基于结构特征的异源图像配准技术研究
|
摘要
异源图像配准是计算机视觉与摄像测量学领域里尚未解决的问题,也是国际上公认的前沿难题之一。论文的研究内容是异源图像之间的配准方法,主要对象为可见光与红外以及雷达图像之间的配准。
基于区域信息的配准方法是同源图像配准领域里成熟的思路之一,却在异源图像配准领域里遇到了很大的挑战。基于特征的配准思路逐渐成为异源图像配准领域的热门方向,论文基于此思路进行了深入地研究,提出并改进了多种基于特征的配准方法,并在第五章中提出了一种全新的基于结构支持度的图像配准思路,实际图像实验证实了论文所提算法的鲁棒性与适应性。
论文的核心内容共分四部分:
1.研究了点特征的检测以及点特征集合的配准。
提出了基于不变性描述的点特征集合配准算法-RBID(Registration Based on Invariant Description)。根据配准模型的不同,又分为基于相似不变性与基于仿射不变性的配准算法。RBID算法的最大特点是在作出假设之前先将集合内的点与点的相对关系用不变的描述子进行描述,从而在对假设进行验证的过程中直接利用描述子之间的差异计算支持度,省去了基于假设求取模型参数,再利用模型参数进行坐标变换运算,相对于现有算法计算量降低至少一个量级。RBID算法还改进了支持度的计算方法,使得成功率和丢失率在点位置噪声以及干扰点数目的影响方面均较现有算法有显著改善。
2.研究了边缘特征的检测与加工。
系统地提出了一套边缘特征的加工算法,包括了边缘之间亲近值(Affinity)定义,基于亲近值的边缘连接策略以及伪边缘的剪除策略,实际图像验证了算法的有效性。最后将该边缘加工算法成功地运用到跑道目标检测应用之中。
3.研究了边缘特征的线段描述以及基于线段描述的边缘轮廓配准。
改进了现有的对边缘进行线段分割的算法,提出了基于变步长迭代的线段分割算法,利用该算法将加工后的边缘特征进行线段分割,得到最佳线段描述,并利用线段描述进行封闭轮廓的检测。论文还利用边缘的最佳线段描述提出了基于线段分割支持度的轮廓配准算法-RBLS(Registration Based on Line-segment Support)。RBLS算法可以用来配准存在任意角度旋转以及较大尺度变换范围的两条边缘轮廓。最后在全图配准模型的约束下删除错误的配准轮廓,实现对两帧图像的配准。
4.提出了基于结构支持度的异源图像配准思路-RBSS(Registration Based on Structure Support),并对该思路进行了深入研究。
RBSS思路绕开了异源图像灰度的关联性不高,共有特征提取重合率低两个问题。在参考图像上利用结构特征,并将这组结构视为对参考图的一种“分割建议”。由于分割是基于目标或者背景的结构特征,待配准图像上对应位置的区域信息必然对这种“分割建议”给予最大程度地认可。RBSS思路通过支持度的概念建立了区域信息与特征之间的联系,最后将对结构具有最大支持度的位置视为配准结果。基于该思路提出了两种结构,三种支持度的图像配准算法,并通过大量的实际图像实验进行算法验证。在多种实验条件下,成功率均达到了95%以上,实验结果接近于工程实用要求。
论文研究的算法是针对异源图像的配准,但同样适用于同源图像之间的配准。
Registration of multi-sensor images is an popular and unresolved problem in the field of computer vision and videometrics. Algorithms for registration between visible, infrared and radar images are studied.
Area-based method, used widely and sucessfully in registration between homo-sensor images, faces big problems in multi-sensor images registration, while the feature-based method becomes a hot research field. The feature-based method is well studied, and a novel registration idea is brought forward in chapter five.
The kernel content includes four parts:
1. Detection of point features and registration between two point sets are studied.
A novel method based on invariable description for the registration between two point sets is put forward-RBID (Registration Based on Invariant Description). According to different registration models, two algorithms are presented, which are based on similarity invariant and affine invariant. The character of RBID is to describe the relation of the poins with invariable description firstly, then the difference between the invariable descriptions is totalized, under a hypothesis. In the process, the meaningless calculation of coordinate transformation is removed. Compared with former methods, the computational complexity is depressed one order of magnitude, and the probability of success and loss behaves well under the noise of point coordinates and the number of disturbed points.
2. Detection and processing of edges are studied.
A systemic method to process edges, including the definition of affinity between edges, the rules to patch edges and the rules to cut spurious edges is given, and testified by real images. At last the method is applied sucessfully in runway detection.
3. Line-segment description of edges and registration between edges are studied.
The method to get the optimal line-segment of edges after processd is modified, and based on the optimal description of line-segment, a method to extract the closed contour is given. And a registration method based on the line-segment support-RBLS (Registration Based on Line-segment Support) is put forward. RBLS can handle registration between two edge contours with arbitary angle rotation and scale change. Finally the false matched contours are deleted under the registration model of two images, so the registration between images is achieved.
4. A novel idea for registration based on the structure support-RBSS (Registration Based on Structure Support) is presented.
Traditional registration methods are based on area or feature information. The gray information is irrelative and the percent of corresponding features extracted from multi-sensor images is small, which confines further development of traditional methods. RBSS using the structure, composed of edges on reference image while area information on realtime image. The connection between them is set up through support measurement. Based on this idea, algorithms about two kinds of structure and three different ways to compute support measurement is brought forward and verified by a lot of real images. The experiment result almostly reaches the requirement of engineering application, as in several cases the correct percentage is more than 95%.
Though the algorithms are performed on the registration between multi-sensor images, they also can be used on the registration between homo-sensor images.
基于区域信息的配准方法是同源图像配准领域里成熟的思路之一,却在异源图像配准领域里遇到了很大的挑战。基于特征的配准思路逐渐成为异源图像配准领域的热门方向,论文基于此思路进行了深入地研究,提出并改进了多种基于特征的配准方法,并在第五章中提出了一种全新的基于结构支持度的图像配准思路,实际图像实验证实了论文所提算法的鲁棒性与适应性。
论文的核心内容共分四部分:
1.研究了点特征的检测以及点特征集合的配准。
提出了基于不变性描述的点特征集合配准算法-RBID(Registration Based on Invariant Description)。根据配准模型的不同,又分为基于相似不变性与基于仿射不变性的配准算法。RBID算法的最大特点是在作出假设之前先将集合内的点与点的相对关系用不变的描述子进行描述,从而在对假设进行验证的过程中直接利用描述子之间的差异计算支持度,省去了基于假设求取模型参数,再利用模型参数进行坐标变换运算,相对于现有算法计算量降低至少一个量级。RBID算法还改进了支持度的计算方法,使得成功率和丢失率在点位置噪声以及干扰点数目的影响方面均较现有算法有显著改善。
2.研究了边缘特征的检测与加工。
系统地提出了一套边缘特征的加工算法,包括了边缘之间亲近值(Affinity)定义,基于亲近值的边缘连接策略以及伪边缘的剪除策略,实际图像验证了算法的有效性。最后将该边缘加工算法成功地运用到跑道目标检测应用之中。
3.研究了边缘特征的线段描述以及基于线段描述的边缘轮廓配准。
改进了现有的对边缘进行线段分割的算法,提出了基于变步长迭代的线段分割算法,利用该算法将加工后的边缘特征进行线段分割,得到最佳线段描述,并利用线段描述进行封闭轮廓的检测。论文还利用边缘的最佳线段描述提出了基于线段分割支持度的轮廓配准算法-RBLS(Registration Based on Line-segment Support)。RBLS算法可以用来配准存在任意角度旋转以及较大尺度变换范围的两条边缘轮廓。最后在全图配准模型的约束下删除错误的配准轮廓,实现对两帧图像的配准。
4.提出了基于结构支持度的异源图像配准思路-RBSS(Registration Based on Structure Support),并对该思路进行了深入研究。
RBSS思路绕开了异源图像灰度的关联性不高,共有特征提取重合率低两个问题。在参考图像上利用结构特征,并将这组结构视为对参考图的一种“分割建议”。由于分割是基于目标或者背景的结构特征,待配准图像上对应位置的区域信息必然对这种“分割建议”给予最大程度地认可。RBSS思路通过支持度的概念建立了区域信息与特征之间的联系,最后将对结构具有最大支持度的位置视为配准结果。基于该思路提出了两种结构,三种支持度的图像配准算法,并通过大量的实际图像实验进行算法验证。在多种实验条件下,成功率均达到了95%以上,实验结果接近于工程实用要求。
论文研究的算法是针对异源图像的配准,但同样适用于同源图像之间的配准。
Registration of multi-sensor images is an popular and unresolved problem in the field of computer vision and videometrics. Algorithms for registration between visible, infrared and radar images are studied.
Area-based method, used widely and sucessfully in registration between homo-sensor images, faces big problems in multi-sensor images registration, while the feature-based method becomes a hot research field. The feature-based method is well studied, and a novel registration idea is brought forward in chapter five.
The kernel content includes four parts:
1. Detection of point features and registration between two point sets are studied.
A novel method based on invariable description for the registration between two point sets is put forward-RBID (Registration Based on Invariant Description). According to different registration models, two algorithms are presented, which are based on similarity invariant and affine invariant. The character of RBID is to describe the relation of the poins with invariable description firstly, then the difference between the invariable descriptions is totalized, under a hypothesis. In the process, the meaningless calculation of coordinate transformation is removed. Compared with former methods, the computational complexity is depressed one order of magnitude, and the probability of success and loss behaves well under the noise of point coordinates and the number of disturbed points.
2. Detection and processing of edges are studied.
A systemic method to process edges, including the definition of affinity between edges, the rules to patch edges and the rules to cut spurious edges is given, and testified by real images. At last the method is applied sucessfully in runway detection.
3. Line-segment description of edges and registration between edges are studied.
The method to get the optimal line-segment of edges after processd is modified, and based on the optimal description of line-segment, a method to extract the closed contour is given. And a registration method based on the line-segment support-RBLS (Registration Based on Line-segment Support) is put forward. RBLS can handle registration between two edge contours with arbitary angle rotation and scale change. Finally the false matched contours are deleted under the registration model of two images, so the registration between images is achieved.
4. A novel idea for registration based on the structure support-RBSS (Registration Based on Structure Support) is presented.
Traditional registration methods are based on area or feature information. The gray information is irrelative and the percent of corresponding features extracted from multi-sensor images is small, which confines further development of traditional methods. RBSS using the structure, composed of edges on reference image while area information on realtime image. The connection between them is set up through support measurement. Based on this idea, algorithms about two kinds of structure and three different ways to compute support measurement is brought forward and verified by a lot of real images. The experiment result almostly reaches the requirement of engineering application, as in several cases the correct percentage is more than 95%.
Though the algorithms are performed on the registration between multi-sensor images, they also can be used on the registration between homo-sensor images.
引文
[1]刘隆和.多模复合寻的制导技术[M].北京:国防工业出版社, 1998.
[2]田捷,包尚联,周明全.医学影像处理与分析[M ].北京:电子工业出版社, 2003: 111~ 113
[3]张继贤,李国胜,曾钰.多源遥感影像高精度自动配准的方法研究[J].遥感学报,2005, 9(1): 73~78
[4]倪国强,刘琼.多源图像配准技术[J].光电工程,2004,31(9):1~6
[5]Brown. A survey of image registration techniques[J].ACM Computing Surveys, 1992, 24(4): 325~376.
[6]ZitováB, FlusserJ. Image registration methods: a survey[J]. Image and Vision Computing, 2003, 21(11): 977~1000.
[7]毛士艺,赵巍.多传感器图像融合技术综述[J].北京航空航天大学学报, 2002, 28(5): 512~518.
[8]倪国强,刘琼.多源图像配准技术分析与展望[J].光电工程,2004, 31(9): 1~6
[9]王鲲鹏,徐一丹,于起峰.红外与可见光图像配准方法分类及现状[J].红外技术,2009, 31(5): 270~274
[10]苑津莎,赵振兵,高强.红外与可见光图像配准研究现状与展望J].激光与红外,2000, 39(7): 693~699
[11]P.Viola, W. M. Wells. Alignment by Maximization of Mutual Information[C]. International Conference on Computer Vision, IEEE Computer Society Press, Los Alamitos, LA, 1995: 16~23
[12]汤敏.结合形态学梯度互信息和多分辨率寻优的图像配准新方法[J].自动化学报, 2008, 34(3): 246~250
[13]张见威,韩国强,沃焱.基于边界距离场互信息的图像配准方法[J].通信学报, 2006, 27(7): 87~93
[14]M. Mellor, M. Brady,. Phase mutual information as a similarity measure for registration[J]. Medical Image Analysis, 2005, 9 330~343
[15]Xuesong Lu, Su Zhang, He Su. Mutual information-based multimodal image registration using a novel joint histogram estimation[J]. Computerized Medical Imaging and Graphics, 2008, 32, 202~209
[16]K. J. Dana, P Anandan. Registration of visible and infrared images[C]. In Proc. SPIE Conf.on Arch, Hardware and FLIR in Auto.Targ.Rec., 1993: 1~12
[17]M. Svedlow, C.D. McGilem, and P.E. Anuta. Experimental Examination of Similarity Measures and Preprocessing Methods Used for Image Registration[C]. Symposiumon Machine Processing of Remotely Sensed Data, Purdue University, Indiana, June 1976, , 4~9
[54] Moravec H.P. Towards automatic visual obstacle avoidance[C]. In 5th International Joint Conference on Artificial Intelligence, 1977 : 584~590
[55] Harris C, Stephens M. A Combined corner and edge detector[J]. Proc 4th Alvey Vision Conference,1988:189~192
[56] K. Mikolajczyk, C. Schmid. Indexing Based on Scale Invariant Interest Points[C]. Proc. Eighth Int’l Conf. Computer Vision, , 2001, 525-531.
[57] Mikolajczyk K, C Schmid. Scale and affine invariant interest point detectors[J]. International Journal of Computer Vision,2004,60(1):63~86
[58] K. Mikolajczyk, C. Schmid. An Affine Invariant Interest Point Detector[C] Proc. Seventh European Conf. Computer Vision,, 2002,128-142
[59] K. Mikolajczyk, C. Schmid. A Performance Evaluation of Local Descriptors[J]. Proc. Conf. Computer Vision and Pattern Recognition, 2003,. 257-264.
[60] Forstner W, A Feature Based Correspondence algorithm For Image Matching[C], ISP Comm. III,1986.
[61]张恒,于起峰,丁晓华等.基于加权Gabor梯度的新型多尺度角点检测方法[J],中国图象图形学报,2007, 12(8):1377~1382.
[62] Lindeberg. Detecting salient blob-like image structures and their scales with a scale-space primal sketch: a method fo focus of attention[J]. International Journal of Computer Vision, 11(3):283~318
[63] Lindeberg. Scale-space theory: A basic tool for analyzing structures at different scales[J]. Journal of Applied Statistics, 21(2):224~270
[64] Lowe D G . Object recognition from scale-invariant features[C]. International Conference of Computer Vision,1999:1150~1157
[65] Lowe D G. Distinctive image features from scale-invariant keypoints[J]. Inter- national Journal of Computer Vision, 2004, 60(2): 91~110
[66] Dobbins. A, Zucker, S. W., Cynader, M. S. Endstopped neurons in the visual cortex as a substrate for calculating curvature[J]. Nature 1987, 329: 438~441
[67] G Scott, H Longuet-Higgins.An Algorithm for Associating the Features of Two Patterns[C].Proceeding of Royal Society London, 1991, B244:21~26.
[68]Maurizio Pilu.A Direct Method for Stereo Correspondence Based on SVD[C]. Proceeding of CVPR’97, 1997:261~266.
[69]Huttenloeher D P, Klanderman G A, Rucklidge W J.Comparing images using the Hausdorff distance[J].IEEE Transactions On Pattern Analysis and Machine Intelligence, 1993, 15(9): 850～863..
[70]Huttenlocher D P, Rucklidge W J. A multi-resolution technique for comparing images using the Hausdorff distance[R]. Technical Report 1321, Cornell University. Department of Computer Science, USA, 1992
[71]Rucklidge W J. Efficiently locating objects using the Hausdorff distance[J]. International Journal of Computer Vision, 1997, 24(3): 251~270
[72]彭晓明,丁明跃,周成平等.一种利用Hausdorff距离的高效目标搜索算法[J].中国图象图形学报, 2004, 9(1): 24~28
[73]Ranade S, Rosenfeld A Point pattern matching by relaxation[J].Pattern Recognition, 1980, 12(4): 269-275
[74]桑农,张天序.旋转与比例不变的点特征松弛匹配算法[J].电子学报, 1999, 26(6): 742~771
[75]陈志刚,宋胜锋,李陆冀.基于相似原理的点特征松弛匹配算法[J].火力与指挥控制,2006,31 (1),50~52
[76]王兆魁,张育林.一种CCD星图星点快速定位算法[J].空间科学学报, 2006,26(3):209~214.
[77]Padgett C, Kreutz, Delgado K. A grid algorithm for autonomous star identification[J]. IEEE Trans on AES, 1997, 33 (1) : 202~213
[78]Canny. A computational approach to edge detection[J]. IEEE Trans on PAMI, 1986, 8(6): 679~69
[79]T.Poggio,H.Voorhees and A.Yuille. A regularized solution to edge detection[J]. MIT, AIM, 1985, May, 833
[80]Shenand S.Castan. An optimal linear operator for step edge detection[J]. CVGIP, 1992, 54(2)
[81]Deriche. Using Canny’s criteria to derive a recursively implemented optimal edge detector[J], Inter. Journal of Computercusion, 1987, 167~187
[82]邓湘金,云日升,吴一戎等.一种新边缘检测算子-正弦算子[J].电子与信息学报, 2002, 24(11): 1462-1469
[83]Shenand S.Castan. An optimal linear operator for step edge detection[J]. CVGIP, 1992, 54(2)
[84]William Tafel Freeman.Steerable Filters and Local Analysis of Image Structure [PhD thesis][D].Stanford:The Massachusetts Institute of Technology, 1992
[85]Iverson, L., Zucker, S.W. Logical/linear operators for image curves[J]. IEEE Trans. PAMI, 1995, 17(10): 982~996
[86]http://www.cs.yale.edu/homes/vision/zucker/index.html
[87]C.Ducottet, T.Fournel, C.Barat. Scale-adaptive detection and local characterization of edges based on wavelet transform[J]. Signal Processing, 2004, 84: 2115~2137
[88]D.J.Williams, M.Shah. Edge contours using multiple scales[J]. Computer Vision, Graphics and Image Processing, 1990, 51: 256~274
[89]杨述斌,彭复员.噪声污染图象中的广义形态边缘检测器[J].计算机工程与应用, 2002, 38(17): 91~92
[90]杨述斌,彭复员,张增常.多尺度自适应加权形态边缘检测器[J].华中科技大学学报, 2002, 30(10): 42~45
[91]Pal S K, King R A. On edge detection of x-ray images using fuzzy sets[J]. IEEE Trans. on PAMI, 1983, 5(1): 69~77
[92]周德龙,潘泉.图像模糊边缘检测的改进算法[J].中国图象图形学报, 2001, 6(4): 353~358
[93]Zhengquan He, Siyal. Edge detection with BP neural networks[C]. Signal Processing ICSP'98, 1998 Fourth International Conference, Oct: 1382~1384
[94]Y. Uchiyama, M. Haseyama, H. Kitajima. Hopfield neural networks for edge detection[C]. Circuits and Systems, 2001. ISCAS 2001. The 2001 IEEE International Symposium on, 2001, May 3: 608~611
[95]M. S. Bhuiyan, Y. Iwahori, A. Iwata. Stepped-down coefficient values associatedwith Hopfield nets improve optimal edge detection[C], Systems, Man, and Cybernetics, 1999. IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on, 5, 12-15 Oct. 1999: 377~382
[96]Siwei Lu, Ziging Wang. Fuzzy neural networks for edge detection[C]. Electrical and Computer Engineering. IEEE 1997 Canadian Conference on, 2, 25-28 May: 446~449
[97]Berkeley Segmentation and Boundary Detection Benchmark and Dataset, 2003, http://www.cs.berkeley.edu/projects/vision/grouping/segbench
[98]M. Maire, P. Arbelaez, C. Fowlkes. Using contours to detect and localize junctions in natural images[C]. CVPR, 2008.
[99]Mumford, D. Elastic and Computer Vision, Algebraic Geometry and Its Applications, Springer-Verlag, New York, 1994
[100]L. Williams and D. Jacobs,“Stochastic Completion Fields: A Neural Model of Illusory Contour Shape and Salience,”Neural Computation, 1997, vol. 9: 849-870
[101]K.K. Thornber and L.R. Williams,“Analytic Solution of Stochastic Completion Fields,”Biological Cybernetics, 1996, vol. 75: 141~151
[102]P. Parent, S.W. Zucker. Trace inference, curvature consistency and curve detection. IEEE Trans. PAMI, 1989, 11 (8): 823~839
[103]J. Elder and S. Zucker. Computing Contour Closure. Proc European Conf Computer Vision, 1996, 399~412
[104]S. Wang, T. Kubota, and J. M. Siskind. Salient boundary detection using ratio Contour. IEEE Transactions on PAMI, 2005, 27(4): 546~560
[105]应龙,栾悉道,吴玲达.高分辨率遥感图像中机场跑道快速检测方法[J].小型微型计算机系统,2006,27(2):282~ 286
[106]Guil, NVillalba, JZapata, E.L.A fast Hough transform for segment detection[J]. Image Processing, IEEE Transactions on 1057-7149, Nov, 1995, 1541~1548
[107]Burns B. Extracting straight lines[J]. IEEE Trans Pattern Analysis and Machine Intelligence,1986,8(4): 425~ 455
[108]Freeman H. On the encoding of arbitrary geometric configurations[J]. IRE Trans. , 1961, 10: 260～268
[109]F reeman H. Comparative analysis of line draw ing modeling schemes[J]. Computer Graphices Image Process, 1980, 12: 203～223
[110]F reeman H. Shape description via the use of critical points[J]. Pattern Recognition, 1978, 10: 159～166
[111]Xiaolong Dai, Siamak Khorram. A Feature-Based Image Registration Algorithm Using Improved Chain-Code Representation Combined with Invariant Moments[J]. IEEE Trans on Geoscience and Remote Sensing, 1999, 37(5): 2351~2362
[112]Imran Siddiqi, Nicole Vincent. A Set of Chain Code Based Features for Writer Recognition[C]. 10th International Conference on Document Analysis and Recognition, 2009 981~985
[113]张显全,王继军,蒋联源.基于Freeman链码的圆识别方法[J].计算机工程2007 33(15) :196~198
[114]王平,董玉德,罗喆帅.基于Freeman链码的直线识别方法[J].计算机工程2005 31(10) :171~174
[115]陆宗骐童韬.链码和在边界形状分析中的应用[J].中国图象图形学报, 2002,7(12): 1323~1328
[116]尚振宏刘明业.运用Freeman准则的直线检测算法[J].计算机辅助设计与图形学学报, 2005, 17(1) 49~54
[117]Elder,, Zucker. Evidence for boundary-specific grouping in human vision[J]. Vision Research, 1998, 38(1): 143~152.
[118]Yen, Finkel.“Pop-Out”of salient contours in a network based on striate cortical connectivity[J]. Investigative Opthalmology and Visual Science (ARVO). 1996, 37(3): 5293
[119]Elder, Zucker. The effect of contour closure on the rapid discrimination of two-dimensional shapes[J]. Vision Research, 1993, 33(7): 981~991
[120]Elder, Goldberg. Ecological statistics of Gestalt laws for the perceptual organization of contours[J]. Journal of Vision, 2002, 2(4), 324-353
[121]Elder, Krupnik, Johnston. (2003) Contour grouping with prior models, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(25): 661~674.
[122]Shashua, Ullman. Structural Saliency: The Detection of Globally Salient Structures Using a Locally Connected Network[C]. Proc. Int’l Conf. Computer Vision, 1988,. 321-327
[123]S. Wang, J. Wang, T. Kubota. From Fragments to Salient Closed Boundaries: An In-Depth Study[C]. Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2004, Vol: 291~298
[124]D.J. Williams, M. Shah. A Fast Algorithm for Active Contours[C]. Proc. Int’l Conf. Computer Vision, 1990, 592~595
[125]L. Williams and D. Jacobs. Stochastic Completion Fields: A Neural Model of Illusory Contour Shape and Salience[J]. Neural Computation, 1997, vol. 9,. 849~870
[126] Kass M, witkinM, Terzopoulos D. Snakes: active contour models[J]. International Journal of Computer Vision, 1987, 4: 321~331
[127]D. Mumford, J. Shah. Optimal Approximations by Piecewise Smooth Functions and associated Variational Problems[J]. Communications in Pure and Applied Mathematics, 1989, vol 42
[128] Xu C, Prince J L. Snakes: shapes and gradient vector flow. IEEE Trans. 1998, 7(3): 359~369
[129]C. Xu, J.L. Prince. Generalized gradient vector flow external force for active contours[J]. Signal Processing,1998, vol. 71, 131-139
[130]罗渝兰.基于Sanke可变模型的方法在超声医学图像分割、三维重建与定量计算中的应用[D].成都:四川大学,2002.4
[131]颜洁.可变形提取磁共振图像脑区域的方法研究[D].河北工业大学,2003.1
[132]陈文娟,石民勇.蛇模型的综述[J].北京广播学院学报, 2003,10(2):17~25
[133] S.Menet, P.Saint-Marc, G.Medioni. B-Snakes: Implementation and application to stereo[J]. DARPA Image Understanding Workshop, 1990,720~726
[134]陆仁枝等. CT序列图像分割的实现及分割结果的重建.计算机工程,2003,29(13), 152~154
[135]P. Radeva, A. Amini, and J. Huang, aDeformable B-Solids and Implicit Snakes for 3D Localization and Tracking of Spamm MRI Data[J]. Computer Vision and Image Understanding, 1997, 66(2): 163~178
[136]Malladi, Sethian, Vemuri. Shape Modeling with Front Propagation: A level Set Approach[J]. IEEE Transactions on PAMI, 1995, 17(2): 158~175
[137]T. Chan, L. Vese. Active Contours without Edges[R]. UCLA Technical Report, 1999: 1~15
[138]黄福珍等.基于Level Set方法的人脸轮廓提取与跟踪[J].计算机学报. 2003, 26(4), 491~496
[139]马波.基于主动轮廓线模型的跟踪及初始化研究[D].哈尔滨:哈尔滨工业大学,2003.6
[140] AMIR A.AMINI. Using dynamic programming for solving variational problem in vision[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990,12(9): 855~867
[141]杨莉,李玉山等.部分最优化动态规划轮廓检测算法[J].电子与信息学报,2004,26(6) ,923~927
[142]L. Williams, K. K. Thornber. A Comparison Measures for Detecting Natural Shapes in Cluttered Background[J]. International Journal of Computer Vision, 2000 34(2 /3): 81~96
[143]S. Wang, T. Kubota, J. M. Siskind. Salient Boundary Detection using Ratio Contour [C]. In Neural Information Processing Systems Conference, 2003
[144]丁险峰,吴洪.形状匹配综述[J].自动化学报, 2001, 27( 5) : 678~694
[145]Hu. Visual Pattern Recognition by Moment Invariants, IRE Trans. Inform Theory, 1962, IT-8920, 179~187
[146]Reiss. The Revised Fundamental Theorem of Moment Invariants[J]. IEEE Transaction on PAMI, 1991, 13(8), 830~834
[147]J.Flusser. Pattern Recognition by Affine Moment Invariants[J]. Pattern Recognition,1993,26(1),167~174
[148]Debasish Bhattacharya, Satyabroto Sinta. Invariant of Stereo Images vis the Theory of Complex Moments[J]. Pattern Recognition, 1997, 20(9):1373~1386
[149]Khotanzad. Zernike Moment Based Rotation Invariant Features for Pattern recognition[J]. SPIE 1988, Vol.1002: 212~219
[150]Bailey Robert R, SrinathM andyam. Orthogonal Moment Feature for use with Parametric and non-parametric classifiers[J]. IEEE T rans on PAM I , 1996, 18 (4): 389~399
[151]Zhan, Roskies. Fourier descriptors for plane closed curves[J]. IEEE T rans on Computer, 1972, 21 (3) : 269~281
[152]Persoon, Fu. Shape discrimination using Fourier descriptors. IEEE Trans on System , Man, Cybernetics, 1977, 7 (3) : 170~179
[153]Chuang Gene, Kuo. Wavelet descriptor of planar curves: theory and application[J]. IEEE Trans on Image Processing , 1996, 5 (1): 56~70
[154]Li , Jay, Kuo. Automatic Target Shape Recognition via Deformable Wavelet templates[C]. SPIE’s International Symposium on Aero space Defense Sensing and Controls, 1996, 8~12
[155]Tieng , BolesW. Recognition of 2D Object Contours using the Wavelet Transform zero-crossing representation[J]. IEEE Trans on PAM I , 1997, 19 (8) : 910~916
[156]Chen Guangyi, Tien D Bui. Invariant Fourier wavelet descriptor for pattern recognition[J]. Pattern Recog nition, 1999, 32 (7) : 1083~1088
[157]Yang Hee Soo, Lee Sang. Recognition of 2D object contours using starting point independent wavelet coefficient matching[J]. Visual Communication and Image Representation, 1998, 9 (2) : 171~181
[158]杨翔英,章毓晋.小波轮廓描述符及在图像查询中的应用[J].计算机学报, 1999, 22 (7) : 752~757
[159]Shih, Pu. Morphological Shape Description Using Geometric Spectrum on Multidimensional Binary images[J]. Pattern Recognition, 1992, 25: 921~927
[160]Loui, Venetsanopoulos , Sm ith. Two-dimensional Shape Representation Using morphological correlation function[C]. In: Proc. IEEE ICA SSP, 1990. 2165~2168
[161]Loncaric S, Dhawan A P. Near-op timal MST based Shape description using Genetic Algorithm. Pattern Recognition, 1995, 28: 571~579
[162]Esa Rahtu, mikko Salo, Janne HeikkilaAffine Invariant Pattern Recognition Using Multiscale Auto convolution[J]. IEEE Transactions on PAMI, 2005, 27(6): 908~918
[163]吴福朝.计算机视觉中的数学方法[M].北京:科学出版社, 2008: 344~345
[2]田捷,包尚联,周明全.医学影像处理与分析[M ].北京:电子工业出版社, 2003: 111~ 113
[3]张继贤,李国胜,曾钰.多源遥感影像高精度自动配准的方法研究[J].遥感学报,2005, 9(1): 73~78
[4]倪国强,刘琼.多源图像配准技术[J].光电工程,2004,31(9):1~6
[5]Brown. A survey of image registration techniques[J].ACM Computing Surveys, 1992, 24(4): 325~376.
[6]ZitováB, FlusserJ. Image registration methods: a survey[J]. Image and Vision Computing, 2003, 21(11): 977~1000.
[7]毛士艺,赵巍.多传感器图像融合技术综述[J].北京航空航天大学学报, 2002, 28(5): 512~518.
[8]倪国强,刘琼.多源图像配准技术分析与展望[J].光电工程,2004, 31(9): 1~6
[9]王鲲鹏,徐一丹,于起峰.红外与可见光图像配准方法分类及现状[J].红外技术,2009, 31(5): 270~274
[10]苑津莎,赵振兵,高强.红外与可见光图像配准研究现状与展望J].激光与红外,2000, 39(7): 693~699
[11]P.Viola, W. M. Wells. Alignment by Maximization of Mutual Information[C]. International Conference on Computer Vision, IEEE Computer Society Press, Los Alamitos, LA, 1995: 16~23
[12]汤敏.结合形态学梯度互信息和多分辨率寻优的图像配准新方法[J].自动化学报, 2008, 34(3): 246~250
[13]张见威,韩国强,沃焱.基于边界距离场互信息的图像配准方法[J].通信学报, 2006, 27(7): 87~93
[14]M. Mellor, M. Brady,. Phase mutual information as a similarity measure for registration[J]. Medical Image Analysis, 2005, 9 330~343
[15]Xuesong Lu, Su Zhang, He Su. Mutual information-based multimodal image registration using a novel joint histogram estimation[J]. Computerized Medical Imaging and Graphics, 2008, 32, 202~209
[16]K. J. Dana, P Anandan. Registration of visible and infrared images[C]. In Proc. SPIE Conf.on Arch, Hardware and FLIR in Auto.Targ.Rec., 1993: 1~12
[17]M. Svedlow, C.D. McGilem, and P.E. Anuta. Experimental Examination of Similarity Measures and Preprocessing Methods Used for Image Registration[C]. Symposiumon Machine Processing of Remotely Sensed Data, Purdue University, Indiana, June 1976, , 4~9
[54] Moravec H.P. Towards automatic visual obstacle avoidance[C]. In 5th International Joint Conference on Artificial Intelligence, 1977 : 584~590
[55] Harris C, Stephens M. A Combined corner and edge detector[J]. Proc 4th Alvey Vision Conference,1988:189~192
[56] K. Mikolajczyk, C. Schmid. Indexing Based on Scale Invariant Interest Points[C]. Proc. Eighth Int’l Conf. Computer Vision, , 2001, 525-531.
[57] Mikolajczyk K, C Schmid. Scale and affine invariant interest point detectors[J]. International Journal of Computer Vision,2004,60(1):63~86
[58] K. Mikolajczyk, C. Schmid. An Affine Invariant Interest Point Detector[C] Proc. Seventh European Conf. Computer Vision,, 2002,128-142
[59] K. Mikolajczyk, C. Schmid. A Performance Evaluation of Local Descriptors[J]. Proc. Conf. Computer Vision and Pattern Recognition, 2003,. 257-264.
[60] Forstner W, A Feature Based Correspondence algorithm For Image Matching[C], ISP Comm. III,1986.
[61]张恒,于起峰,丁晓华等.基于加权Gabor梯度的新型多尺度角点检测方法[J],中国图象图形学报,2007, 12(8):1377~1382.
[62] Lindeberg. Detecting salient blob-like image structures and their scales with a scale-space primal sketch: a method fo focus of attention[J]. International Journal of Computer Vision, 11(3):283~318
[63] Lindeberg. Scale-space theory: A basic tool for analyzing structures at different scales[J]. Journal of Applied Statistics, 21(2):224~270
[64] Lowe D G . Object recognition from scale-invariant features[C]. International Conference of Computer Vision,1999:1150~1157
[65] Lowe D G. Distinctive image features from scale-invariant keypoints[J]. Inter- national Journal of Computer Vision, 2004, 60(2): 91~110
[66] Dobbins. A, Zucker, S. W., Cynader, M. S. Endstopped neurons in the visual cortex as a substrate for calculating curvature[J]. Nature 1987, 329: 438~441
[67] G Scott, H Longuet-Higgins.An Algorithm for Associating the Features of Two Patterns[C].Proceeding of Royal Society London, 1991, B244:21~26.
[68]Maurizio Pilu.A Direct Method for Stereo Correspondence Based on SVD[C]. Proceeding of CVPR’97, 1997:261~266.
[69]Huttenloeher D P, Klanderman G A, Rucklidge W J.Comparing images using the Hausdorff distance[J].IEEE Transactions On Pattern Analysis and Machine Intelligence, 1993, 15(9): 850～863..
[70]Huttenlocher D P, Rucklidge W J. A multi-resolution technique for comparing images using the Hausdorff distance[R]. Technical Report 1321, Cornell University. Department of Computer Science, USA, 1992
[71]Rucklidge W J. Efficiently locating objects using the Hausdorff distance[J]. International Journal of Computer Vision, 1997, 24(3): 251~270
[72]彭晓明,丁明跃,周成平等.一种利用Hausdorff距离的高效目标搜索算法[J].中国图象图形学报, 2004, 9(1): 24~28
[73]Ranade S, Rosenfeld A Point pattern matching by relaxation[J].Pattern Recognition, 1980, 12(4): 269-275
[74]桑农,张天序.旋转与比例不变的点特征松弛匹配算法[J].电子学报, 1999, 26(6): 742~771
[75]陈志刚,宋胜锋,李陆冀.基于相似原理的点特征松弛匹配算法[J].火力与指挥控制,2006,31 (1),50~52
[76]王兆魁,张育林.一种CCD星图星点快速定位算法[J].空间科学学报, 2006,26(3):209~214.
[77]Padgett C, Kreutz, Delgado K. A grid algorithm for autonomous star identification[J]. IEEE Trans on AES, 1997, 33 (1) : 202~213
[78]Canny. A computational approach to edge detection[J]. IEEE Trans on PAMI, 1986, 8(6): 679~69
[79]T.Poggio,H.Voorhees and A.Yuille. A regularized solution to edge detection[J]. MIT, AIM, 1985, May, 833
[80]Shenand S.Castan. An optimal linear operator for step edge detection[J]. CVGIP, 1992, 54(2)
[81]Deriche. Using Canny’s criteria to derive a recursively implemented optimal edge detector[J], Inter. Journal of Computercusion, 1987, 167~187
[82]邓湘金,云日升,吴一戎等.一种新边缘检测算子-正弦算子[J].电子与信息学报, 2002, 24(11): 1462-1469
[83]Shenand S.Castan. An optimal linear operator for step edge detection[J]. CVGIP, 1992, 54(2)
[84]William Tafel Freeman.Steerable Filters and Local Analysis of Image Structure [PhD thesis][D].Stanford:The Massachusetts Institute of Technology, 1992
[85]Iverson, L., Zucker, S.W. Logical/linear operators for image curves[J]. IEEE Trans. PAMI, 1995, 17(10): 982~996
[86]http://www.cs.yale.edu/homes/vision/zucker/index.html
[87]C.Ducottet, T.Fournel, C.Barat. Scale-adaptive detection and local characterization of edges based on wavelet transform[J]. Signal Processing, 2004, 84: 2115~2137
[88]D.J.Williams, M.Shah. Edge contours using multiple scales[J]. Computer Vision, Graphics and Image Processing, 1990, 51: 256~274
[89]杨述斌,彭复员.噪声污染图象中的广义形态边缘检测器[J].计算机工程与应用, 2002, 38(17): 91~92
[90]杨述斌,彭复员,张增常.多尺度自适应加权形态边缘检测器[J].华中科技大学学报, 2002, 30(10): 42~45
[91]Pal S K, King R A. On edge detection of x-ray images using fuzzy sets[J]. IEEE Trans. on PAMI, 1983, 5(1): 69~77
[92]周德龙,潘泉.图像模糊边缘检测的改进算法[J].中国图象图形学报, 2001, 6(4): 353~358
[93]Zhengquan He, Siyal. Edge detection with BP neural networks[C]. Signal Processing ICSP'98, 1998 Fourth International Conference, Oct: 1382~1384
[94]Y. Uchiyama, M. Haseyama, H. Kitajima. Hopfield neural networks for edge detection[C]. Circuits and Systems, 2001. ISCAS 2001. The 2001 IEEE International Symposium on, 2001, May 3: 608~611
[95]M. S. Bhuiyan, Y. Iwahori, A. Iwata. Stepped-down coefficient values associatedwith Hopfield nets improve optimal edge detection[C], Systems, Man, and Cybernetics, 1999. IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on, 5, 12-15 Oct. 1999: 377~382
[96]Siwei Lu, Ziging Wang. Fuzzy neural networks for edge detection[C]. Electrical and Computer Engineering. IEEE 1997 Canadian Conference on, 2, 25-28 May: 446~449
[97]Berkeley Segmentation and Boundary Detection Benchmark and Dataset, 2003, http://www.cs.berkeley.edu/projects/vision/grouping/segbench
[98]M. Maire, P. Arbelaez, C. Fowlkes. Using contours to detect and localize junctions in natural images[C]. CVPR, 2008.
[99]Mumford, D. Elastic and Computer Vision, Algebraic Geometry and Its Applications, Springer-Verlag, New York, 1994
[100]L. Williams and D. Jacobs,“Stochastic Completion Fields: A Neural Model of Illusory Contour Shape and Salience,”Neural Computation, 1997, vol. 9: 849-870
[101]K.K. Thornber and L.R. Williams,“Analytic Solution of Stochastic Completion Fields,”Biological Cybernetics, 1996, vol. 75: 141~151
[102]P. Parent, S.W. Zucker. Trace inference, curvature consistency and curve detection. IEEE Trans. PAMI, 1989, 11 (8): 823~839
[103]J. Elder and S. Zucker. Computing Contour Closure. Proc European Conf Computer Vision, 1996, 399~412
[104]S. Wang, T. Kubota, and J. M. Siskind. Salient boundary detection using ratio Contour. IEEE Transactions on PAMI, 2005, 27(4): 546~560
[105]应龙,栾悉道,吴玲达.高分辨率遥感图像中机场跑道快速检测方法[J].小型微型计算机系统,2006,27(2):282~ 286
[106]Guil, NVillalba, JZapata, E.L.A fast Hough transform for segment detection[J]. Image Processing, IEEE Transactions on 1057-7149, Nov, 1995, 1541~1548
[107]Burns B. Extracting straight lines[J]. IEEE Trans Pattern Analysis and Machine Intelligence,1986,8(4): 425~ 455
[108]Freeman H. On the encoding of arbitrary geometric configurations[J]. IRE Trans. , 1961, 10: 260～268
[109]F reeman H. Comparative analysis of line draw ing modeling schemes[J]. Computer Graphices Image Process, 1980, 12: 203～223
[110]F reeman H. Shape description via the use of critical points[J]. Pattern Recognition, 1978, 10: 159～166
[111]Xiaolong Dai, Siamak Khorram. A Feature-Based Image Registration Algorithm Using Improved Chain-Code Representation Combined with Invariant Moments[J]. IEEE Trans on Geoscience and Remote Sensing, 1999, 37(5): 2351~2362
[112]Imran Siddiqi, Nicole Vincent. A Set of Chain Code Based Features for Writer Recognition[C]. 10th International Conference on Document Analysis and Recognition, 2009 981~985
[113]张显全,王继军,蒋联源.基于Freeman链码的圆识别方法[J].计算机工程2007 33(15) :196~198
[114]王平,董玉德,罗喆帅.基于Freeman链码的直线识别方法[J].计算机工程2005 31(10) :171~174
[115]陆宗骐童韬.链码和在边界形状分析中的应用[J].中国图象图形学报, 2002,7(12): 1323~1328
[116]尚振宏刘明业.运用Freeman准则的直线检测算法[J].计算机辅助设计与图形学学报, 2005, 17(1) 49~54
[117]Elder,, Zucker. Evidence for boundary-specific grouping in human vision[J]. Vision Research, 1998, 38(1): 143~152.
[118]Yen, Finkel.“Pop-Out”of salient contours in a network based on striate cortical connectivity[J]. Investigative Opthalmology and Visual Science (ARVO). 1996, 37(3): 5293
[119]Elder, Zucker. The effect of contour closure on the rapid discrimination of two-dimensional shapes[J]. Vision Research, 1993, 33(7): 981~991
[120]Elder, Goldberg. Ecological statistics of Gestalt laws for the perceptual organization of contours[J]. Journal of Vision, 2002, 2(4), 324-353
[121]Elder, Krupnik, Johnston. (2003) Contour grouping with prior models, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(25): 661~674.
[122]Shashua, Ullman. Structural Saliency: The Detection of Globally Salient Structures Using a Locally Connected Network[C]. Proc. Int’l Conf. Computer Vision, 1988,. 321-327
[123]S. Wang, J. Wang, T. Kubota. From Fragments to Salient Closed Boundaries: An In-Depth Study[C]. Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2004, Vol: 291~298
[124]D.J. Williams, M. Shah. A Fast Algorithm for Active Contours[C]. Proc. Int’l Conf. Computer Vision, 1990, 592~595
[125]L. Williams and D. Jacobs. Stochastic Completion Fields: A Neural Model of Illusory Contour Shape and Salience[J]. Neural Computation, 1997, vol. 9,. 849~870
[126] Kass M, witkinM, Terzopoulos D. Snakes: active contour models[J]. International Journal of Computer Vision, 1987, 4: 321~331
[127]D. Mumford, J. Shah. Optimal Approximations by Piecewise Smooth Functions and associated Variational Problems[J]. Communications in Pure and Applied Mathematics, 1989, vol 42
[128] Xu C, Prince J L. Snakes: shapes and gradient vector flow. IEEE Trans. 1998, 7(3): 359~369
[129]C. Xu, J.L. Prince. Generalized gradient vector flow external force for active contours[J]. Signal Processing,1998, vol. 71, 131-139
[130]罗渝兰.基于Sanke可变模型的方法在超声医学图像分割、三维重建与定量计算中的应用[D].成都:四川大学,2002.4
[131]颜洁.可变形提取磁共振图像脑区域的方法研究[D].河北工业大学,2003.1
[132]陈文娟,石民勇.蛇模型的综述[J].北京广播学院学报, 2003,10(2):17~25
[133] S.Menet, P.Saint-Marc, G.Medioni. B-Snakes: Implementation and application to stereo[J]. DARPA Image Understanding Workshop, 1990,720~726
[134]陆仁枝等. CT序列图像分割的实现及分割结果的重建.计算机工程,2003,29(13), 152~154
[135]P. Radeva, A. Amini, and J. Huang, aDeformable B-Solids and Implicit Snakes for 3D Localization and Tracking of Spamm MRI Data[J]. Computer Vision and Image Understanding, 1997, 66(2): 163~178
[136]Malladi, Sethian, Vemuri. Shape Modeling with Front Propagation: A level Set Approach[J]. IEEE Transactions on PAMI, 1995, 17(2): 158~175
[137]T. Chan, L. Vese. Active Contours without Edges[R]. UCLA Technical Report, 1999: 1~15
[138]黄福珍等.基于Level Set方法的人脸轮廓提取与跟踪[J].计算机学报. 2003, 26(4), 491~496
[139]马波.基于主动轮廓线模型的跟踪及初始化研究[D].哈尔滨:哈尔滨工业大学,2003.6
[140] AMIR A.AMINI. Using dynamic programming for solving variational problem in vision[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990,12(9): 855~867
[141]杨莉,李玉山等.部分最优化动态规划轮廓检测算法[J].电子与信息学报,2004,26(6) ,923~927
[142]L. Williams, K. K. Thornber. A Comparison Measures for Detecting Natural Shapes in Cluttered Background[J]. International Journal of Computer Vision, 2000 34(2 /3): 81~96
[143]S. Wang, T. Kubota, J. M. Siskind. Salient Boundary Detection using Ratio Contour [C]. In Neural Information Processing Systems Conference, 2003
[144]丁险峰,吴洪.形状匹配综述[J].自动化学报, 2001, 27( 5) : 678~694
[145]Hu. Visual Pattern Recognition by Moment Invariants, IRE Trans. Inform Theory, 1962, IT-8920, 179~187
[146]Reiss. The Revised Fundamental Theorem of Moment Invariants[J]. IEEE Transaction on PAMI, 1991, 13(8), 830~834
[147]J.Flusser. Pattern Recognition by Affine Moment Invariants[J]. Pattern Recognition,1993,26(1),167~174
[148]Debasish Bhattacharya, Satyabroto Sinta. Invariant of Stereo Images vis the Theory of Complex Moments[J]. Pattern Recognition, 1997, 20(9):1373~1386
[149]Khotanzad. Zernike Moment Based Rotation Invariant Features for Pattern recognition[J]. SPIE 1988, Vol.1002: 212~219
[150]Bailey Robert R, SrinathM andyam. Orthogonal Moment Feature for use with Parametric and non-parametric classifiers[J]. IEEE T rans on PAM I , 1996, 18 (4): 389~399
[151]Zhan, Roskies. Fourier descriptors for plane closed curves[J]. IEEE T rans on Computer, 1972, 21 (3) : 269~281
[152]Persoon, Fu. Shape discrimination using Fourier descriptors. IEEE Trans on System , Man, Cybernetics, 1977, 7 (3) : 170~179
[153]Chuang Gene, Kuo. Wavelet descriptor of planar curves: theory and application[J]. IEEE Trans on Image Processing , 1996, 5 (1): 56~70
[154]Li , Jay, Kuo. Automatic Target Shape Recognition via Deformable Wavelet templates[C]. SPIE’s International Symposium on Aero space Defense Sensing and Controls, 1996, 8~12
[155]Tieng , BolesW. Recognition of 2D Object Contours using the Wavelet Transform zero-crossing representation[J]. IEEE Trans on PAM I , 1997, 19 (8) : 910~916
[156]Chen Guangyi, Tien D Bui. Invariant Fourier wavelet descriptor for pattern recognition[J]. Pattern Recog nition, 1999, 32 (7) : 1083~1088
[157]Yang Hee Soo, Lee Sang. Recognition of 2D object contours using starting point independent wavelet coefficient matching[J]. Visual Communication and Image Representation, 1998, 9 (2) : 171~181
[158]杨翔英,章毓晋.小波轮廓描述符及在图像查询中的应用[J].计算机学报, 1999, 22 (7) : 752~757
[159]Shih, Pu. Morphological Shape Description Using Geometric Spectrum on Multidimensional Binary images[J]. Pattern Recognition, 1992, 25: 921~927
[160]Loui, Venetsanopoulos , Sm ith. Two-dimensional Shape Representation Using morphological correlation function[C]. In: Proc. IEEE ICA SSP, 1990. 2165~2168
[161]Loncaric S, Dhawan A P. Near-op timal MST based Shape description using Genetic Algorithm. Pattern Recognition, 1995, 28: 571~579
[162]Esa Rahtu, mikko Salo, Janne HeikkilaAffine Invariant Pattern Recognition Using Multiscale Auto convolution[J]. IEEE Transactions on PAMI, 2005, 27(6): 908~918
[163]吴福朝.计算机视觉中的数学方法[M].北京:科学出版社, 2008: 344~345