基于谱图理论的点模式匹配算法研究
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摘要
点模式匹配是计算机视觉和模式识别中基础而重要的问题,也是目前各领域关注的一个热点。它是一个普遍存在的问题,不仅限于计算机视觉领域,在航位与姿态估计、目标识别、遥感图像配准、医学图像配准、计算生物和化学等方面都有广泛的应用。而谱图理论应用于该课题的研究具有计算效率高、效果较好的优势。
本文通过分析Scott和Longuet-Higgins, Shapiro和Brady两种点模式匹配谱图分析法的不足,提出了一种新的点模式匹配的谱图分析方法。方法的核心部分是构造了一种新的邻近矩阵,这种方法在图像较大幅度仿射变换下和点抖动的情况下得到的结果要好于前面两种方法,在算法的复杂度上具有谱图法的优点,效率比近几年提出的一些需要迭代的方法高。新方法经过了较为全面的检验,包括在合成数据和真实数据上的测试,都取得了较好的效果。
本文在总结以往文献中谱图理论匹配算法的基础上,做出了一些改进和提炼,提出了一个算法框架,算法分为两个步骤,第一步是选择距离函数的组合,框架本身提供一组改进的距离函数,也可以根据应用需要另外加入函数。最终得到的距离函数为所选函数的乘积,这样的乘积可以突出适合特定匹配需求的距离函数的作用。第二步是构建距离函数的高斯加权邻近矩阵或者Laplacian矩阵,作SVD分解,得到匹配关系。这个框架的优点可根据具体应用的需要生成多种算法,具有较好的灵活性和适应性,在实现上,每一步产生的代码可以复用,易于编程实现。
Point pattern matching is an essential part of many computer version or pattern recognition tasks; it has very wide range of applications, and is currently the hotpot of various studies. Now, Point pattern matching is widely used in stereovision, autonomous navigation, object recognition and tracking, medical imaging analysis, remote imaging registration, drug design and DNA sequences prediction, etc. Spectral graph theory is applied to this problem have some advantages, such as high efficiency and good effect.
This work analyzed the drawback of Scott and Longuet-Higgins method and Shapiro and Brady method, proposed a novel approach of spectral graph method. The most important part of this new method is constructing a new-type proximity matrix. This method does pretty well in the condition of large scale transformation and point-jitter of images, and has the advantages of graph spectral method: algorithmic complexity is better than iterative method proposed in last two decades. The new method proposed in this work were tested extensively in heterogeneous case, include synthetic data and real image taken from benchmark of computer version.
This work summarizes the spectral graph methods about the matching algorithm in previous papers, and made some improvements and refinement, proposed an algorithm framework. The algorithm framework is divided into two steps, the first step is to choose a combination of distance function, the framework itself provides a set of improved distance function, and additional functions can also be added depending on the application requirement. The resulting distance function is the product of the selected function, this product give prominence to the distance functions that are appropriate for the particular application. The second step is to build the Gaussian weighted proximity matrix or Laplacian matrix for singular value decomposition. The advantages of this framework is algorithms can be generated according to the specific needs of applications, the framework have good flexibility in implementation, in each step, the generated code can be re-used, reduce the programming time.
本文通过分析Scott和Longuet-Higgins, Shapiro和Brady两种点模式匹配谱图分析法的不足,提出了一种新的点模式匹配的谱图分析方法。方法的核心部分是构造了一种新的邻近矩阵,这种方法在图像较大幅度仿射变换下和点抖动的情况下得到的结果要好于前面两种方法,在算法的复杂度上具有谱图法的优点,效率比近几年提出的一些需要迭代的方法高。新方法经过了较为全面的检验,包括在合成数据和真实数据上的测试,都取得了较好的效果。
本文在总结以往文献中谱图理论匹配算法的基础上,做出了一些改进和提炼,提出了一个算法框架,算法分为两个步骤,第一步是选择距离函数的组合,框架本身提供一组改进的距离函数,也可以根据应用需要另外加入函数。最终得到的距离函数为所选函数的乘积,这样的乘积可以突出适合特定匹配需求的距离函数的作用。第二步是构建距离函数的高斯加权邻近矩阵或者Laplacian矩阵,作SVD分解,得到匹配关系。这个框架的优点可根据具体应用的需要生成多种算法,具有较好的灵活性和适应性,在实现上,每一步产生的代码可以复用,易于编程实现。
Point pattern matching is an essential part of many computer version or pattern recognition tasks; it has very wide range of applications, and is currently the hotpot of various studies. Now, Point pattern matching is widely used in stereovision, autonomous navigation, object recognition and tracking, medical imaging analysis, remote imaging registration, drug design and DNA sequences prediction, etc. Spectral graph theory is applied to this problem have some advantages, such as high efficiency and good effect.
This work analyzed the drawback of Scott and Longuet-Higgins method and Shapiro and Brady method, proposed a novel approach of spectral graph method. The most important part of this new method is constructing a new-type proximity matrix. This method does pretty well in the condition of large scale transformation and point-jitter of images, and has the advantages of graph spectral method: algorithmic complexity is better than iterative method proposed in last two decades. The new method proposed in this work were tested extensively in heterogeneous case, include synthetic data and real image taken from benchmark of computer version.
This work summarizes the spectral graph methods about the matching algorithm in previous papers, and made some improvements and refinement, proposed an algorithm framework. The algorithm framework is divided into two steps, the first step is to choose a combination of distance function, the framework itself provides a set of improved distance function, and additional functions can also be added depending on the application requirement. The resulting distance function is the product of the selected function, this product give prominence to the distance functions that are appropriate for the particular application. The second step is to build the Gaussian weighted proximity matrix or Laplacian matrix for singular value decomposition. The advantages of this framework is algorithms can be generated according to the specific needs of applications, the framework have good flexibility in implementation, in each step, the generated code can be re-used, reduce the programming time.
引文
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[2]M. K. Leungo A. N. Choudhary, J. H. Patel, et al. Point matching in a time sequence of stereo image pairs and its parallel implementation on a multiprocessor. Proceedings Workshop on Visual Motion.1989.321-328.
[3]L. Moisan, B. Stival. Automatic detection of rigid point matches.2002 Workshop on Motion and Video Computing.2002,235-240.
[4]A. I. Mourikis, N. Trawnyo S. I. Roumeliotis, et al. Vision Aided Inertial Navigation for Precise Planetary Landing:Analysis and Experiments. Robotics Systems and Science Conference Proceedings.2007.357-378.
[5]N. Trawny, A. I. Mourikis, S. I. Roumeliotis, et al. Vision. Aided Inertial Navigation for Pin-Point Landing using Observations of Mapped Landmarks. Journal of Field Robotics, 2007,24(5):357-364.
[6]W. Dimes. The Mars Exploration Rovers Descent Image motion Estimation System. IEEE Intelligent System,2004.19(3):13-21.
[7]A. Johnson, R. Willson, Y. Cheng, et al. Design Through Operation of an Image—Based Velocity Estimation System for Mars Landing. International Journal of Computer Vision. 2007,74(3):319-341.
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[10]N. Mingtian. Point Pattern Matching and Its Application in GCXGC:[Ph. D. Dissertation]. The University of Nebraska-Lincoln.2004.
[11]R. Nussinov. H. J. Wolfson. Efficient detection of three. dimensional structural motifs in biological macromolecules by computer vision techniques. Proceedings of the National Academy of Sciences of the United States of America,1991.88(23):10495-10499.
[12]H. Chui, W. Lawrence, S. Robert, et al. A Unified Non. rigid Feature Registration Method For Brain Mapping. Medical Image Analysis.2003(7):113-130.
[13]B. Zitova,J. Flusser. Image registration methods:a survey. Image and Vision Computing, 2003,21(11):977-1000.
[14]H. Guo, A. Rangarajan, S. Joshi, et al. Non-rigid registration of shapes via diffeomorphic point matching. IEEE International Symposium on Biomedical Imaging.2004,924-927.
[15]J. Xu. W. Hong,Y. Wu. An efficient rotation. invariance remote image matching algorithm based on feature points matching.2005 IEEE International Geosciences and Remote Sensing Symposium.2005.647-649.
[16]B. Domrongwatthanayothin, A. Roeksabutr, A. Kanjanavapastit, et al. An efficient point matching algorithm for stereo aerial images.2005 IEEE International Geosciences and Remote Sensing Symposium 2005.1530-1533.
[17]R. Yu, X. Deng, K. Qing. An efficient point matching algorithm of remote sensing image based on dynamic template.2005 IEEE International Geosciences and Remote Sensing Symposium.2005.3864-3866.
[18]邓小炼,王长耀,,亢庆等。一种基于角点提取的遥感影像地面控制点自适应匹配算法宇航学报,2006,27(1)：45.50-88.
[19]S. Chikkerur. N. Ratha. Impact of singular point detection on fingerprint matching performance. Fourth IEEE Workshop on Automatic Identification Advanced Technologies. 2005.207-212.
[20]Y. Pengyeng. Particle swarm optimization for point pattern matching. Journal of Visual Communication and Image Representation,2006,17(11):143-162.
[21]M. C. K. Yang. J. S. Lee. Object Identification from multiple images based on point matching under a general transformation. IEEE Transactions on Pattern Analysis and Machine Intelligence,1994,16(7):751-756.
[22]S. Umeyama. Parameterized point pattern-matching and its application to recognition of object families. IEEE Transactions on Pattern Analysis and Machine Intelligence.1993. 15(2):136-144.
[23]P. J. Besl. N. D. Mckay. A method for registration of 3D shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence,1992,14(2):239-256.
[24]S. Sclaroff,A. P. Pentland. Modal matching for correspondence and recognition. IEEE Transactions on Pattern Analysis and machine Intelligence 1995,17(6):545.561.
[25]S. Islam, L. Zhu. Matching interest points of an object. IEEE International Conference on Image Processing.2005.373-376.
[26]Scott, GL., Longuet-Higgins, H.C. An algorithm for associating the features of two images. Proc. Royal Society London 1991, B-244,21-26.
[27]L. S. Shapiro. J. M. Brady. Feature-based correspondence:An eigenvector approach. Image and Vision Computing,1992,10(5):283-288.
[28]M. Carcassoni, E. R. Hancock. Spectral correspondence for point pattern matching, Pattern Recognition.2003。36(1):193-204.
[29]张立华,徐文立。基于p2不变量的透视变换下的点模式匹配方法。中国图象图形学报：A辑,2000(11)：948-952.
[30]C. Gope. N. Kehtarnavaz. Affine invariant comparison of point-sets using convex hulls and hausdorff distances. Pattern Recognition,2007,40(1):309-320.
[31]张立华,徐文立。基于凸壳的透视变换下的点模式匹配方法。自动化学报,2002,28(2)：306-309.
[32]K. Voss, H. Suesse. Affine point pattern matching. Pattern Recognition:23rd DAGM Symposium Proceedings.2001. Munich, Germany.155-162.
[33]孙焘,王秀坤,邵刚等。二维点模式图像的仿射变换配准。计算机辅助设计与图形学学报,2005,17(7)：1497.1 503.
[34]H. Ogawa. Labeled point pattern matching by fuzzy relaxation. Pattern Recognition,1984,17(5)：569-573.
[35]N. Ahuja. Dot Pattern Processing Using Voronoi Neighborhood. IEEE Trans on Pattern Analysis and Machine Intelligence,1982,4(3):336-342.
[36]孙焘,王秀坤,邵刚等.基于Voronoi图表和进化策略的图像特征点配准方法.大连理工大学学报,2005,45(3)：443448.
[37]A. D. J. Cross. E. R. Hancock. Graph matching with a dual-step EM algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence.1998,20(11):1236-1253.
[38]B. Luo, E. R. Hancock. Structural graph matching using the EM algorithm and singular value decomposition. IEEE Transactions on Pattern Analysis and Machine Intelligence.2001.23(10)：1120-1136.
[39]朱庆,吴波,赵杰.基于自适应三角形约束的可靠影像匹配方法.计算机学报,2005,28(10)：1734-1739.
[40]N. Ansari, M. H. Chen, E. S. H. Hou. Point pattern matching by a genetic algorithm.16th Annual Conference of IEEE industrial Electronics Society.1990.1233-1238.
[41]陈海峰,纪圣谋.利用改进遗传算法实现图像特征点的匹配.南京大学学报：自然科学版,2000,36(2)：171-176.
[42]张立华,徐文立.基于遗传算法的点模式匹配方法.电子学报,2000,28(10)：36-40.
[43]L. H. Zhang, W. L. Xu, C. Chang. Genetic algorithm for affine point pattern matching. Patten Recognition Letters,2003,24(1-3):9-19.
[44]V. V. Vindo. S. Ghose. Point matching using asymmetric neural networks. Pattern Recognition。1993,26(8):1207-1214.
[45]S. Rippa. An algorithm for selecting a good value for the parameter C in radial basis function interpolation. Advances in Computational Mathematics,1999,11(2):193-210.
[46]N. Arad, N. Dyn, D. Reisfeld, et al. Image warping by radial basis functions:applications to facial expressions.1994, Academic Press, Inc.161-172.
[47]NieXuan, ZhaoRongchun, ZhangCheng, et al. An Improved Radial Basis Function Based Method For Image Warping. Journal of Electronics (China),2005,22(4):422-426.
[48]F. L. Bookstein. Principal Warps. Thin—Plate Spines and the Decomposition of Deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence,1989, 11(6):567-585.
[49]L. Collatz, U. Sinogowitz. Spektren endlicher grafen [J]. Abh. Math. Sem. Univ. Hamburg, 1957,21:63-77.
[50]D. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs -Theory and Application (third edition) [M]. New Yorlc:Johann Ambrosius Barth Verlag,1995.
[51]N. L. Biggs. Algebraic Graph Theory [M].Cambridge:Cambridge University Press,1974.
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