模式识别领域中形变不变量的若干关键问题研究
|
摘要
随着人类社会生产力的不断发展，人类生活、生产及科研的活动越来越复杂。分类识别是人类生活、生产及科研中最基本最重要的活动之一。利用机器实现自动模式识别是人类生产力进一步发展的要求。随着计算机的出现，人工智能的兴起，自动模式识别迅速发展并成功地应用于工业、农业、国防、科研、医疗卫生、气象、天文等许多领域。这些成果很大程度上取决于不变量相关理论和方法的发展。模式识别的一个核心问题是如何构建恰当的不变量。恰当的不变量可在区别不同对象的同时辨识同一对象的不同形态或模式。然而目前模式识别领域的不变量相关研究仍面临着诸多挑战，比如如何更高效率地计算已有的不变量，如何设计复杂形变下的比如弹性形变或投影变换下的恰当的不变量以及如何组合不变量以更高效地进行模式识别等问题。
本文首先回顾了模式识别领域的不变量研究历史和现状，在总结前人工作的基础上提出了一种新的不变量定义和求解方法，即隐性不变量定义和求解方法，为模式识别领域不变量的研究开拓了一个新的思路。同时，对上面提到的模式识别领域的不变量研究存在的若干挑战分别做出了相应的研究。本文的主要内容及贡献如下：
本文提出了一种在大规模点集下求解模式识别领域的一个基本不变量——凸包的高效算法。在回顾总结当前凸包求解算法的原理的基础上，本文模拟人类视觉注意机理，设计了一种快速求解大规模点集的凸包的算法。算法的核心思想是快速排除模式初始凸包质心附近的大量冗余点。与当前几个最好的凸包算法的比较实验结果表明该算法在求解大规模点集的凸包时性能卓越。
弹性形变或投影变换下的不变量设计是模式识别的一大难点。本文设计了一种基于点集拓扑结构的不变量。我们首先对点集进行环向的凸包分层分解，然后再依据凸包顶点分布对各凸包分层进行径向的分区，最后通过统计各分区内点的数量来求得不变量。当形变不破坏点集的拓扑结构时，该不变量均可保持不变。这些形变包括了投影变换和一定程度的弹性变换等。此外，该不变量还可抵抗一定程度的噪声。
本文在对模式识别原理进行总结回顾的基础上，提出了一种新的不变量定义和求解方法。该方法的核心思想是通过设计基于形变的函数并解决该函数的最优化问题从而得到模式的归一化状态，即模式的隐性不变量。该方法的两个应用要素是设计一个定义在形变上的函数和求解该函数的最优化问题。本文给出了该方法在仿射变换下的一个应用框架算法，并成功地将该框架算法用于路牌的自动识别。
如何将各种不变量进行优化组合，构建性能更好的模式分类器，也是不变量在模式识别中应用的一个重要命题。决策树算法是解决不变量的优化组合问题的有效工具。本文提出了一种新的决策树算法，逆向快速决策树算法，以提高决策树算法实时生成组合不变量用以标识并匹配模式的能力。该算法从目标函数出发，采用一种新的分类性能度量标准，该标准主要考虑不同属性对应的样本分布偏置的快慢。实验结果表明该算法生成规则的效率优于传统的ID3决策树算法。
本文为模式识别领域的不变量相关理论和方法的研究开辟了新的思路，为自动模式识别的探索和应用提供了一些有意义的参考。
Along with the ceaseless development of social productivity, human life,production and scientific research activities are becoming more and more complex.Recognition is the most basic and important one of the activities in human life,production and scientific research. It is the demand of the development of humanproductivity to use a machine to realize the automatic pattern recognition. With theadvent of the computer and the emergence of artificial intelligence, automatic patternrecognition develops rapidly and is applied in many fields such as industry, agriculture,national defense, scientific research, medical and health, meteorology, astronomy andetc. These achievements depend largely on the development of invariant theory andmethods. A major concern of pattern recognition is how to build appropriate invariants.Proper invariants can be used to differentiate an object from other objects while theycan also be used to recognize the transformed patterns of the same object. However, atpresent, invariant related research in the field of pattern recognition is still facing manychallenges, for example, how to compute the invariants more efficiently, how to designinvariants for complex transformations such as elastic transformations and projectivetransformations, and how to combine some invariants to recognize patterns moreefficiently.
This paper first reviews the research history and status quo of invariants in the fieldof pattern recognition. Base on a summary of previous works, this paper puts forward anew invariant methodology, i.e. the methodology of embedded invariant. This opens upa new train of thought for the research of invariants in pattern recognition. At the sametime, we also face the challenges of invariant research mentioned above. The maincontributions of the paper are as follows:
This paper presents a fast convex hull algorithm for a large point set. The algorithmimitates the procedure of human visual attention derived in a psychological experiment.The merit of human visual attention is to neglect most inner points directly. Incomparison with the two best convex hull algorithms in a latest review of2004, theproposed algorithm achieved a significant saving in time and space. Furthermore, wepropose to use an affine transformation to solve the narrow shape problem forcomputing the convex hull faster.
The design of invariant under elastic transformation or projection transformation is one of the difficulties in pattern recognition. In this paper, an invariant is designed basedon the topology of a point set. We first apply convex hull decomposition on the point set,and then, according to the distribution of the vertexes of the convex hull, we divide thepoint set into different sub sets radially. Finally, the sizes of the sub sets are used toderive an invariant. When the transformations such as projective transformations do notbreak the topological structure of the point set, the invariant will not change. In addition,the invariant is resistant to a certain amount of noise.
This paper puts forward a new invariant methodology based on a summary ofprevious works. The main idea of the proposed methodology is to transform the patternsof the objects to an optimal state defined by a function on the transformationsautomatically. Such an optimal pattern is named as an embedded invariant. The keypoint to apply this methodology is to design a function of the transformation and solvethe optimization problem of the function. A framework of application of themethodology under affine transformation is proposed. An algorithm under thisframework is applied successfully in automatic road sign recognition.
One important issue of the application of invariants in pattern recognition is tocombine different invariants to construct a more powerful recognition system. Decisiontree is an efficient tool for solving the combination problem of invariants. This paperproposes a novel algorithm of decision tree, i.e. the reverse decision tree algorithm. Thealgorithm aims to produce decision trees and rules rapidly. It begins with the targetattribute and adopts a new measure of classification ability. This measure concernsmainly on the speed of examples deflection due to different attributes. The experimentalresults show that the fast inverse decision tree algorithm deduces the same rules fasterthan a remarkable decision tree algorithm, the ID3.
The paper opens up a new train of thought for the research of invariant theory andmethods in the field of pattern recognition. It provides some valuable references to theexploration and application of automatic pattern recognition.
本文首先回顾了模式识别领域的不变量研究历史和现状，在总结前人工作的基础上提出了一种新的不变量定义和求解方法，即隐性不变量定义和求解方法，为模式识别领域不变量的研究开拓了一个新的思路。同时，对上面提到的模式识别领域的不变量研究存在的若干挑战分别做出了相应的研究。本文的主要内容及贡献如下：
本文提出了一种在大规模点集下求解模式识别领域的一个基本不变量——凸包的高效算法。在回顾总结当前凸包求解算法的原理的基础上，本文模拟人类视觉注意机理，设计了一种快速求解大规模点集的凸包的算法。算法的核心思想是快速排除模式初始凸包质心附近的大量冗余点。与当前几个最好的凸包算法的比较实验结果表明该算法在求解大规模点集的凸包时性能卓越。
弹性形变或投影变换下的不变量设计是模式识别的一大难点。本文设计了一种基于点集拓扑结构的不变量。我们首先对点集进行环向的凸包分层分解，然后再依据凸包顶点分布对各凸包分层进行径向的分区，最后通过统计各分区内点的数量来求得不变量。当形变不破坏点集的拓扑结构时，该不变量均可保持不变。这些形变包括了投影变换和一定程度的弹性变换等。此外，该不变量还可抵抗一定程度的噪声。
本文在对模式识别原理进行总结回顾的基础上，提出了一种新的不变量定义和求解方法。该方法的核心思想是通过设计基于形变的函数并解决该函数的最优化问题从而得到模式的归一化状态，即模式的隐性不变量。该方法的两个应用要素是设计一个定义在形变上的函数和求解该函数的最优化问题。本文给出了该方法在仿射变换下的一个应用框架算法，并成功地将该框架算法用于路牌的自动识别。
如何将各种不变量进行优化组合，构建性能更好的模式分类器，也是不变量在模式识别中应用的一个重要命题。决策树算法是解决不变量的优化组合问题的有效工具。本文提出了一种新的决策树算法，逆向快速决策树算法，以提高决策树算法实时生成组合不变量用以标识并匹配模式的能力。该算法从目标函数出发，采用一种新的分类性能度量标准，该标准主要考虑不同属性对应的样本分布偏置的快慢。实验结果表明该算法生成规则的效率优于传统的ID3决策树算法。
本文为模式识别领域的不变量相关理论和方法的研究开辟了新的思路，为自动模式识别的探索和应用提供了一些有意义的参考。
Along with the ceaseless development of social productivity, human life,production and scientific research activities are becoming more and more complex.Recognition is the most basic and important one of the activities in human life,production and scientific research. It is the demand of the development of humanproductivity to use a machine to realize the automatic pattern recognition. With theadvent of the computer and the emergence of artificial intelligence, automatic patternrecognition develops rapidly and is applied in many fields such as industry, agriculture,national defense, scientific research, medical and health, meteorology, astronomy andetc. These achievements depend largely on the development of invariant theory andmethods. A major concern of pattern recognition is how to build appropriate invariants.Proper invariants can be used to differentiate an object from other objects while theycan also be used to recognize the transformed patterns of the same object. However, atpresent, invariant related research in the field of pattern recognition is still facing manychallenges, for example, how to compute the invariants more efficiently, how to designinvariants for complex transformations such as elastic transformations and projectivetransformations, and how to combine some invariants to recognize patterns moreefficiently.
This paper first reviews the research history and status quo of invariants in the fieldof pattern recognition. Base on a summary of previous works, this paper puts forward anew invariant methodology, i.e. the methodology of embedded invariant. This opens upa new train of thought for the research of invariants in pattern recognition. At the sametime, we also face the challenges of invariant research mentioned above. The maincontributions of the paper are as follows:
This paper presents a fast convex hull algorithm for a large point set. The algorithmimitates the procedure of human visual attention derived in a psychological experiment.The merit of human visual attention is to neglect most inner points directly. Incomparison with the two best convex hull algorithms in a latest review of2004, theproposed algorithm achieved a significant saving in time and space. Furthermore, wepropose to use an affine transformation to solve the narrow shape problem forcomputing the convex hull faster.
The design of invariant under elastic transformation or projection transformation is one of the difficulties in pattern recognition. In this paper, an invariant is designed basedon the topology of a point set. We first apply convex hull decomposition on the point set,and then, according to the distribution of the vertexes of the convex hull, we divide thepoint set into different sub sets radially. Finally, the sizes of the sub sets are used toderive an invariant. When the transformations such as projective transformations do notbreak the topological structure of the point set, the invariant will not change. In addition,the invariant is resistant to a certain amount of noise.
This paper puts forward a new invariant methodology based on a summary ofprevious works. The main idea of the proposed methodology is to transform the patternsof the objects to an optimal state defined by a function on the transformationsautomatically. Such an optimal pattern is named as an embedded invariant. The keypoint to apply this methodology is to design a function of the transformation and solvethe optimization problem of the function. A framework of application of themethodology under affine transformation is proposed. An algorithm under thisframework is applied successfully in automatic road sign recognition.
One important issue of the application of invariants in pattern recognition is tocombine different invariants to construct a more powerful recognition system. Decisiontree is an efficient tool for solving the combination problem of invariants. This paperproposes a novel algorithm of decision tree, i.e. the reverse decision tree algorithm. Thealgorithm aims to produce decision trees and rules rapidly. It begins with the targetattribute and adopts a new measure of classification ability. This measure concernsmainly on the speed of examples deflection due to different attributes. The experimentalresults show that the fast inverse decision tree algorithm deduces the same rules fasterthan a remarkable decision tree algorithm, the ID3.
The paper opens up a new train of thought for the research of invariant theory andmethods in the field of pattern recognition. It provides some valuable references to theexploration and application of automatic pattern recognition.
引文
[1]孙即祥，王晓华。模式识别中的特征提取与计算机视觉不变量[M].北京:国防工业出版社，2001.
[2] R.C.G.onzalez，M.G.Thomason.濮群徐风家徐光佑译.句法模式识别[M].北京:清华大学出版社，1984.
[3] J. Wood. Invariant Pattern Recognition: A Review[J]. Pattern Recognition,1996,29(1):1-17.
[4] Y. Y. Tang and C. Y. Suen. New Algorithms for Fixed and Elastic GeometricTransformation Models [J]. IEEE Trans. Image Processing,1994,3(4):355-366.
[5] I. Weiss. Geometric Invariants and Object Recognition [J]. International Journal of ComputerVision,1993,10(3):207-231.
[6] F. Klein. Entwicklung der Mathematik [M]. Berlin:1926.
[7] Bhaskaracharya. Beejaganit, Ujjain,1150.
[8] D. Hilbert. über die Theorie der algebraischen Formen[J]. Mathematische Annalen,1890,36:473-534.
[9] D. Hilbert. über die vollen Invariantensysteme [J]. Mathematische Annalen,1893,42:313-373.
[10] M. Halphen. Sur les invariants differentiels des courbes gauches [J]. J. Ec. Polyt.,1880,28:1.
[11] E.J. Wilczynski. Projective Differential Geometry of Curves and Ruled Surfaces [M]. Teubner:Leipzig,1906.
[12] E.J. Wilczynski. Projective differential geometry of curved surfaces (Second Memoir)[J],Amer. Math. Soc. Trans.,1908,79.
[13] Fubini and ech. Geometria Proiettiva Differenziale [M]. Zanichetli: Bologna,1927.
[14] E.P. Lane. A Treatise on Projective Differential Geometry. University of Chicago Press,1942.
[15] H. Weyl. The Classical Groups [M]. Princeton University Press,1939.
[16] E. Cartan. La théorie des groupes continus et la géometrie, Oeuvres Complètes [M], III/2,Paris: Gauthier-Villars,1955:1727-1861.
[17] D. Mumford. Geometric Invariant Theory [M]. New York: Springer,1965.
[18] J. Nagata. Complete reducibility of rational representations of a matric group [J]. J. Math.Kyoto Univ.,1963,3:369-377.
[19] S.S. Abhyankar. AlgebraicGeometry for Scientists and Engineers [M]. Providence, RI:American Mathematical Society,1990.
[20] Barbara Zitova′, Jan Flusser. Image registration methods: a survey [J]. Image and VisionComputing,2003,(21):977–1000.
[21] J.Flusser, T.Suk. Pattern recognition by affine moment invariants[J]. Pattern Recognition,1993,(26):167-174.
[22] A.Goshtasby, G.C. Stockman, C.V.Page. A region-based approach to digital image registrationwith subpixel accuracy [J]. IEEE Transactions on Geoscience and Remote Sensing,1986,(24):390-399.
[23] A.Goshtasby, G.C. Stockman. Point pattern matching using convex hull edges[J]. IEEEtransactions on Systems, Man and Cybernetics,1985,(15):631-637.
[24] M.Holm. Towards automatic rectification of satellite images using feature based matching, inProceedings of the International Geoscience and Remote Sensing Symposium IGARSS’91[c].Finland: Espoo,1991.2439-2442.
[25] Y.C. Hsieh, D.M. Mckeown, F.P.Perlant. Performance evaluation of scene registration andstereo matching for cartographic feature extraction[J]. IEEE Transactions on Pattern Analysisand Machine Intelligence,1992,(14):214-237.
[26] M.Seter, H.Hild, D.Fritsch. Definition of ground control features for image registration usingGIS data, in Proceedings of the Symposium on Object Recognition and Scene Classificationfrom Multispectral and Multisensor Pixels[c]. Columbus: Ohio,1998.7.
[27] M. Roux. Automatic registration of SPOT images and digitized maps, in Proceedings of theIEEE International Conference on Image Processing ICIP’96[C]. Switzerland: Lausanne,1996.625-628.
[28] P.A. Brivio, A.D. Ventura, A. Rampini, R. Schettini. Automatic selection of control pointsfrom shadow structures[J]. International Journal of Remote Sensing,1992,(13):1853-1860.
[29] N.R. Pal, S.K. Pal. A review on image segmentation techniques[J]. Pattern Recognition,1993,(26):1277-1294.
[30] P. Arbeláez, M. Maire, C. Fowlkes, J. Malik. Contour Detection and Hierarchical ImageSegmentation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2011,33(5):898-916.
[31] S.Moss, E.R. Hancock. Multiple line-template matching with EM algorithm[J]. PatternRecognition Letters,1997,(18):1283-1292.
[32] W.H. Wang, Y.C. Chen. Image registration by control points pairing using the invariantproperties of line segments [J]. Pattern Recognition Letters,1997,(18):269-281.
[33] X.Dai, S,Khorram. Development of a feature-based approach to automated image registrationfor multitemporal and multisensor remotely sened imagery, in Proceedings of InternationalGeoscience and Remote Sensing Symposium IGARSS’97[C]. Singapore:1997.243-245.
[34] V.Govindu, C. Shekhar, R.Chellapa. Using geometric properties for correspondence-lessimage alignment, in Proceedings of the International Conference on Pattern RecognitionICPR’98[C]. Australia: Brisbane,1998.37-41.
[35] H.Li, B.S. Manjunath, S.K. Mitra. A contour-based approach to multisensor imageregistration[J], IEEE Transactions on Image Processing.1995,(4):320-334.
[36] H.Maitre, Y.Wu. Improving dynamic programming to solve image registration [J]. PatternRecognition,1987,(20):443-462.
[37] D.Shin, J.K. Pollard, J.P. Muller. Accurate geometric correction of ATSR images[J]. IEEETransactions on Geoscience and Remote Sensing,1997,(35):997-1006.
[38] S.Z. Li, J. Kittler, M. Petrou, Matching and recognition of road networks from acrial images,in Proceedings of the Second European Conference on Computer Vision ECCV’92[C]. Italy:St.Margherita,1992.857-861.
[39] N.Vujovic, D.Brzakovic. Establishing the correspondence between control points in pairs ofmammographic images[J]. IEEE Transacions on Image Processing,1997,(6):1388-1399.
[40] J.Canny. A computational approach to edge detection [J]. IEEE Transactions on PatternAnalysis and Machine Intelligence,1986,(8):679-698.
[41] D.Marr, E.Hildreth. Theory of edge detection[J]. Proceedings of the Royal Society of London,B,1980(207):187-217.
[42] D.Ziou, S. Tabbone. Edge detection techniques——an overview [EB/01].http://citeseer.nj.nec.com/ziou97edge.html,1997,2011-11-02.
[43] J.B.A. Maintz, P.A. van den Elsen, M.A. Viergever. Comparison of edge-based andridge-based registration of CT and MR brain images [J]. Medical Image Analysis,1996,(1):151-161.
[44] J.B.A. Maintz, P.A. van den Elsen, M.A. Viergever. Evaluation on ridge seeding operators formultimodality medical image matching [J]. IEEE Transactions on Pattern Analysis andMachine Intelligence,1996(18):353-365.
[45] M. Basu. Gaussian-Based Edge Detection Methods—A Survey [J]. IEEE Transactions onSystems, Man, and Cybernetics—Part C: Applications and Reviews,2002,32(3):252-260.
[46] M. Tello Alonso, C. Lopez-Martinez, J.J. Mallorqui, P. Salembier. Edge EnhancementAlgorithm Based on the Wavelet Transform for Automatic Edge Detection in SAR Images [J].IEEE Transactions on Geoscience and Remote Sensing.2011,49(1):222–235.
[47] G.Stockman, S.Kopstein, S.Benett. Matching images to models for registration and objectdetection via clustering [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1982,(4):229-241.
[48] A.S. Vasileisky, B. Zhukov, M. Berger. Automated image co-registration based on linearfeature recognition, in Proceedings of the Second Conference Fusion of Earth Data[C]. France:Sophia Antipolis,1998.59-66.
[49] S.Growe, R.Tonjes. A knowledge based approach to automatic image registration, inProceedings of the IEEE International Conference on Image Processing ICIP’97[C].California: Santa Barbara,1997.228-231.
[50] J. Ton, A.K. Jain. Registering landsat images by point matching [J]. IEEE Transactions onGeoscience and Remote Sensing,1989,(27):642-651.
[51] M.Ehlers. Region-based matching for image registration in remote sensing databases, inProceedings of the International Geoscience and Remote Sensing Symposium IGARSS’91[C].Finland: Espoo,1991.2231-2234.
[52] B.S. Manjunath, C.Shekhar, R.Chellapa. A new approach to image feature detection withapplications[J]. Pattern Recognition,1996,(29):627-640.
[53] Q.Zheng, R.Chellapa. A computational vision approach to image registration [J]. IEEETransactions on Image Processing,1993,(2):311-325.
[54] W.S.I. Ali, F.S.Cohen. Registering coronal histological2-D sections of a rat brain with coronalsections of a3-D brain atlas using geometric curve invariants and B-spline representation [J].IEEE Transactions on Medical Imaging,1998,(17):957-966.
[55] S.Banerjee, D.P. Mukherjee, D.D. Majumdar. Point landmarks for registration of CT and NMRimages [J]. Pattern Recognition Letters,1995,(16):1033-1042.
[56] L.M.G. Fonseca, M.H.M. Costa. Automatic registration of satellite images, in Proceedings ofthe Brazilian Symposium on Computer Graphic and Image Processing[C]. Brazil:1997.219-226.
[57] J.W. Hsieh, H.Y.M. Liao, K.C. Fan, M.T.ko. A fast algorithm for image registration withoutpredetermining correspondence, in Proceedings of the International Conference on PatternRecognition ICPR’96[C]. Austria: Vienna,1996.765-769.
[58] B.Likar, F.Pernus. Automatic extraction of corresponding points for the registration of medicalimages [J]. Medical Physics,1999(26):1678-1686.
[59] D.Bhattacharya, S.Sinha. Invariance of stereo images via theory of complex moments [J].Pattern Recognition,1997,(30):1373-1386.
[60] C.Y. Wang, H. Sun, S.Yadas, A. Rosenfeld. Some experiments in relaxation image matchingusing corner features [J]. Pattern Recognition,1983,(16):167-182.
[61] K.Rohr. Localization properties of direct corner detectors [J]. Journal of MathematicalImaging and Vision,1994,(4):139-150.
[62] K.Rohr. Landmark-Based Image Analysis: Using Geometric and Intensity Models,Computational Imaging and Vision Series, vil.21[M]. Dordrecht: Kluwer Academic Publishers,2001.
[63] S.M. Smith, SUSAN. Low level image processing[EB/01].http://www.fmrib.ox.ac.uk/-spacesteve/susan,2012-01-09.
[64] Z.Zheng, H. Wang, E.K. Teoh. Analysis of gray level corner detection [J]. Pattern RecognitionLetters,1999,(20):149-162.
[65] S.M. Smith, J.M. Brady, SUSAN. A new approach to low level image processing [J].International Journal of Computer Vision,1997,(23):45-78.
[66] D. G. Lowe. Object recognition from local scale-invariant features, in the Proceeding of IEEEInt. Conf. Comput. Vision [C]. IEEE,1999,(2):1150-1157.
[67] Grassmann, H. Der Ort der Hamilton’schen Quaternionen in der Ausdehnungslehre [J].Math.Ann.,1877,(12):375.
[68] Clifford, W.K. Applications of Grassmann’s extensive algebra [J]. Am.J.Math.,1878,(1):350-358.
[69] E. Bayro-Corrochano, and J. Lasenby. Object modelling and motion analysis using Cliffordalgebra, in Proceedings of Europe-China Workshop on Geometric Modeling and Invariants forComputer Vision [C]. China, Xi’an:1995.
[70] B. Rosenhahn, and G. Sommer. Adaptive pose estimation for different corresponding entities[J]. Lecture Notes in Computer Science,2002, ISSU2449:265-273.
[71] J. Lasenby, E. Bayro-Corrochano, A.N. Lasenby, G. Sommer. A New Methodology forComputing Invariants in Computer Vision, in Proceedings of ICPR’96[C]. IEEE,1996.1015-4651
[72] B. Chazelle. On the Convex Layers of a Planar Set [J]. IEEE Transactions on InformationTheory,1985, IT-31(4):509-517.
[73] H. Khazaei, A. Mohades. Fingerprint matching and classification using an onion layeralgorithm of computational geometry [J]. International Journal of Mathematics and Computersin Simulation,2007,1(1):26-32.
[74] W. Yang, Y. Wang, and G. Mori. Recognizing human actions from still images with latentposes [C]. In the Proceeding of Computer Vision and Pattern Recognition (CVPR), CA: SanFrancisco,2010.2030–2037.
[75] M. Ferraro and T. M. Caeili. Relationship between integral transform invariances and Liegroup theory [J]. J. Optical Soc, America A,1988,(5):738-742.
[76] R.N.Bracewell. The Fourier Transform and Its Applications. Electrical and ElectronicEngineering Series [M]. McGraw-Hill Book Company,1978.
[77] E.Brigham. The Fast Fourier Transform and Its Applications [M]. Prentice-Hall,1988.
[78] M.Clausen and U.Baum. Fast Fourier Transforms [M]. Wissenschaftsverlag: Mannheim,1993.
[79] H. Wechsler. Invariance in pattern recognition [J]. Advances in Electronics and ElectronPhysics,1987,(69):262-322.
[80] A. Grace and M. Spann, A comparison between Fourier-Mellin descriptors and moment basedfeatures for invariant object recognition using neural networks [J]. Pattern Recognition Letter,1991,(12):635-643.
[81] D. Mendlovic, H.M. Ozaktas. Fractional Fourier transforms and their optical implementation:part I [J]. Journal of the Optical Society of America A: Optics and Image Science, and Vision,1993,10(9):1875–1881.
[82] H.M. Ozaktas, D. Mendlovic. Fractional Fourier transforms and their optical implementation:part II [J]. Journal of the Optical Society of America A: Optics and Image Science, and Vision,1993,10(12):2522–2531.
[83] L.B. Almeida, The fractional Fourier transform and time–frequency representations[J]. IEEETransactions on Signal Processing,1994,42(11):3084–3091.
[84] A.I. Zayed. On the relationship between the Fourier and fractional Fourier transforms[J]. IEEESignal Processing Letters,196,3(12):310–311.
[85] G. Cariolaro, T. Erseghe, P. Kraniauskas, N. Laurenti. A unified framework for the fractionalFourier transform, IEEE Transactions on Signal Processing,1998,46(12):3206–3219.
[86] H.M. Ozaktas, Z. Zalevsky, M.A. Kutay, The Fractional Fourier Transform withApplications in Optics and Signal Processing [M], John Wiley, Chichester, New York, USA,2001.
[87] E. Sejdic′, Igor Djurovic′, LJubisa Stankovic′. Fractional Fourier transform as a signalprocessing tool: An overview of recent developments [J]. Signal Processing,2011,91:1351–1369.
[88] W. Pan, K. Qin, and Y. Chen. An Adaptable-Multilayer Fractional Fourier TransformApproach for Image Registration [J].Ieee Transactions on Pattern Analysis and MachineIntelligence,2009.31(3):400-413.
[89] H. Lee, H. Maeng, and Y. Bae. Fake Finger Detection Using the Fractional Fourier Transform[J]. Biometric ID Management and Multimodal Communication, Lecture Notes in ComputerScience,2009,5707:318-324.
[90] Y. Li. Reforming the theory of invariant moments for pattern recognition [J]. PatternRecognition,1992,(25):723-730.
[91] Y. Sheng and H. H. Arsenault. Experiments on pattern recognition using invariantFourier-Mellin descriptors [J]. J. Optical Soc. America A (Optics and Image Sci.),1986,(3):771-776.
[92] R. Wu and H. Stark. Three dimensional object recognition from multiple views [J]. J. OpticalSoc. America A (Optics and Image Sci.),1986,(3):1543-1557.
[93] T.M.Caelli, Zhi-Qiang Liu. On the minimum number of templates required for shift, rotation,and size invariant pattern recognition [J]. Pattern Recognition,1988,(21):205-216.
[94] D. Casasent and D. Psaltis, Position, rotation and scale-invariant optical correlation [J]. Appl.Optics,1976,15:1795-1799.
[95] D. Casasent and D. Psaltis, Hybrid processor to compute invariant moments for patternrecognition [J]. Optics Letter,1980,5:395-397.
[96] Nanrun Zhou, Yixian Wang, Lihua Gong. Novel optical image encryption scheme based onfractional Mellin transform [J].Optics Communications,2011,284:3234–3242.
[97] D. Pintsov. Invariant pattern recognition, symmetry and Radon transforms [J]. J. Optical Soc.America A,1989,6(10):1544-1554.
[98] A. Delopoulos, A. Tirakis and S. Kollias. Invariant image classification usingtriple-correlation-based neural networks [J]. IEEE Trans. Neural Networks,1994,(5):392-408.
[99] P.Viola, W.M. Wells. Alignment by maximization of mutual information [J]. InternationalJournal of Computer Vision,1997,(24):137-154.
[100] G.P. Penney, J.Weese, J.A. Little, P.Desmedt, D.L.G. Hill, D. J. Hawkes. A comparison ofsimilarity measures for use in2D-3D medical image registration [J]. IEEE Transactions onMedical Imaging,1998,(17):586-595.
[101] J.P.W. Pluim, J.B.A. Maintz, J.A. Little, M.A. Viergever. Mutual-Information-BasedRegistration of Medical Images: A Survey [J]. IEEE Transactions on Medical Imaging,2003,(8):986-1004.
[102] H. Peng, F. Long, C. Ding. Feature selection based on mutual information criteria ofmax-dependency, max-relevance, and min-redundancy [J]. IEEE Transactions on PatternAnalysis and Machine Intelligence,2005,(8):1226-1238.
[103] H. Liu, J. Sun, L. Liu, and H. Zhang. Feature selection with dynamic mutual information[J].Pattern Recognition,2009,42:1330-1339.
[104] Q. Hu, W. Pan, S. An, P. Ma and J. Wei. An efficient gene selection technique for cancerrecognition based on neighborhood mutual information [J]. International Journal of MachineLearning and Cybernetics,2010,1(1-4):63-74.
[105] A. Nabatchian, E.Abdel-Raheem, M. Ahmadi. Illumination invariant feature extraction andmutual-information-based local matching for face recognition under illumination variation andocclusion [J]. Pattern Recognition,2011,44:2576–2587
[106] Flusser, J., Suk, T. and Zitová, B. Moments and Moment Invariants in Pattern Recognition[M].Chichester, UK: John Wiley&Sons, Ltd,2009
[107] Dong Xu, and Hua Li. Geometric moment invariants [J].Pattern Recognition,2008,41:240–249.
[108] R. P. Srivastava. Transformation and distortion tolerant recognition of numerals using neuralnetworks, in Proceedings of1991ACM Computer Science Conference [C]. New York: ACM,1991.402-408.
[109] M. K. Hu. Visual pattern recognition by moment invariants [J]. IEEE Trans. Inform. Theory g,1962:179-187.
[110] Y. Sheng and J. Duvernoy. Circular Fourier radial Mellin transform descriptors for patternrecognition [J]. J. Optical Soc. America A (Optics and Image Sci.,1986,(3):885-888.
[111] S. Perantonis and P. Lisboa. Translation, rotation and scale invariant pattern recognition byhigh-order neural networks and moment classifiers [J]. IEEE Trans. Neural Networks,1992,(3):241-251.
[112] B. Chen, H. Shu, G. Chen, J. Ge, and L. Luo. Color Face Recognition Based on QuaternionZernike Moment Invariants and Quaternion BP Neural Network [J].Energy Procedia,2011,13:551-558.
[113] A. Khotanzad and Y. H. Hong. Invariant image recognition by Zernike moments [J]. IEEETrans. Pattern Analysis Mach. Intell.,1990,(12):489-497.
[114] K.M. Hosny. Efficient computation of Legendre moments for gray level images [J].International Journal of Image Graph,2007,7(4):735–747.
[115] C.W. Chong, R. Paramesran, and R. Mukundan. Translation and scale invariants of Legendremoments. Pattern Recognition,2004,37:119–129.
[116] M.R. Spiegel. Schaum’s Handbook of Formulas and Tables[M]. New York: MacGraw Hill,1968.
[117] S.X. Liao, M. Pawlak. On image analysis by moments [J]. IEEE Trans. Pattern Anal. MachineIntell.1996,18(3),254–266.
[118] K. M. Hosny. Refined translation and scale Legendre moment invariants [J].PatternRecognition Letters,2010,31:533–538.
[119] A. Shvedov, A. Schmidt and V. Yakubovich. Invariant systems of features in patternrecognition [J]. Automation Remote Control,1979,(40):131-142.
[120]J. Flusser and T. Suk. Pattern recognition by affine moment invariants [J]. Pattern Recognition,1993,(26):167-174.
[121] P. Simard, B. Victorri, Y. Le Cun and J. Denker. Tangent prop--a formalism for specifyingselected invariances in an adaptive network, in Proceedings of NIPS-4[C].1991.895-903.
[122] D. E. Rumelhart, G. E. Hinton and R. J. Williams. Learning internal representations by errorpropagation [J]. Parallel Distributed Processing: Explorations in the Microstructures ofCognition,1986,(1):318-362..
[123] Y. Le Cun. Generalization and network design strategies.Connectionism in perspective [M].Amsterdam: Elsevier Science,1989.143-155.
[124] T. Kanaoka, R. Cheilappa, M. Yoshitaka and S. Tomita. A higher-order neural network fordistortion invariant pattern recognition [J]. Pattern Recognition Letter,1992,(13):837-841.
[125] R. Duren, B. Peikari. A comparison of second-order neural networks to transform-basedmethod for translation-and orientation-invariant object recognition, in Proceedings of the1991IEEE Workshop on Neural Networks for Signal Processing [C].1991.236-245.
[126] R. Duren and B. Peikari. A new neural network architecture for rotationally invariant objectrecognition, in Proceedings of the34th Midwest Symposium on Circuits and Systems [C].IEEE,1992. Vol.1,320-323.
[127] L. Spirkovska and M. Reid. Robust position, scale and rotation invariant object recognitionusing higher order neural networks [J]. Pattern Recognition,1992,(25):975-985.
[128] C.L. Giles and T. Maxwell. Learning, invariance, and generalization in high-order neuralnetworks [J]. Appl. Optics,1987,(26):4972--4978.
[129] M. Fukumi, S. Omatu, F. Takeda and T. Kosaka. Rotation-invariant neural pattern recognitionsystem with application to coin recognition [J]. IEEE Trans. Neural Networks,1992,(3):272-279.
[130] K. Lang and G. Hinton. The development of TDNN architecture for speech recognition,Technical Report CMU-CS-88-152[R]. Carnegie-Mellon University,1988.
[131] J. Shawe-Taylor. Building symmetries into feedforward networks, in Proceedings of FirstIEEE Conference on Artificial Neural Networks [C]. IEEE,1989.158-162.
[132] Z.L. Gaing. Wavelet-based neural network for power disturbance recognition andclassification [J]. IEEE Transactions on Power Delivery,2004,19(4):1560-1568.
[133] E. Stergiopoulou, and N. Papamarkos. Hand gesture recognition using a neural network shapefitting technique [J]. Engineering Applications of Artificial Intelligence,2009,22(8):1141–1158.
[134] M.Baqar, S. Azhar, Z. Iqbal, I. Shakeel, L. Ahmed, M.Moinuddin. Efficient iris recognitionsystem based on dual boundary detection using robust variable learning rate Multilayer FeedForward neural network [M]. In proceedings of7th International Conference on InformationAssurance and Security (IAS), Melaka:2011:326–330.
[135] L. Xu, M. Q.H. Meng, K. Wang, W. Lu, N. Li. Pulse images recognition using fuzzy neuralnetwork [J]. Expert Systems with Applications,2009,36(2):3805–3811.
[136] S. Wang, and H. Deng. Face Recognition Using Principal Component Analysis-Fuzzy LinearDiscriminant Analysis and Dynamic Fuzzy Neural Network [J]. Future Wireless Networks andInformation Systems,2012,143:577-586.
[137] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by Simulated Annealing [J].Science,1983, New Series,220(4598):671-680.
[138] F. P. Preparata, and M. lan Shamos. Computational geometry: An introduction [M]. New York,:Springer-Verlag,1985.
[139] M. Tajine, and D. Elizondo. New methods for testing linear separability [J]. Neurocomputing,2002,(47):161-188
[140] R. Minhas, and J. Wu. Invariant feature set in convex hull for fast image registration, inProceedings of IEEE Int. Conf. Syst. Man Cybern [C].2007.1557-1561.
[141] J.S. Fan, S.W. Xiong, and J.Z. Wang. The Multi-Objective Differential Evolution AlgorithmBased on Quick Convex Hull Algorithms, in Proceedings of5th International Conference onNatural Computation.2009.
[142] P. Szczypinski, and A. Klepaczko. Automated Recognition of Abnormal Structures in WCEImages Based on Texture Most Discriminative Descriptors [J]. Advances in Intelligent andSoft Computing,2010,(84):263-270
[143] X. Zhou, W. Jiang, Y. Tian, and Y. Shi. Kernel subclass convex hull sample selection methodfor SVM on face recognition [J]. Neurocomputing,2010,(73):2234-2246.
[144] F. Murtagh. A new approach to point pattern matching [J]. Publ. Astron. Soc. Pac.,1992,(104):301-307.
[145] R.V. Chadnov, and A.V. Skvortsov. Convex hull algorithms review, in Proceedings of the8thRussian-Korean International Symposium on Science and Technology [C].2004,(2):112-115.
[146] R.L. Graham. An efficient algorithm for determining the convex hull of a finite planar set [J].Inf. Process. Letter,1972,(1):132-133.
[147] A.M. Andrew. Another efficient algorithm for convex hulls in two dimensions [J]. Inf. Process.Letter,1979,(9):216-219.
[148] C. B. Barber, D.P. Dobkin, and H. Huhdanpaa. The quickhull algorithm for convex hulls [J].ACM Trans. Math. Softw,1996,(22):469-483.
[149] A. Datta, and S.K. Parui: A dynamic neural net to compute convex hull [J]. Neurocomputing,1996,(10):375-384..
[150] S. Naher, and D. Schmitt. A Framework for Multi-Core Implementations of Divide andConquer Algorithms and its Application to the Convex Hull Problem, in Proceedings of20thAnnual Canadian Conference on Computational Geometry.2008.
[151] H.K. Ahn, and Y. Okamoto. Adaptive Algorithms for Planar Convex Hull Problems [J]. IEICETrans. Inf. System,2011,(E94-D):182-189.
[152] F. Cantin, A. Legay, and P. Wolper. Computing Convex Hulls by Automata Iteration [J].Implementation and Applications of Automata,2008,(5148):112-121
[153] Y. J. Kim, J. Lee, M.S. Kim, and G. Elber. Efficient convex hull computation for planarfreeform curves [J]. Comput. Graph,2011,(35):698-705.
[154] M. Sharif, S.Z.Z. Naqvi, M. Raza, and W. Haider. A new Approach to Compute Convex Hull[J]. Innovative Systems Design and Engineering,2011,(2):187-193.
[155] A. Allport. Visual attention, in Foundations of cognitive science [M]. Cambridge: MITPress/Bradford Books,1989.
[156]R.A. Jarvis. On the identification of the convex hull of a finite set of points in the plane [J]. Inf.Process. Letter,1973,(2):18-21.
[157] J.B. Antoine Maintz, and M.A. Viergever. A survey of medical image registration. Med [J].Image Anal.,1998,(2):1-36.
[158] J. Hong, and X. Tan. A new approach to point pattern matching, in Proceedings of9th Int.Conf. Pattern Recognition [C].1988.
[159] T. Wakahara, and K. Odaka. Adaptive normalization of handwritten characters usingglobal/local affine transformation [J]. IEEE Trans. Pattern Anal. Mach. Intell.,1998,(20):1332—1341.
[160] Z. Yang, and F. S. Cohen. Image Registration and Object Recognition Using Affine Invariantsand Convex Hulls [J]. IEEE Trans. Image Process.,1999,(8):934-946.
[161] I. E. Rube, M. Ahmed, and M. Kamel. Wavelet Approximation-Based Affine Invariant ShapeRepresentation Functions [J]. IEEE Trans. Pattern Anal. Mach. Intell.,2006,(28):323-327.
[162] Y. Mei, and D. Androutsos. Affine invariant shape descriptors: the ICA-Fourier descriptor andthe PCA-Fourier descriptor, in Proceedings of19th Int. Conf. Pattern Recognition.2008.
[163] R. Fisher, S. Perkins, A. Walker, and E. Wolfart. Affine Transformation.http://homepages.inf.ed.ac.uk/rbf/HIPR2/affine.htm.2011,2011-06-06
[164] Z.W. Zhang, and X.C. WU. Algorithm for Convex Hull of Planar Massive Scattered Point Set[J]. Computer Engineering,2009,(35):43-45,48.
[165] L.G. Brown. A survey of image registration techniques [J]. ACM Comput. Surveys,1992,(24):325-376.
[166] F.H. Cheng, W.H. Hsu, and M.C. Kuo. Recognition of handprinted Chinese characters viastroke relaxation. Pattern Recognition,1993,(26):579-593.
[167]A. ROSENFELD. Image analysis and computer vision:1998[J]. Comput. Vis. Image Underst.,1998,(74):36-95.
[168] G.S.Cox, and G.DeJager. A survey of point pattern matching techniques and a new approach topoint pattern recognition, in Proceedings of South African Symposium on Communicationsand Signal Processing [C].1993.
[169] B.Li, Q.Meng, and H.Holstein. Point Pattern Matching and Applications-A Review, inProceedings of Conf. Proc. IEEE Int. Conf. Syst. Man Cybern [C].2003,(1):729-736.
[170]F. Preparata, and M. Shamos. Computational geometry: An introduction [M]. Addison-Wesley,1985.
[171] B. Yuan, and C. L. Tan. Convex hull based skew estimation [J]. Pattern Recognition,2007,(40):456-475.
[172] F. Murtagh. A New Approach to Point Pattern Matching[J]. Astronomical Society of thePacific,1992,(104):301-307.
[173] M. M. McQUEEN, and G. T. Toussaint. On the ultimate convex hull algorithm in practice [J].Pattern Recognition Letters,1985,(3):29-34.
[174] T. S. Caetano, T. Caelli, D. Schuurmans, and D. A. C. Barone. Graphical Models and PointPattern Matching [J]. IEEE Trans. Pattern Anal. Mach. Intell.,2006,(28):1646-1663.
[175] L. Shapiro, and J. Brady. Feature-Based Correspondence—An Eigenvector Approach [J].Image Vis. Comput.,1992,(10):283-288.
[176] H. Chui, and A. Rangarajan. A New Algorithm for Non-Rigid Point Matching, inProceedings of Conf. Computer Vision and Pattern Recognition,2000,(2):44-51.
[177] Carnegie Mellon University. CMU VASC Image Database.http://vasc.ri.cmu.edu//idb/html/motion/house/index.html.2010-12-11.
[178] D. G. Lowe. Distinctive Image Features from Scale-Invariant Keypoints [J]. InternationalJournal of Computer Vision,2004,60(2):91-110.
[179] R. Z. Liu and B. Fang and Y. Y. Tang and J. Wen and J. Qian. A fast convex hull algorithmwith maximum inscribed circle affine transformation [J]. Neurocomputing,2012,77:212—221.
[180] Y. Avrithis and Y. Xirouhakis and S. Kollias. Affine-invariant curve normalization for objectshape representation, classification, and retrieval [J]. Machine Vision and Applications,2001,13(2):80—94.
[181] J. P. Marques.模式识别-原理、方法及应用[M].吴逸飞,译.北京:清华大学出版社,2002.
[182]夏国恩.客户流失预测的现状与发展研究[J].计算机应用研究，2010，27(2):413-416.
[183]王伟达,刘文剑.一种基于混合决策树的调度知识获取算法[J].计算机应用研究,2007,24(12):54-59.
[184] Mitchell, T.M.机器学习[M].曾华军等,译.北京:机械工业出版社,2003.
[185] Quinlan J R. Induction of decision trees [J]. Machine Learning,1986,(1):81-106.
[186]洪家荣,丁明峰,李星原,王丽薇.一种新的决策树归纳学习算法[J].计算机学报,1995,18(6):470～474.
[187]刘小虎,李生.决策树的优化算法[J].软件学报,1998,9(10):797～800.
[188] Oliver J, Dowe A D L, Wallace C S. Inferring decision graphs using the minimum messagelength principle, in: Proceedings of the1992Australia Joint Conference on ArtificialIntelligence.1992[C]. Hobart, Tasmania,1992.361-367.
[2] R.C.G.onzalez，M.G.Thomason.濮群徐风家徐光佑译.句法模式识别[M].北京:清华大学出版社，1984.
[3] J. Wood. Invariant Pattern Recognition: A Review[J]. Pattern Recognition,1996,29(1):1-17.
[4] Y. Y. Tang and C. Y. Suen. New Algorithms for Fixed and Elastic GeometricTransformation Models [J]. IEEE Trans. Image Processing,1994,3(4):355-366.
[5] I. Weiss. Geometric Invariants and Object Recognition [J]. International Journal of ComputerVision,1993,10(3):207-231.
[6] F. Klein. Entwicklung der Mathematik [M]. Berlin:1926.
[7] Bhaskaracharya. Beejaganit, Ujjain,1150.
[8] D. Hilbert. über die Theorie der algebraischen Formen[J]. Mathematische Annalen,1890,36:473-534.
[9] D. Hilbert. über die vollen Invariantensysteme [J]. Mathematische Annalen,1893,42:313-373.
[10] M. Halphen. Sur les invariants differentiels des courbes gauches [J]. J. Ec. Polyt.,1880,28:1.
[11] E.J. Wilczynski. Projective Differential Geometry of Curves and Ruled Surfaces [M]. Teubner:Leipzig,1906.
[12] E.J. Wilczynski. Projective differential geometry of curved surfaces (Second Memoir)[J],Amer. Math. Soc. Trans.,1908,79.
[13] Fubini and ech. Geometria Proiettiva Differenziale [M]. Zanichetli: Bologna,1927.
[14] E.P. Lane. A Treatise on Projective Differential Geometry. University of Chicago Press,1942.
[15] H. Weyl. The Classical Groups [M]. Princeton University Press,1939.
[16] E. Cartan. La théorie des groupes continus et la géometrie, Oeuvres Complètes [M], III/2,Paris: Gauthier-Villars,1955:1727-1861.
[17] D. Mumford. Geometric Invariant Theory [M]. New York: Springer,1965.
[18] J. Nagata. Complete reducibility of rational representations of a matric group [J]. J. Math.Kyoto Univ.,1963,3:369-377.
[19] S.S. Abhyankar. AlgebraicGeometry for Scientists and Engineers [M]. Providence, RI:American Mathematical Society,1990.
[20] Barbara Zitova′, Jan Flusser. Image registration methods: a survey [J]. Image and VisionComputing,2003,(21):977–1000.
[21] J.Flusser, T.Suk. Pattern recognition by affine moment invariants[J]. Pattern Recognition,1993,(26):167-174.
[22] A.Goshtasby, G.C. Stockman, C.V.Page. A region-based approach to digital image registrationwith subpixel accuracy [J]. IEEE Transactions on Geoscience and Remote Sensing,1986,(24):390-399.
[23] A.Goshtasby, G.C. Stockman. Point pattern matching using convex hull edges[J]. IEEEtransactions on Systems, Man and Cybernetics,1985,(15):631-637.
[24] M.Holm. Towards automatic rectification of satellite images using feature based matching, inProceedings of the International Geoscience and Remote Sensing Symposium IGARSS’91[c].Finland: Espoo,1991.2439-2442.
[25] Y.C. Hsieh, D.M. Mckeown, F.P.Perlant. Performance evaluation of scene registration andstereo matching for cartographic feature extraction[J]. IEEE Transactions on Pattern Analysisand Machine Intelligence,1992,(14):214-237.
[26] M.Seter, H.Hild, D.Fritsch. Definition of ground control features for image registration usingGIS data, in Proceedings of the Symposium on Object Recognition and Scene Classificationfrom Multispectral and Multisensor Pixels[c]. Columbus: Ohio,1998.7.
[27] M. Roux. Automatic registration of SPOT images and digitized maps, in Proceedings of theIEEE International Conference on Image Processing ICIP’96[C]. Switzerland: Lausanne,1996.625-628.
[28] P.A. Brivio, A.D. Ventura, A. Rampini, R. Schettini. Automatic selection of control pointsfrom shadow structures[J]. International Journal of Remote Sensing,1992,(13):1853-1860.
[29] N.R. Pal, S.K. Pal. A review on image segmentation techniques[J]. Pattern Recognition,1993,(26):1277-1294.
[30] P. Arbeláez, M. Maire, C. Fowlkes, J. Malik. Contour Detection and Hierarchical ImageSegmentation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2011,33(5):898-916.
[31] S.Moss, E.R. Hancock. Multiple line-template matching with EM algorithm[J]. PatternRecognition Letters,1997,(18):1283-1292.
[32] W.H. Wang, Y.C. Chen. Image registration by control points pairing using the invariantproperties of line segments [J]. Pattern Recognition Letters,1997,(18):269-281.
[33] X.Dai, S,Khorram. Development of a feature-based approach to automated image registrationfor multitemporal and multisensor remotely sened imagery, in Proceedings of InternationalGeoscience and Remote Sensing Symposium IGARSS’97[C]. Singapore:1997.243-245.
[34] V.Govindu, C. Shekhar, R.Chellapa. Using geometric properties for correspondence-lessimage alignment, in Proceedings of the International Conference on Pattern RecognitionICPR’98[C]. Australia: Brisbane,1998.37-41.
[35] H.Li, B.S. Manjunath, S.K. Mitra. A contour-based approach to multisensor imageregistration[J], IEEE Transactions on Image Processing.1995,(4):320-334.
[36] H.Maitre, Y.Wu. Improving dynamic programming to solve image registration [J]. PatternRecognition,1987,(20):443-462.
[37] D.Shin, J.K. Pollard, J.P. Muller. Accurate geometric correction of ATSR images[J]. IEEETransactions on Geoscience and Remote Sensing,1997,(35):997-1006.
[38] S.Z. Li, J. Kittler, M. Petrou, Matching and recognition of road networks from acrial images,in Proceedings of the Second European Conference on Computer Vision ECCV’92[C]. Italy:St.Margherita,1992.857-861.
[39] N.Vujovic, D.Brzakovic. Establishing the correspondence between control points in pairs ofmammographic images[J]. IEEE Transacions on Image Processing,1997,(6):1388-1399.
[40] J.Canny. A computational approach to edge detection [J]. IEEE Transactions on PatternAnalysis and Machine Intelligence,1986,(8):679-698.
[41] D.Marr, E.Hildreth. Theory of edge detection[J]. Proceedings of the Royal Society of London,B,1980(207):187-217.
[42] D.Ziou, S. Tabbone. Edge detection techniques——an overview [EB/01].http://citeseer.nj.nec.com/ziou97edge.html,1997,2011-11-02.
[43] J.B.A. Maintz, P.A. van den Elsen, M.A. Viergever. Comparison of edge-based andridge-based registration of CT and MR brain images [J]. Medical Image Analysis,1996,(1):151-161.
[44] J.B.A. Maintz, P.A. van den Elsen, M.A. Viergever. Evaluation on ridge seeding operators formultimodality medical image matching [J]. IEEE Transactions on Pattern Analysis andMachine Intelligence,1996(18):353-365.
[45] M. Basu. Gaussian-Based Edge Detection Methods—A Survey [J]. IEEE Transactions onSystems, Man, and Cybernetics—Part C: Applications and Reviews,2002,32(3):252-260.
[46] M. Tello Alonso, C. Lopez-Martinez, J.J. Mallorqui, P. Salembier. Edge EnhancementAlgorithm Based on the Wavelet Transform for Automatic Edge Detection in SAR Images [J].IEEE Transactions on Geoscience and Remote Sensing.2011,49(1):222–235.
[47] G.Stockman, S.Kopstein, S.Benett. Matching images to models for registration and objectdetection via clustering [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1982,(4):229-241.
[48] A.S. Vasileisky, B. Zhukov, M. Berger. Automated image co-registration based on linearfeature recognition, in Proceedings of the Second Conference Fusion of Earth Data[C]. France:Sophia Antipolis,1998.59-66.
[49] S.Growe, R.Tonjes. A knowledge based approach to automatic image registration, inProceedings of the IEEE International Conference on Image Processing ICIP’97[C].California: Santa Barbara,1997.228-231.
[50] J. Ton, A.K. Jain. Registering landsat images by point matching [J]. IEEE Transactions onGeoscience and Remote Sensing,1989,(27):642-651.
[51] M.Ehlers. Region-based matching for image registration in remote sensing databases, inProceedings of the International Geoscience and Remote Sensing Symposium IGARSS’91[C].Finland: Espoo,1991.2231-2234.
[52] B.S. Manjunath, C.Shekhar, R.Chellapa. A new approach to image feature detection withapplications[J]. Pattern Recognition,1996,(29):627-640.
[53] Q.Zheng, R.Chellapa. A computational vision approach to image registration [J]. IEEETransactions on Image Processing,1993,(2):311-325.
[54] W.S.I. Ali, F.S.Cohen. Registering coronal histological2-D sections of a rat brain with coronalsections of a3-D brain atlas using geometric curve invariants and B-spline representation [J].IEEE Transactions on Medical Imaging,1998,(17):957-966.
[55] S.Banerjee, D.P. Mukherjee, D.D. Majumdar. Point landmarks for registration of CT and NMRimages [J]. Pattern Recognition Letters,1995,(16):1033-1042.
[56] L.M.G. Fonseca, M.H.M. Costa. Automatic registration of satellite images, in Proceedings ofthe Brazilian Symposium on Computer Graphic and Image Processing[C]. Brazil:1997.219-226.
[57] J.W. Hsieh, H.Y.M. Liao, K.C. Fan, M.T.ko. A fast algorithm for image registration withoutpredetermining correspondence, in Proceedings of the International Conference on PatternRecognition ICPR’96[C]. Austria: Vienna,1996.765-769.
[58] B.Likar, F.Pernus. Automatic extraction of corresponding points for the registration of medicalimages [J]. Medical Physics,1999(26):1678-1686.
[59] D.Bhattacharya, S.Sinha. Invariance of stereo images via theory of complex moments [J].Pattern Recognition,1997,(30):1373-1386.
[60] C.Y. Wang, H. Sun, S.Yadas, A. Rosenfeld. Some experiments in relaxation image matchingusing corner features [J]. Pattern Recognition,1983,(16):167-182.
[61] K.Rohr. Localization properties of direct corner detectors [J]. Journal of MathematicalImaging and Vision,1994,(4):139-150.
[62] K.Rohr. Landmark-Based Image Analysis: Using Geometric and Intensity Models,Computational Imaging and Vision Series, vil.21[M]. Dordrecht: Kluwer Academic Publishers,2001.
[63] S.M. Smith, SUSAN. Low level image processing[EB/01].http://www.fmrib.ox.ac.uk/-spacesteve/susan,2012-01-09.
[64] Z.Zheng, H. Wang, E.K. Teoh. Analysis of gray level corner detection [J]. Pattern RecognitionLetters,1999,(20):149-162.
[65] S.M. Smith, J.M. Brady, SUSAN. A new approach to low level image processing [J].International Journal of Computer Vision,1997,(23):45-78.
[66] D. G. Lowe. Object recognition from local scale-invariant features, in the Proceeding of IEEEInt. Conf. Comput. Vision [C]. IEEE,1999,(2):1150-1157.
[67] Grassmann, H. Der Ort der Hamilton’schen Quaternionen in der Ausdehnungslehre [J].Math.Ann.,1877,(12):375.
[68] Clifford, W.K. Applications of Grassmann’s extensive algebra [J]. Am.J.Math.,1878,(1):350-358.
[69] E. Bayro-Corrochano, and J. Lasenby. Object modelling and motion analysis using Cliffordalgebra, in Proceedings of Europe-China Workshop on Geometric Modeling and Invariants forComputer Vision [C]. China, Xi’an:1995.
[70] B. Rosenhahn, and G. Sommer. Adaptive pose estimation for different corresponding entities[J]. Lecture Notes in Computer Science,2002, ISSU2449:265-273.
[71] J. Lasenby, E. Bayro-Corrochano, A.N. Lasenby, G. Sommer. A New Methodology forComputing Invariants in Computer Vision, in Proceedings of ICPR’96[C]. IEEE,1996.1015-4651
[72] B. Chazelle. On the Convex Layers of a Planar Set [J]. IEEE Transactions on InformationTheory,1985, IT-31(4):509-517.
[73] H. Khazaei, A. Mohades. Fingerprint matching and classification using an onion layeralgorithm of computational geometry [J]. International Journal of Mathematics and Computersin Simulation,2007,1(1):26-32.
[74] W. Yang, Y. Wang, and G. Mori. Recognizing human actions from still images with latentposes [C]. In the Proceeding of Computer Vision and Pattern Recognition (CVPR), CA: SanFrancisco,2010.2030–2037.
[75] M. Ferraro and T. M. Caeili. Relationship between integral transform invariances and Liegroup theory [J]. J. Optical Soc, America A,1988,(5):738-742.
[76] R.N.Bracewell. The Fourier Transform and Its Applications. Electrical and ElectronicEngineering Series [M]. McGraw-Hill Book Company,1978.
[77] E.Brigham. The Fast Fourier Transform and Its Applications [M]. Prentice-Hall,1988.
[78] M.Clausen and U.Baum. Fast Fourier Transforms [M]. Wissenschaftsverlag: Mannheim,1993.
[79] H. Wechsler. Invariance in pattern recognition [J]. Advances in Electronics and ElectronPhysics,1987,(69):262-322.
[80] A. Grace and M. Spann, A comparison between Fourier-Mellin descriptors and moment basedfeatures for invariant object recognition using neural networks [J]. Pattern Recognition Letter,1991,(12):635-643.
[81] D. Mendlovic, H.M. Ozaktas. Fractional Fourier transforms and their optical implementation:part I [J]. Journal of the Optical Society of America A: Optics and Image Science, and Vision,1993,10(9):1875–1881.
[82] H.M. Ozaktas, D. Mendlovic. Fractional Fourier transforms and their optical implementation:part II [J]. Journal of the Optical Society of America A: Optics and Image Science, and Vision,1993,10(12):2522–2531.
[83] L.B. Almeida, The fractional Fourier transform and time–frequency representations[J]. IEEETransactions on Signal Processing,1994,42(11):3084–3091.
[84] A.I. Zayed. On the relationship between the Fourier and fractional Fourier transforms[J]. IEEESignal Processing Letters,196,3(12):310–311.
[85] G. Cariolaro, T. Erseghe, P. Kraniauskas, N. Laurenti. A unified framework for the fractionalFourier transform, IEEE Transactions on Signal Processing,1998,46(12):3206–3219.
[86] H.M. Ozaktas, Z. Zalevsky, M.A. Kutay, The Fractional Fourier Transform withApplications in Optics and Signal Processing [M], John Wiley, Chichester, New York, USA,2001.
[87] E. Sejdic′, Igor Djurovic′, LJubisa Stankovic′. Fractional Fourier transform as a signalprocessing tool: An overview of recent developments [J]. Signal Processing,2011,91:1351–1369.
[88] W. Pan, K. Qin, and Y. Chen. An Adaptable-Multilayer Fractional Fourier TransformApproach for Image Registration [J].Ieee Transactions on Pattern Analysis and MachineIntelligence,2009.31(3):400-413.
[89] H. Lee, H. Maeng, and Y. Bae. Fake Finger Detection Using the Fractional Fourier Transform[J]. Biometric ID Management and Multimodal Communication, Lecture Notes in ComputerScience,2009,5707:318-324.
[90] Y. Li. Reforming the theory of invariant moments for pattern recognition [J]. PatternRecognition,1992,(25):723-730.
[91] Y. Sheng and H. H. Arsenault. Experiments on pattern recognition using invariantFourier-Mellin descriptors [J]. J. Optical Soc. America A (Optics and Image Sci.),1986,(3):771-776.
[92] R. Wu and H. Stark. Three dimensional object recognition from multiple views [J]. J. OpticalSoc. America A (Optics and Image Sci.),1986,(3):1543-1557.
[93] T.M.Caelli, Zhi-Qiang Liu. On the minimum number of templates required for shift, rotation,and size invariant pattern recognition [J]. Pattern Recognition,1988,(21):205-216.
[94] D. Casasent and D. Psaltis, Position, rotation and scale-invariant optical correlation [J]. Appl.Optics,1976,15:1795-1799.
[95] D. Casasent and D. Psaltis, Hybrid processor to compute invariant moments for patternrecognition [J]. Optics Letter,1980,5:395-397.
[96] Nanrun Zhou, Yixian Wang, Lihua Gong. Novel optical image encryption scheme based onfractional Mellin transform [J].Optics Communications,2011,284:3234–3242.
[97] D. Pintsov. Invariant pattern recognition, symmetry and Radon transforms [J]. J. Optical Soc.America A,1989,6(10):1544-1554.
[98] A. Delopoulos, A. Tirakis and S. Kollias. Invariant image classification usingtriple-correlation-based neural networks [J]. IEEE Trans. Neural Networks,1994,(5):392-408.
[99] P.Viola, W.M. Wells. Alignment by maximization of mutual information [J]. InternationalJournal of Computer Vision,1997,(24):137-154.
[100] G.P. Penney, J.Weese, J.A. Little, P.Desmedt, D.L.G. Hill, D. J. Hawkes. A comparison ofsimilarity measures for use in2D-3D medical image registration [J]. IEEE Transactions onMedical Imaging,1998,(17):586-595.
[101] J.P.W. Pluim, J.B.A. Maintz, J.A. Little, M.A. Viergever. Mutual-Information-BasedRegistration of Medical Images: A Survey [J]. IEEE Transactions on Medical Imaging,2003,(8):986-1004.
[102] H. Peng, F. Long, C. Ding. Feature selection based on mutual information criteria ofmax-dependency, max-relevance, and min-redundancy [J]. IEEE Transactions on PatternAnalysis and Machine Intelligence,2005,(8):1226-1238.
[103] H. Liu, J. Sun, L. Liu, and H. Zhang. Feature selection with dynamic mutual information[J].Pattern Recognition,2009,42:1330-1339.
[104] Q. Hu, W. Pan, S. An, P. Ma and J. Wei. An efficient gene selection technique for cancerrecognition based on neighborhood mutual information [J]. International Journal of MachineLearning and Cybernetics,2010,1(1-4):63-74.
[105] A. Nabatchian, E.Abdel-Raheem, M. Ahmadi. Illumination invariant feature extraction andmutual-information-based local matching for face recognition under illumination variation andocclusion [J]. Pattern Recognition,2011,44:2576–2587
[106] Flusser, J., Suk, T. and Zitová, B. Moments and Moment Invariants in Pattern Recognition[M].Chichester, UK: John Wiley&Sons, Ltd,2009
[107] Dong Xu, and Hua Li. Geometric moment invariants [J].Pattern Recognition,2008,41:240–249.
[108] R. P. Srivastava. Transformation and distortion tolerant recognition of numerals using neuralnetworks, in Proceedings of1991ACM Computer Science Conference [C]. New York: ACM,1991.402-408.
[109] M. K. Hu. Visual pattern recognition by moment invariants [J]. IEEE Trans. Inform. Theory g,1962:179-187.
[110] Y. Sheng and J. Duvernoy. Circular Fourier radial Mellin transform descriptors for patternrecognition [J]. J. Optical Soc. America A (Optics and Image Sci.,1986,(3):885-888.
[111] S. Perantonis and P. Lisboa. Translation, rotation and scale invariant pattern recognition byhigh-order neural networks and moment classifiers [J]. IEEE Trans. Neural Networks,1992,(3):241-251.
[112] B. Chen, H. Shu, G. Chen, J. Ge, and L. Luo. Color Face Recognition Based on QuaternionZernike Moment Invariants and Quaternion BP Neural Network [J].Energy Procedia,2011,13:551-558.
[113] A. Khotanzad and Y. H. Hong. Invariant image recognition by Zernike moments [J]. IEEETrans. Pattern Analysis Mach. Intell.,1990,(12):489-497.
[114] K.M. Hosny. Efficient computation of Legendre moments for gray level images [J].International Journal of Image Graph,2007,7(4):735–747.
[115] C.W. Chong, R. Paramesran, and R. Mukundan. Translation and scale invariants of Legendremoments. Pattern Recognition,2004,37:119–129.
[116] M.R. Spiegel. Schaum’s Handbook of Formulas and Tables[M]. New York: MacGraw Hill,1968.
[117] S.X. Liao, M. Pawlak. On image analysis by moments [J]. IEEE Trans. Pattern Anal. MachineIntell.1996,18(3),254–266.
[118] K. M. Hosny. Refined translation and scale Legendre moment invariants [J].PatternRecognition Letters,2010,31:533–538.
[119] A. Shvedov, A. Schmidt and V. Yakubovich. Invariant systems of features in patternrecognition [J]. Automation Remote Control,1979,(40):131-142.
[120]J. Flusser and T. Suk. Pattern recognition by affine moment invariants [J]. Pattern Recognition,1993,(26):167-174.
[121] P. Simard, B. Victorri, Y. Le Cun and J. Denker. Tangent prop--a formalism for specifyingselected invariances in an adaptive network, in Proceedings of NIPS-4[C].1991.895-903.
[122] D. E. Rumelhart, G. E. Hinton and R. J. Williams. Learning internal representations by errorpropagation [J]. Parallel Distributed Processing: Explorations in the Microstructures ofCognition,1986,(1):318-362..
[123] Y. Le Cun. Generalization and network design strategies.Connectionism in perspective [M].Amsterdam: Elsevier Science,1989.143-155.
[124] T. Kanaoka, R. Cheilappa, M. Yoshitaka and S. Tomita. A higher-order neural network fordistortion invariant pattern recognition [J]. Pattern Recognition Letter,1992,(13):837-841.
[125] R. Duren, B. Peikari. A comparison of second-order neural networks to transform-basedmethod for translation-and orientation-invariant object recognition, in Proceedings of the1991IEEE Workshop on Neural Networks for Signal Processing [C].1991.236-245.
[126] R. Duren and B. Peikari. A new neural network architecture for rotationally invariant objectrecognition, in Proceedings of the34th Midwest Symposium on Circuits and Systems [C].IEEE,1992. Vol.1,320-323.
[127] L. Spirkovska and M. Reid. Robust position, scale and rotation invariant object recognitionusing higher order neural networks [J]. Pattern Recognition,1992,(25):975-985.
[128] C.L. Giles and T. Maxwell. Learning, invariance, and generalization in high-order neuralnetworks [J]. Appl. Optics,1987,(26):4972--4978.
[129] M. Fukumi, S. Omatu, F. Takeda and T. Kosaka. Rotation-invariant neural pattern recognitionsystem with application to coin recognition [J]. IEEE Trans. Neural Networks,1992,(3):272-279.
[130] K. Lang and G. Hinton. The development of TDNN architecture for speech recognition,Technical Report CMU-CS-88-152[R]. Carnegie-Mellon University,1988.
[131] J. Shawe-Taylor. Building symmetries into feedforward networks, in Proceedings of FirstIEEE Conference on Artificial Neural Networks [C]. IEEE,1989.158-162.
[132] Z.L. Gaing. Wavelet-based neural network for power disturbance recognition andclassification [J]. IEEE Transactions on Power Delivery,2004,19(4):1560-1568.
[133] E. Stergiopoulou, and N. Papamarkos. Hand gesture recognition using a neural network shapefitting technique [J]. Engineering Applications of Artificial Intelligence,2009,22(8):1141–1158.
[134] M.Baqar, S. Azhar, Z. Iqbal, I. Shakeel, L. Ahmed, M.Moinuddin. Efficient iris recognitionsystem based on dual boundary detection using robust variable learning rate Multilayer FeedForward neural network [M]. In proceedings of7th International Conference on InformationAssurance and Security (IAS), Melaka:2011:326–330.
[135] L. Xu, M. Q.H. Meng, K. Wang, W. Lu, N. Li. Pulse images recognition using fuzzy neuralnetwork [J]. Expert Systems with Applications,2009,36(2):3805–3811.
[136] S. Wang, and H. Deng. Face Recognition Using Principal Component Analysis-Fuzzy LinearDiscriminant Analysis and Dynamic Fuzzy Neural Network [J]. Future Wireless Networks andInformation Systems,2012,143:577-586.
[137] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by Simulated Annealing [J].Science,1983, New Series,220(4598):671-680.
[138] F. P. Preparata, and M. lan Shamos. Computational geometry: An introduction [M]. New York,:Springer-Verlag,1985.
[139] M. Tajine, and D. Elizondo. New methods for testing linear separability [J]. Neurocomputing,2002,(47):161-188
[140] R. Minhas, and J. Wu. Invariant feature set in convex hull for fast image registration, inProceedings of IEEE Int. Conf. Syst. Man Cybern [C].2007.1557-1561.
[141] J.S. Fan, S.W. Xiong, and J.Z. Wang. The Multi-Objective Differential Evolution AlgorithmBased on Quick Convex Hull Algorithms, in Proceedings of5th International Conference onNatural Computation.2009.
[142] P. Szczypinski, and A. Klepaczko. Automated Recognition of Abnormal Structures in WCEImages Based on Texture Most Discriminative Descriptors [J]. Advances in Intelligent andSoft Computing,2010,(84):263-270
[143] X. Zhou, W. Jiang, Y. Tian, and Y. Shi. Kernel subclass convex hull sample selection methodfor SVM on face recognition [J]. Neurocomputing,2010,(73):2234-2246.
[144] F. Murtagh. A new approach to point pattern matching [J]. Publ. Astron. Soc. Pac.,1992,(104):301-307.
[145] R.V. Chadnov, and A.V. Skvortsov. Convex hull algorithms review, in Proceedings of the8thRussian-Korean International Symposium on Science and Technology [C].2004,(2):112-115.
[146] R.L. Graham. An efficient algorithm for determining the convex hull of a finite planar set [J].Inf. Process. Letter,1972,(1):132-133.
[147] A.M. Andrew. Another efficient algorithm for convex hulls in two dimensions [J]. Inf. Process.Letter,1979,(9):216-219.
[148] C. B. Barber, D.P. Dobkin, and H. Huhdanpaa. The quickhull algorithm for convex hulls [J].ACM Trans. Math. Softw,1996,(22):469-483.
[149] A. Datta, and S.K. Parui: A dynamic neural net to compute convex hull [J]. Neurocomputing,1996,(10):375-384..
[150] S. Naher, and D. Schmitt. A Framework for Multi-Core Implementations of Divide andConquer Algorithms and its Application to the Convex Hull Problem, in Proceedings of20thAnnual Canadian Conference on Computational Geometry.2008.
[151] H.K. Ahn, and Y. Okamoto. Adaptive Algorithms for Planar Convex Hull Problems [J]. IEICETrans. Inf. System,2011,(E94-D):182-189.
[152] F. Cantin, A. Legay, and P. Wolper. Computing Convex Hulls by Automata Iteration [J].Implementation and Applications of Automata,2008,(5148):112-121
[153] Y. J. Kim, J. Lee, M.S. Kim, and G. Elber. Efficient convex hull computation for planarfreeform curves [J]. Comput. Graph,2011,(35):698-705.
[154] M. Sharif, S.Z.Z. Naqvi, M. Raza, and W. Haider. A new Approach to Compute Convex Hull[J]. Innovative Systems Design and Engineering,2011,(2):187-193.
[155] A. Allport. Visual attention, in Foundations of cognitive science [M]. Cambridge: MITPress/Bradford Books,1989.
[156]R.A. Jarvis. On the identification of the convex hull of a finite set of points in the plane [J]. Inf.Process. Letter,1973,(2):18-21.
[157] J.B. Antoine Maintz, and M.A. Viergever. A survey of medical image registration. Med [J].Image Anal.,1998,(2):1-36.
[158] J. Hong, and X. Tan. A new approach to point pattern matching, in Proceedings of9th Int.Conf. Pattern Recognition [C].1988.
[159] T. Wakahara, and K. Odaka. Adaptive normalization of handwritten characters usingglobal/local affine transformation [J]. IEEE Trans. Pattern Anal. Mach. Intell.,1998,(20):1332—1341.
[160] Z. Yang, and F. S. Cohen. Image Registration and Object Recognition Using Affine Invariantsand Convex Hulls [J]. IEEE Trans. Image Process.,1999,(8):934-946.
[161] I. E. Rube, M. Ahmed, and M. Kamel. Wavelet Approximation-Based Affine Invariant ShapeRepresentation Functions [J]. IEEE Trans. Pattern Anal. Mach. Intell.,2006,(28):323-327.
[162] Y. Mei, and D. Androutsos. Affine invariant shape descriptors: the ICA-Fourier descriptor andthe PCA-Fourier descriptor, in Proceedings of19th Int. Conf. Pattern Recognition.2008.
[163] R. Fisher, S. Perkins, A. Walker, and E. Wolfart. Affine Transformation.http://homepages.inf.ed.ac.uk/rbf/HIPR2/affine.htm.2011,2011-06-06
[164] Z.W. Zhang, and X.C. WU. Algorithm for Convex Hull of Planar Massive Scattered Point Set[J]. Computer Engineering,2009,(35):43-45,48.
[165] L.G. Brown. A survey of image registration techniques [J]. ACM Comput. Surveys,1992,(24):325-376.
[166] F.H. Cheng, W.H. Hsu, and M.C. Kuo. Recognition of handprinted Chinese characters viastroke relaxation. Pattern Recognition,1993,(26):579-593.
[167]A. ROSENFELD. Image analysis and computer vision:1998[J]. Comput. Vis. Image Underst.,1998,(74):36-95.
[168] G.S.Cox, and G.DeJager. A survey of point pattern matching techniques and a new approach topoint pattern recognition, in Proceedings of South African Symposium on Communicationsand Signal Processing [C].1993.
[169] B.Li, Q.Meng, and H.Holstein. Point Pattern Matching and Applications-A Review, inProceedings of Conf. Proc. IEEE Int. Conf. Syst. Man Cybern [C].2003,(1):729-736.
[170]F. Preparata, and M. Shamos. Computational geometry: An introduction [M]. Addison-Wesley,1985.
[171] B. Yuan, and C. L. Tan. Convex hull based skew estimation [J]. Pattern Recognition,2007,(40):456-475.
[172] F. Murtagh. A New Approach to Point Pattern Matching[J]. Astronomical Society of thePacific,1992,(104):301-307.
[173] M. M. McQUEEN, and G. T. Toussaint. On the ultimate convex hull algorithm in practice [J].Pattern Recognition Letters,1985,(3):29-34.
[174] T. S. Caetano, T. Caelli, D. Schuurmans, and D. A. C. Barone. Graphical Models and PointPattern Matching [J]. IEEE Trans. Pattern Anal. Mach. Intell.,2006,(28):1646-1663.
[175] L. Shapiro, and J. Brady. Feature-Based Correspondence—An Eigenvector Approach [J].Image Vis. Comput.,1992,(10):283-288.
[176] H. Chui, and A. Rangarajan. A New Algorithm for Non-Rigid Point Matching, inProceedings of Conf. Computer Vision and Pattern Recognition,2000,(2):44-51.
[177] Carnegie Mellon University. CMU VASC Image Database.http://vasc.ri.cmu.edu//idb/html/motion/house/index.html.2010-12-11.
[178] D. G. Lowe. Distinctive Image Features from Scale-Invariant Keypoints [J]. InternationalJournal of Computer Vision,2004,60(2):91-110.
[179] R. Z. Liu and B. Fang and Y. Y. Tang and J. Wen and J. Qian. A fast convex hull algorithmwith maximum inscribed circle affine transformation [J]. Neurocomputing,2012,77:212—221.
[180] Y. Avrithis and Y. Xirouhakis and S. Kollias. Affine-invariant curve normalization for objectshape representation, classification, and retrieval [J]. Machine Vision and Applications,2001,13(2):80—94.
[181] J. P. Marques.模式识别-原理、方法及应用[M].吴逸飞,译.北京:清华大学出版社,2002.
[182]夏国恩.客户流失预测的现状与发展研究[J].计算机应用研究，2010，27(2):413-416.
[183]王伟达,刘文剑.一种基于混合决策树的调度知识获取算法[J].计算机应用研究,2007,24(12):54-59.
[184] Mitchell, T.M.机器学习[M].曾华军等,译.北京:机械工业出版社,2003.
[185] Quinlan J R. Induction of decision trees [J]. Machine Learning,1986,(1):81-106.
[186]洪家荣,丁明峰,李星原,王丽薇.一种新的决策树归纳学习算法[J].计算机学报,1995,18(6):470～474.
[187]刘小虎,李生.决策树的优化算法[J].软件学报,1998,9(10):797～800.
[188] Oliver J, Dowe A D L, Wallace C S. Inferring decision graphs using the minimum messagelength principle, in: Proceedings of the1992Australia Joint Conference on ArtificialIntelligence.1992[C]. Hobart, Tasmania,1992.361-367.