基于改进BP神经网络的物体识别研究
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摘要
计算机视觉在众多领域都有广泛的应用,比如家庭智能机器人、仪表自动监测、汽车低速自动导航驾驶和航空图片中的物体识别,并且随着计算机视觉技术的发展,计算机视觉将具有更广泛的应用前景。而计算机视觉的重要研究课题之一是物体识别,并且特征提取和分类是物体识别的关键步骤。在识别物体的方法和过程中,还存在许多问题和挑战,比如如何从2D图片中快速而准确的识别出物体。人类的视觉系统就能够轻易地快速识别2D图片中的物体,这实际上是一个由2D信息出发辅以先验知识识别物体的过程。本文就从物体的形状信息出发,提出一种基于改进BP神经网络的物体识别方法。
在特征提取方面,利用矩算法提取物体的不变性特征,并详细讨论了Hu矩及其修正算法。不变矩方法,能够反映物体的形状信息,并具有较好的抗噪性能,同时因不受被识别物体大小、位置、方位的影响而被广泛应用于物体识别、景物匹配、图像分析及字符识别等许多方面。并且修正的Hu不变矩,不管在连续的状态下还是在离散状态下都对平移、缩放、旋转具有不变性,而且具有较小的时间复杂度,可以用来有效的识别物体。本文在MATLAB实验环境下对修正的Hu不变矩算法进行了实现。
在分类识别方面,先分析了BP神经网络的结构,算法,存在的缺点并提出加入动量项、共轭梯度法、正则化方法、弹性BP算法、自适应学习速率动量梯度下降反向传播算法,这一系列改进的学习算法,以满足解决不同问题的需要。其中自适应学习速率动量梯度下降反向传播算法,可以有效避免BP网络收敛速度慢和存在所谓“局部最小值”问题。最后在MATLAB实验环境中,将该改进后的BP算法用于识别Coil-20(columbia object image library)图像数据库中的物体。并且该实验是在无噪声和有噪声两种情况下分别进行的。
与基于传统BP算法的物体识别方法进行实验比较,该改进后的BP算法进一步提高了BP神经网络在处理非线性和不确定因素问题上的能力,并且该改进算法无论是在无噪声情况下,还是在有噪声情况下,都比传统的BP算法具有更高的识别率和更快的收敛速度。从而证明了该算法的可行性、鲁棒性和有效性。
Computer vision finds wide application in multiple areas such as household intelligence robots, automatic inspection of instruments, automonous navigation of automobiles and object recognition of aero-sensing images, and sees a brighter prospect in the bloom of a variety of related techniques, Yet object recognition is one of the most important problems in computer vision.Furthermore,to object recognition, feature extraction and classification are pivotal.Object recognition faces a great many challenges in method.One problem is how to identify the object rapidly and accurately from two dimensional images.This task could easily resolved by human visual system which infers from an image of two dimensional and apriori assumptions. This paper puts forward an algorithm of object recognition based on modified BP Neural Network from the shape information of the object.
About feature extraction,invariant feature is extracted by moments.Hu moments and the modified algorithm are dicussed amply in the paper.Invariant moments can reflect the shape of object,possess the capability of resisting noise,and is not influenced by the size, position and orientation.Therefore, invariant moments are widely applied on object recognition, scenery matching,image analysis, character recognition,and so on. The modified Hu invariant moments are invariant to the translation , rotating and scale of object,when object is in sequential state or discrete state.Moreover they have small time complexity.So they can recognize object efficiently. This method is examined in the MATLAB laboratory environment.
About classification and recognition,the structure,algorithms and shortcomings of BP neural network are introduced.Moreover,adding momentum,conjugate grads, regularization, stretch BP algorithm, back propagation algorithm based on self adapting learning rate with momentum gradient reduction are presented in the paper to meet different problems. Especially back propagation algorithm based on self adapting learning rate with momentum gradient reduction can avoid efficiently the slow convergence and the problem of‘local infinitesimal value’of BP network. The modified BP algorithm is examined in the MATLAB laboratory environment, to recognize objects in Coil-20.The experiments are performed in the noise-free environment,as well as in the noisy environment.
Compared with object recognition based on traditional BP algorithm,the modified BP algorithm improves the capability of processing nonlinear and uncertain problems.and it has higher recognition rate and quicker convergence in the noise-free environment as well as in the noisy environment. Consequently the feasibility, robustness, efficiency are proved in the paper.
在特征提取方面,利用矩算法提取物体的不变性特征,并详细讨论了Hu矩及其修正算法。不变矩方法,能够反映物体的形状信息,并具有较好的抗噪性能,同时因不受被识别物体大小、位置、方位的影响而被广泛应用于物体识别、景物匹配、图像分析及字符识别等许多方面。并且修正的Hu不变矩,不管在连续的状态下还是在离散状态下都对平移、缩放、旋转具有不变性,而且具有较小的时间复杂度,可以用来有效的识别物体。本文在MATLAB实验环境下对修正的Hu不变矩算法进行了实现。
在分类识别方面,先分析了BP神经网络的结构,算法,存在的缺点并提出加入动量项、共轭梯度法、正则化方法、弹性BP算法、自适应学习速率动量梯度下降反向传播算法,这一系列改进的学习算法,以满足解决不同问题的需要。其中自适应学习速率动量梯度下降反向传播算法,可以有效避免BP网络收敛速度慢和存在所谓“局部最小值”问题。最后在MATLAB实验环境中,将该改进后的BP算法用于识别Coil-20(columbia object image library)图像数据库中的物体。并且该实验是在无噪声和有噪声两种情况下分别进行的。
与基于传统BP算法的物体识别方法进行实验比较,该改进后的BP算法进一步提高了BP神经网络在处理非线性和不确定因素问题上的能力,并且该改进算法无论是在无噪声情况下,还是在有噪声情况下,都比传统的BP算法具有更高的识别率和更快的收敛速度。从而证明了该算法的可行性、鲁棒性和有效性。
Computer vision finds wide application in multiple areas such as household intelligence robots, automatic inspection of instruments, automonous navigation of automobiles and object recognition of aero-sensing images, and sees a brighter prospect in the bloom of a variety of related techniques, Yet object recognition is one of the most important problems in computer vision.Furthermore,to object recognition, feature extraction and classification are pivotal.Object recognition faces a great many challenges in method.One problem is how to identify the object rapidly and accurately from two dimensional images.This task could easily resolved by human visual system which infers from an image of two dimensional and apriori assumptions. This paper puts forward an algorithm of object recognition based on modified BP Neural Network from the shape information of the object.
About feature extraction,invariant feature is extracted by moments.Hu moments and the modified algorithm are dicussed amply in the paper.Invariant moments can reflect the shape of object,possess the capability of resisting noise,and is not influenced by the size, position and orientation.Therefore, invariant moments are widely applied on object recognition, scenery matching,image analysis, character recognition,and so on. The modified Hu invariant moments are invariant to the translation , rotating and scale of object,when object is in sequential state or discrete state.Moreover they have small time complexity.So they can recognize object efficiently. This method is examined in the MATLAB laboratory environment.
About classification and recognition,the structure,algorithms and shortcomings of BP neural network are introduced.Moreover,adding momentum,conjugate grads, regularization, stretch BP algorithm, back propagation algorithm based on self adapting learning rate with momentum gradient reduction are presented in the paper to meet different problems. Especially back propagation algorithm based on self adapting learning rate with momentum gradient reduction can avoid efficiently the slow convergence and the problem of‘local infinitesimal value’of BP network. The modified BP algorithm is examined in the MATLAB laboratory environment, to recognize objects in Coil-20.The experiments are performed in the noise-free environment,as well as in the noisy environment.
Compared with object recognition based on traditional BP algorithm,the modified BP algorithm improves the capability of processing nonlinear and uncertain problems.and it has higher recognition rate and quicker convergence in the noise-free environment as well as in the noisy environment. Consequently the feasibility, robustness, efficiency are proved in the paper.
引文
[1] 李庆,周曼丽,柳健.三维物体识别研究进展[J].中国图形图像学报,2000,5(12):985-993.
[2] T.S. Benice,Jacob Raber.Object recognition analysis in mice using nose-point digital video tracking[J].Journal of Neuroscience Methods,2008,168,(2):422-430.
[3] Gruber, B.Maess, N.J.Trujillo-Barreto.Gamma-Band responses during a simple object recognition task: A replication study in human MEG[J].Brain Research,2008,1196:74-84.
[4] Sungho Kim,Kuk-Jin Yoon,In So Kweon.Object recognition using a generalized robust invariant feature and Gestalt's law of proximity and similarity[J].Pattern Recognition,2008, 41(2):726-741.
[5] Eugene Charniak,Robert P.Goldman.A Bayesian model of plan recognition[J].Artificial Intelligence,1993,64(1):53-79.
[6] Shen-Chi Tien,Tsorng-Lin Chia,Yibin Lu.Using cross-ratios to model curve data for aircraft recognition[J].Pattern Recognition Letters,2003,24(12):2047-2060.
[7] Thomas Heseltine, Nick Pears,Jim Austin.Three-dimensional face recognition using combinations of surface feature map subspace components[J].Image and Vision Computing, 2008,26(3):382-396.
[8] V.V. Srinivas,Shivam Tripathi,A.Ramachandra Rao,Rao S.Govindaraju.Regional flood frequency analysis by combining self-organizing feature map and fuzzy clustering[J].Journal of Hydrology,2008,348(1):148-166.
[9] 陈拓,赵荣椿.几何不变性及其在 3D 物体识别中的应用[J].中国图像图形学报,2003,8(9): 993-1000.
[10] 申金媛,李现国,常胜江.相位特征在三维物体识别中的应用[J].物理学报,2005,54(11): 5157-5163.
[11] 黄黎红.家用机器人的部分遮挡物体的识别[J].现代电子技术,2005,192:112-117.
[12] Manuele Bicego,Umberto Castellani,Vittorio Murino.A Hidden Markov Model approach for appearance-based 3D object recognition[J].Pattern Recongnition Letters,2005,(26):2588-2599.
[13] Bo G P,Kyoung M L,Sang U L.Recogniton of partially occluded objects using probabilistic ARG based matching[J].Comput.Vision Image Understanding. 2003,3(90):217-241.
[14] Cecilia Di Ruberto.Recognition of shapes byattributed skeletal graphs[J].PatternRecongnition,2004(37):21-31.
[15] Maria Stepanova,Feng Lin,Valerie C.-L.Lin.Establishing a statistic model for recognition of steroid hormone response elements[J].Computational Biology and Chemistry,2006,30(5): 339-347.
[16] Mike R. Schoenberg,Kyra A. Dawson,Kevin Duff.Test performance and classification statistics for the Rey Auditory Verbal Learning Test in selected clinical samples[J].Archives of Clinical Neuropsychology,2006,21(7):693-703.
[17] Hu Jin,Zhiyong Zheng,Minjie Gao.Effective induction of phytase in Pichia pastoris fed-batch culture using an ANN pattern recognition model-based on-line adaptive control strategy[J]. Biochemical Engineering Journal,2007,37(1):26-33.
[18] Prasad D.Polur,Gerald E.Miller.Investigation of an HMM/ANN hybrid structure in pattern recognition application using cepstral analysis of dysarthric (distorted)speech signals[J]. Medical Engineering & Physics,2006,28(8):741-748.
[19] Hong-Kyu Kim,Dong Wook Sohn.An analysis of the relationship between land use density of office buildings and urban street configuration: Case studies of two areas in Seoul by space syntax analysis[J].Cities,2002,19(6):409-418.
[20] Nadir Farah, Labiba Souici ,Mokhtar Sellami.Classifiers combination and syntax analysis for Arabic literal amount recognition[J].Engineering Applications of Artificial Intelligence,2006, 19,(1):29-39.
[21] F.Chevalier,J.P.Domenger,J. Benois-Pineau.Retrieval of objects in video by similarity based on graph matching[J].Pattern Recognition Letters,2007,28,1-11.
[22] Alexey Kostin,Joser Kittler,William Christmas.Object recognition by symmetrised graph matching using relaxation labelling with an inhibitory mechanism[J],Pattern Recognition Letters,2005,26(3):381-393.
[23] Hochul Shin,Seong-Dae Kim,Hae-Chul Choi.Generalized elastic graph matching for face recognition[J], Pattern Recognition Letters,2007,28(9):1077-1082.
[24] Wen-Liang Hung,Miin-Shen Yang.On the J-divergence of intuitionistic fuzzy sets with its application to pattern recognition[J].Information Sciences,2008,178(6):1641-1650.
[25] Adrian David Cheok, Zhang Jian, Eng Siong Chng.Efficient mobile phone Chinese optical character recognition systems by use of heuristic fuzzy rules and bigram Markov language models[J].Applied Soft Computing,2008,8(2):1005-1017.
[26] S.Marsili-Libelli.Control of SBR switching by fuzzy pattern recognition[J].Water Research, 2006,40(5):1095-1107.
[27] 丘江,刘波,杨静.基于高阶胡氏矩的多目标图像识别算法[J].光子学报,2001,30(9):1141-1145.
[28] Javad Haddadnia.An Efficient Human Face Recognition System Using Pseudo Zernike Moment Invariant And Radial Basis Function Neural Network[J].International Journal of Pattern Recognition and Artificial Intelligence,2003,17(1):41-62.
[29] Hu M K.Visual pattern recognition by moment invariant[J].IRE Trans Information Theory, 1962,1(8):179-187.
[30] 袁非牛,廖光煊,张永明. 计算机视觉火灾探测中的特征提取[J].中国科学技术大学学报,2006,36(1):39-43.
[31] 刘寅,滕晓龙,刘重庆.复杂背景下基于傅立叶描述子的手势识别[J].计算机仿真,2005, 22(12):158-161.
[32] H.P.Ren,Z.L.Ping,W.R.G.BO.Cell Image Recognition With Radial Harmonic Fourier Moment [J].Chinese Physics,2003,12(6):41-62.
[33] 禹晶,段娟,苏开娜.一种基于 Hough 变换的步态特征提取方法的研究[J].中国图象图形学报,2005,10(10):1304-1309.
[34] Markus Ulricha, Carsten Steger, Albert Baumgartne.Real-time object recognition using a modified generalized[J].Hough transform Pattern Recognition,2003,36:2557–2570.
[35] 董江曼,李应岐,邓飚.SAR 图像舰船目标的特征识别[J].陕西师范大学学报(自然科学版),2004,32:203-206.
[36] Dudani S A,Breeding K J,McGhee R B.Aircraft identification by moment invariant[J].IEEE Tran,Comout,1977,1(C-26):39-46.
[37] 杜亚娟,张洪才,潘泉.基于矩特征的三维飞机目标识别[J].数据采集与处理,2000,15(3): 390-394.
[38] 梅雪,李久贤.基于矩和多分辨分析的图像识别[J].南京工业大学学报,2003,25(6):50-53.
[39] Y.Li.Reforming the theory of invariant moments for pattern recognition[J].Pattern Recognition,1992,25:723-730.
[40] YE B,PENG JX,Improvement and invariance analysis of Zimike moments using as a region-based shape descriptor[J].Journal of Pattern Recognition and Image Analysis,2002,12(4): 419-428.
[41] 柏正尧,周纪勤.基于复数矩不变性的图像检索方法研究[J].计算机应用,2000,20(10):42-44.
[42] Z.L.Ping,R.G.Wu,Y.L.Sheng.Describing image with Chebyshev - FourierMoments[J].J.Opt. Soc.Am,2002,19(9):1748-1754.
[43] Chen C C.Improved moment invariants for shape discrimination.Pattern Recognition,1993,26: 915-927.
[44] 吕洪涛,周继成.离散状态下的不变矩算法研究[J].数据采集与处理,1993,8(2):156-160.
[45] Tadashi Kondo, Abhijit S. Pandya Recognition of X-ray Images by Using Revised GMDH-type Neural Networks[J]. Knowledge-Based Intelligent Information and Engineering Systems. 2003,2774:849-855.
[46] Zhihong Yao,Minrui Fei,Kang Li,Hainan Kong,Bo Zhao.Recognition of blue-green algae in lakes using distributive genetic algorithm-based neural networks[J].Neurocomputing,2007, 70(4):641-647.
[47] Wisnu JatmikoToshio Fukuda,Fumihito Arai.Artificial Odor Discrimination System Using Multiple Quartz Resonator Sensors and Various Neural Networks for Recognizing Fragrance Mixtures[J].IEEE Sensors Journal,2006,6(1):223-233.
[48] Pei-Chann Chang,Yen-Wen Wang,Chen-Hao Liu.Fuzzy back-propagation network for PCB sales forecasting[J].Advances in Natural Computation,2005,3610:364-373.
[49] Shih-Wei Lin,Shuo-Yan Chou,Shih-Chieh Chen.Irregular shapes classification by back-propagation neural network[J].The International Journal of Advanced Manufacturing Technology,2007,34(11):1164-1172.
[50] D.Benny Karunakar,G.L.Datta.Prevention of defects in castings using back propagation neural networks[J].The International Journal of Advanced Manufacturing Technology,2007, 34(9):1035-1043.
[51] 吴青,刘三阳,张乐友.最小二乘支持向量机的预优共轭梯度法[J].系统工程与电子技术,2007,29(10):1746-1749.
[52] 江玲玲,殷海青,冯象初.一种结合稀疏表示和投影正则化的图像分解方法[J].西安电子科技大学学报(自然科学版),2007,34(5):800-804.
[53] 刘洪,夏立显,廖丽萍等.应用弹性 BP 算法预测贵州金矿储量[J].地球物理学进展,2005,20(2):399-401.
[2] T.S. Benice,Jacob Raber.Object recognition analysis in mice using nose-point digital video tracking[J].Journal of Neuroscience Methods,2008,168,(2):422-430.
[3] Gruber, B.Maess, N.J.Trujillo-Barreto.Gamma-Band responses during a simple object recognition task: A replication study in human MEG[J].Brain Research,2008,1196:74-84.
[4] Sungho Kim,Kuk-Jin Yoon,In So Kweon.Object recognition using a generalized robust invariant feature and Gestalt's law of proximity and similarity[J].Pattern Recognition,2008, 41(2):726-741.
[5] Eugene Charniak,Robert P.Goldman.A Bayesian model of plan recognition[J].Artificial Intelligence,1993,64(1):53-79.
[6] Shen-Chi Tien,Tsorng-Lin Chia,Yibin Lu.Using cross-ratios to model curve data for aircraft recognition[J].Pattern Recognition Letters,2003,24(12):2047-2060.
[7] Thomas Heseltine, Nick Pears,Jim Austin.Three-dimensional face recognition using combinations of surface feature map subspace components[J].Image and Vision Computing, 2008,26(3):382-396.
[8] V.V. Srinivas,Shivam Tripathi,A.Ramachandra Rao,Rao S.Govindaraju.Regional flood frequency analysis by combining self-organizing feature map and fuzzy clustering[J].Journal of Hydrology,2008,348(1):148-166.
[9] 陈拓,赵荣椿.几何不变性及其在 3D 物体识别中的应用[J].中国图像图形学报,2003,8(9): 993-1000.
[10] 申金媛,李现国,常胜江.相位特征在三维物体识别中的应用[J].物理学报,2005,54(11): 5157-5163.
[11] 黄黎红.家用机器人的部分遮挡物体的识别[J].现代电子技术,2005,192:112-117.
[12] Manuele Bicego,Umberto Castellani,Vittorio Murino.A Hidden Markov Model approach for appearance-based 3D object recognition[J].Pattern Recongnition Letters,2005,(26):2588-2599.
[13] Bo G P,Kyoung M L,Sang U L.Recogniton of partially occluded objects using probabilistic ARG based matching[J].Comput.Vision Image Understanding. 2003,3(90):217-241.
[14] Cecilia Di Ruberto.Recognition of shapes byattributed skeletal graphs[J].PatternRecongnition,2004(37):21-31.
[15] Maria Stepanova,Feng Lin,Valerie C.-L.Lin.Establishing a statistic model for recognition of steroid hormone response elements[J].Computational Biology and Chemistry,2006,30(5): 339-347.
[16] Mike R. Schoenberg,Kyra A. Dawson,Kevin Duff.Test performance and classification statistics for the Rey Auditory Verbal Learning Test in selected clinical samples[J].Archives of Clinical Neuropsychology,2006,21(7):693-703.
[17] Hu Jin,Zhiyong Zheng,Minjie Gao.Effective induction of phytase in Pichia pastoris fed-batch culture using an ANN pattern recognition model-based on-line adaptive control strategy[J]. Biochemical Engineering Journal,2007,37(1):26-33.
[18] Prasad D.Polur,Gerald E.Miller.Investigation of an HMM/ANN hybrid structure in pattern recognition application using cepstral analysis of dysarthric (distorted)speech signals[J]. Medical Engineering & Physics,2006,28(8):741-748.
[19] Hong-Kyu Kim,Dong Wook Sohn.An analysis of the relationship between land use density of office buildings and urban street configuration: Case studies of two areas in Seoul by space syntax analysis[J].Cities,2002,19(6):409-418.
[20] Nadir Farah, Labiba Souici ,Mokhtar Sellami.Classifiers combination and syntax analysis for Arabic literal amount recognition[J].Engineering Applications of Artificial Intelligence,2006, 19,(1):29-39.
[21] F.Chevalier,J.P.Domenger,J. Benois-Pineau.Retrieval of objects in video by similarity based on graph matching[J].Pattern Recognition Letters,2007,28,1-11.
[22] Alexey Kostin,Joser Kittler,William Christmas.Object recognition by symmetrised graph matching using relaxation labelling with an inhibitory mechanism[J],Pattern Recognition Letters,2005,26(3):381-393.
[23] Hochul Shin,Seong-Dae Kim,Hae-Chul Choi.Generalized elastic graph matching for face recognition[J], Pattern Recognition Letters,2007,28(9):1077-1082.
[24] Wen-Liang Hung,Miin-Shen Yang.On the J-divergence of intuitionistic fuzzy sets with its application to pattern recognition[J].Information Sciences,2008,178(6):1641-1650.
[25] Adrian David Cheok, Zhang Jian, Eng Siong Chng.Efficient mobile phone Chinese optical character recognition systems by use of heuristic fuzzy rules and bigram Markov language models[J].Applied Soft Computing,2008,8(2):1005-1017.
[26] S.Marsili-Libelli.Control of SBR switching by fuzzy pattern recognition[J].Water Research, 2006,40(5):1095-1107.
[27] 丘江,刘波,杨静.基于高阶胡氏矩的多目标图像识别算法[J].光子学报,2001,30(9):1141-1145.
[28] Javad Haddadnia.An Efficient Human Face Recognition System Using Pseudo Zernike Moment Invariant And Radial Basis Function Neural Network[J].International Journal of Pattern Recognition and Artificial Intelligence,2003,17(1):41-62.
[29] Hu M K.Visual pattern recognition by moment invariant[J].IRE Trans Information Theory, 1962,1(8):179-187.
[30] 袁非牛,廖光煊,张永明. 计算机视觉火灾探测中的特征提取[J].中国科学技术大学学报,2006,36(1):39-43.
[31] 刘寅,滕晓龙,刘重庆.复杂背景下基于傅立叶描述子的手势识别[J].计算机仿真,2005, 22(12):158-161.
[32] H.P.Ren,Z.L.Ping,W.R.G.BO.Cell Image Recognition With Radial Harmonic Fourier Moment [J].Chinese Physics,2003,12(6):41-62.
[33] 禹晶,段娟,苏开娜.一种基于 Hough 变换的步态特征提取方法的研究[J].中国图象图形学报,2005,10(10):1304-1309.
[34] Markus Ulricha, Carsten Steger, Albert Baumgartne.Real-time object recognition using a modified generalized[J].Hough transform Pattern Recognition,2003,36:2557–2570.
[35] 董江曼,李应岐,邓飚.SAR 图像舰船目标的特征识别[J].陕西师范大学学报(自然科学版),2004,32:203-206.
[36] Dudani S A,Breeding K J,McGhee R B.Aircraft identification by moment invariant[J].IEEE Tran,Comout,1977,1(C-26):39-46.
[37] 杜亚娟,张洪才,潘泉.基于矩特征的三维飞机目标识别[J].数据采集与处理,2000,15(3): 390-394.
[38] 梅雪,李久贤.基于矩和多分辨分析的图像识别[J].南京工业大学学报,2003,25(6):50-53.
[39] Y.Li.Reforming the theory of invariant moments for pattern recognition[J].Pattern Recognition,1992,25:723-730.
[40] YE B,PENG JX,Improvement and invariance analysis of Zimike moments using as a region-based shape descriptor[J].Journal of Pattern Recognition and Image Analysis,2002,12(4): 419-428.
[41] 柏正尧,周纪勤.基于复数矩不变性的图像检索方法研究[J].计算机应用,2000,20(10):42-44.
[42] Z.L.Ping,R.G.Wu,Y.L.Sheng.Describing image with Chebyshev - FourierMoments[J].J.Opt. Soc.Am,2002,19(9):1748-1754.
[43] Chen C C.Improved moment invariants for shape discrimination.Pattern Recognition,1993,26: 915-927.
[44] 吕洪涛,周继成.离散状态下的不变矩算法研究[J].数据采集与处理,1993,8(2):156-160.
[45] Tadashi Kondo, Abhijit S. Pandya Recognition of X-ray Images by Using Revised GMDH-type Neural Networks[J]. Knowledge-Based Intelligent Information and Engineering Systems. 2003,2774:849-855.
[46] Zhihong Yao,Minrui Fei,Kang Li,Hainan Kong,Bo Zhao.Recognition of blue-green algae in lakes using distributive genetic algorithm-based neural networks[J].Neurocomputing,2007, 70(4):641-647.
[47] Wisnu JatmikoToshio Fukuda,Fumihito Arai.Artificial Odor Discrimination System Using Multiple Quartz Resonator Sensors and Various Neural Networks for Recognizing Fragrance Mixtures[J].IEEE Sensors Journal,2006,6(1):223-233.
[48] Pei-Chann Chang,Yen-Wen Wang,Chen-Hao Liu.Fuzzy back-propagation network for PCB sales forecasting[J].Advances in Natural Computation,2005,3610:364-373.
[49] Shih-Wei Lin,Shuo-Yan Chou,Shih-Chieh Chen.Irregular shapes classification by back-propagation neural network[J].The International Journal of Advanced Manufacturing Technology,2007,34(11):1164-1172.
[50] D.Benny Karunakar,G.L.Datta.Prevention of defects in castings using back propagation neural networks[J].The International Journal of Advanced Manufacturing Technology,2007, 34(9):1035-1043.
[51] 吴青,刘三阳,张乐友.最小二乘支持向量机的预优共轭梯度法[J].系统工程与电子技术,2007,29(10):1746-1749.
[52] 江玲玲,殷海青,冯象初.一种结合稀疏表示和投影正则化的图像分解方法[J].西安电子科技大学学报(自然科学版),2007,34(5):800-804.
[53] 刘洪,夏立显,廖丽萍等.应用弹性 BP 算法预测贵州金矿储量[J].地球物理学进展,2005,20(2):399-401.