Recognition,1988,21(4):355-357.
[2]J. A. Landay and B.A.Myers. Interactive Sketching for the Early Stages of User Interface De-sign[J], Proc. of Human Factors in Computing Systems CHI95, Denvef, CO,1995:43—50.
[3]Mierosoft Presspass. Digital lnk.Breakthrough technology in tablet PC:Brings the Power of The Pen to the desktop[OL]. http://www.microsoft.com/presspass/features/2002/
[4]Microsoft Presspass. With launch of tablet PCs, Pen-based computing is a reality[OL]. http://www.microsoft.com/Press-pass/features/2002/
[5]孙正兴,冯桂焕,周若鸿等.基于草图的人机交互技术研究发展[J].计算机辅助设计与图形学学报.2005,17(9)：1890-1896
[6]李建新,廖士中.一个基于支持向量机的草图识别系统[D].天津：天津大学计算机应用技术.2006.
[7]常新立,徐东平.手绘几何图形的识别研究[D].武汉：武汉理工大学.2009
[8]Rubine D. Specifying gestures by example[J]. Computer Graphics,1991,21(4):329-327.
[9]Witkin A. P.. Scale space filtering:Anew approach to multi-scale description [J]. Image Under-standing.1984:183-192.
[10]Sezgin T. M.. Feature point detection and curve approximation for early processing of free-hand sketches [D]. Master thesis of MIT.2001
[11]Gross M. D.. The Electronic Cocktail Napkin-A Computational Environment for Working with Design Diagrams[J]. Design Studies.1996,17:53-59.
[12]Revankar S.& Yegnanarayanna B.. Machine Recognition and correction of Freehand Geo-metric Line Sketches [C]. Proc. of IEEE International conference on Systems, Man, and Cy-berneties.1991,1:87-92.
[13]Takayuki D.K., Ajay A & Van V.. Recognizing Multi-stroke Geometric Shapes:An Experi-mental Evaluation[C]. Proc. of 6th Annual ACM Symposium on User Interface Software and Technology.1993:121-128.
[14]孙正兴,彭彬彬,丛兰兰,等.在线草图识别中的用户适应性研究[J].计算机辅助设计与图形学学报,2004,16(9)：1207-1215
[15]Sun Z X, Zhang B, Qiu Q H. Freehand Sketchy Graphic Input System:SketchGIS[C]. The Second International Conference on Machine Learning and Cybernetics.2003:3232-3237.
[16]Tian Feng, Qin Yan-Yan et al. Analysis and design on PIBG Toolkit:A pen-based user inter-face toolkit[J]. Chinese Journal of Computer,2005,28(6):1036-1042
[17]姜映映,田丰,王旭刚,戴国忠.基于模板匹配和SVM的草图符号自适应识别方法.计算机学报.2009,32(2)：252-260.
[18]Mitsuo Ishii,et al.. An experimental input system of hand-drawn logic circuit diagram[C]. Proc.of 16thDA Conf,1979.
[19]俞斌,林行刚,吴佑寿.基于BAG的矢量化方法及其在手画逻辑电路图识别中的应用[J].电子学报.1990,18(4)：76-81.
[20]李宏,薛冰,杨英科,左少平,谢虹.一个具有自动输入功能的电路CAD系统[J].造船技术.1998,7：32-38.
[21]刘玉军,付左权,黄国庆,陈耀辉,刘达广.手绘模拟电路图识别技术研究[J].系统工程理论与实践.1999,9：92-99.
[22]王国余,李正明,花世群.手写电气元件符号的识别算法.江南大学学报(自然科学版)[J].2003,2(1)：53-55.
[23]王国余,李正明,王继生.基于神经网络的手写电气元件符号识别系统.江苏理工大学学报(自然科学版)[J].2001,22(2)：82-85.
[24]Leslie Gennari, et al. Combining geometry and domain knowledge to interpret hand-drawn diagrams[J]. Computers & graphics,2005,29:547-562.
[25]周建新,戴永,王求真.基于智能像卡输入的手绘电气符号特征提取方法研究[J].工程图形学报,2006,27(4)：19-23.
[26]莫建平,陈平.电路原理图纸识别系统研究与实现[J].微计算机信息.2006,22(4-2)：283-286.
[27]徐俊文,廖达雄,王淑侠,张小亮.在线手绘电路图的识别研究[J].科学技术与工程.2007,7(6)：1089-1094.
[28]Guihuan Feng, Christian Viard-Gaudin and Zhengxing Sun. On-line hand-drawn electric cir-cuit diagram recognition using 2D dynamic programming[J]. Pattern Recognition.2009, 42(12):3215-3223.
[29]G Boccignoe, A. Chianese, etc.. Recovering Dynamic Information from Static Handwriting[J]. Pattern Recognition,1993,26:409-419.
[30]D.S.Doermann and A. Rosenfeld. Recovery of Temporal Information from Static Images of Handwriting[J]. International Journal on Computer Vision.1995,15:143-164.
[31]余楚中.联机手写汉字识别中的笔画分类以及笔画识别[J]．重庆大学学报(自然科学版).1998,21(2)：131-134.
[32]黄襄念,程萍,杨波等人.自然手写汉字预处理子系统[J].重庆大学学报(自然科学版).2000,23(4)：33-36.
[33]李翠芸,裴继红.联机手绘图形识别的自适应HMM方法[D].西安：西安电子科技大学.2003.
[34]F.Nouboud and R.Plamondon, On-line Recognition of Handprinted Characters:Survey and Beta Tests[J]. Pattern Recognition.1990,25(9):1031-1044.
[35]R.Plamondon, D.Lopresti, etc., on-line Handwriting Recognition[J]. Encyclopedia of Electri-cal and Electronics Eng.,7.GWebster, eds., Wiley, New York,1999,15:123-146.
[36]张宏林.Visual C++数字图像模式识别技术及工程实践(第2版)[M].北京：人民邮电出版社.2008.159.
[37]Sergios Theodoridis, Konstantinos Koutroumbas.模式识别(第三版)[M].北京：电子工业出版社.2008.138.
[38]Wang Hui, Bell D., Murtagh F.. Axiomatic approach to feature subset selection based on relevance[C]. IEEE Transactions on Pattern Analysis Machine Intelligence.1999,21(3): 271-277.
[39]Narendra P.M., Fukunaga K.. A branch and bound algorithm for feature subset selection[J]. IEEE Transactions on Computers,1977,26(9):917-922.
[40]Dumain S., Platt J., Heckerman D., Sahami M.. Inductive learning algorithm and representa-tions for text categorization[M]. Bethesda:Proceedings of the CIKM-98,7th ACM Interna-tional Conference on Information and Knowledge Management,1998:148-155.
[41]孙晓楠.基于RBF神经网络的DNA序列分类方法[D].吉林：吉林大学电子科学与工程学院.2008.
[42]Park J, Sandberg I W. Universal Approximation Using Radial Basis Function Networks[J]. Neural Computation,1991,5(3):245-257.
[43]Bianchini M, Frasconi P, Cori M. Learning Without Local Minima in Radial Basis Function Networks[J]. IEEE Trans on Neural Networks,1995,6(3):749-756.
[44]Manolis Wallace, Nicolas, Tsapatsoulis, Stefanos Kollias. Intelligent initialization of resource allocating RBF networks[J]. Neural Networks.2005,18(2):117-122.
[45]韩立群.人工神经网络理论、设计及应用[M].北京：化学工业出版社,2007：164-176.
[46]高隽.人工神经网络原理及仿真实例[M].北京：机械工业出版社,2007：56-63.
[47]曾敏.一种基于RBF神经网络的命令集语音识别系统研究[D].南宁：广西大学.2007
[48]文秀琼.一种基于RBF神经网络的车牌识别技术的研究[D].南宁：广西大学.2008
[49]张小亮,孙根正.手绘流程图的在线识别研究[D].西安：西北工业大学航空宇航制造工程.2007.
[50]俞庆英,吴建国.联机手写汉字识别系统的研究与实现[D].安徽：安徽大学计算机应用技术,2005.
[51]宋卫东.解析几何[B].北京：高等教育出版社,2003.
[52]王淑侠,廖达雄.支持概念设计的手绘图在线识别研究[D].西安：西北工业大学航空宇航制造工程.2006.
[53]王淑侠,高满屯,齐乐华.基于二次曲线的在线手绘图识别[J].西北工业大学学报,2007,25(1)：37-40.
[54]刘妹琴,廖晓昕.RBF神经网络的一种鲁棒学习算法[J].华中理工大学学报,2000,28(2)：8-10.
[55]Suen C Y, Legault R, Nadal C, Cheriet M, Lam L. Building a new generation of handwriting recognition system[J]. Pattern Recognition Letters,1993,14(4):303-315.
[56]Huang Y S, Suen C Y, Combination of multiple classifiers with measurement values[C]. Pro-ceedings of the third Internal Conference of Document Analysis and recognition,1993: 598-601.
[57]金连文,徐秉铮.基于多级神经网络结构的手写体汉字识别[J].通信学报,1997,18(5)：21-27.
[58]Mark W K. On the multistage bayes classifier[J]. Pattern Recognition,1988,21(4):355-357.