可变形形状分析与识别中若干问题的研究
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摘要
计算机视觉、图像理解相关的研究方向是让机器“看”到世界的科学,涉及到神经生物学、信号处理、图像处理、机器学习等众多方向,是人工智能研究中的重要领域。与其相关的技术成果能极大的改变人类的生产和生活,可广泛应用于大至航空航天、工(农)业生产、军事国防,小至日常家居、医疗卫生、交通导航等各个方面。
形状是一种高级的视觉特征,是计算机视觉、图像理解等研究领域中最主要的研究内容之一。形状特征最重要的特点就是形状的可变形特性。为了解决形变大的形状匹配难的问题,本文主要从形状拓扑特性和形状的局部“子形状”两个层面入手,对可变形形状的点集对应关系、分类和相似性这几个方面进行了深入的研究,提出了全局拓扑信息的度量算法、灰度图像中计算形状轮廓长度的算法、基于子形状的形状分类以及基于子形状的形状相似度度量算法。
本文的主要研究工作如下：
1.提出了一种优先考虑整体拓扑性质的点集对应关系匹配算法。
传统点集匹配中难以处理拓扑一致而变形较大的形状,针对这一问题,先把形状转化为图,然后提出了能有效度量两个形状全局拓扑相似性的“加权伪公共路径”的概念；在此基础上,分析了传统基于优化的点集匹配算法的能量函数,总结得出点集匹配中都显式或隐式的含有点集的空间变换和局部邻接两种信息的结论；并由此设计了一种平衡全局拓扑相似性和局部形状相似性且可用动态规划求解的能量函数,该能量函数不仅能找到可变形形状的点集对应关系,还能估计可变形状除去整体形变影响下的相似度。实验结果表明相比于经典的点集匹配算法,考虑整体拓扑性质的模型能在点集匹配过程中保持可变形形状的整体拓扑不变性,不会因为形状形变大而失效。
2.提出了一种基于三次样条插值和像素灰度信息的形状轮廓长度估计算法。
应用三次样条拟合灰度剪影图像中局部轮廓边缘,再通过泰勒级数近似估计样条函数的弧长；整个计算过程避免了计算拟合形状轮廓的样条曲线的具体参数,仅用到了估计位置周围4列、若干行的像素值,具有线性计算复杂度；理论的误差分析表明在不同分辨率,随着像素收敛量化阶的降低,相对误差上限成指数级降低。实验结果表明,该算法相对于经典算法,在经典人工数据集上的相对误差更低；在模拟实际数据集上具有和人工数据上同数量级的相对误差；而且相对于经典B样条的估计算法,该算法随着图像分辨率的提高,相对误差稳定降低。
3.提出了一种基于子形状的形状分类算法。
针对可变形状的分类问题,应用子形状方法描述可变形形状或形状类,能排除含有遮蔽形状的影响。提出了基于最优公共部分距离的子形状描述算法,该算法不仅能用于形状匹配,还可以结合其他图像点集特征识别或匹配图像；提出“频繁形状类”的定义,应用互信息的方法,给出度量子形状类表示形状类能力的“二类区分度”定义；并提出了一种基于子形状类的形状分类算法。该算法提高了经典数据集上的可变形形状的按类检索率。
4.提出了一种基于子形状的形状相似度算法。
针对子形状能充分体现可变形形状的局部形状不变性的特点,提出了基于轮廓的子形状相似性度量算法；针对局部形状的关节变形问题,提出了基于区域的子形状相似性度量算法；并提出了结合两种子形状度量的算法：分别在适用于轮廓、区域的度量算法的形状部分应用对应的度量算法,以减小形变对形状相似度的“影响。该算法可以明显提高在经典数据集上可变形形状的检索率。
The related research of computer vision, image understanding aims to make themachine “see” the world. The research is the interdisciplinary of neurobiology, signalprocessing, image processing, machine learning, and is an important area of artificialintelligence. Theassociatedtechnologicalachievementscangreatlychangetheproduc-tion of human life, which can be widely used in aerospace, industrial and agriculturalproduction, militarydefense, household, healthcare, transportation, navigationandoth-er aspects.
Shape is an advanced visual feature, which is one of the most important research-es in the field of computer vision, image understanding. The most important featureof the shape is the deformation characteristics. In order to solve the difficulty defor-mation matching problem, in this paper, two levels start from the shape topologicalcharacteristics and the local sub-shape. The corresponding relationship, classificationand similarity of the set of points about the deformed shape are carried out in-depthresearch. We present the global topology information measure algorithm, the algorithmof calculating the contour length of shape in the gray-scale image, the shape classifica-tion method based on the sub-shape and the similarity measure algorithm based on thesub-shape.
The main works of this paper are as follows:
1. We propose a novel corresponding relationship matching method for the set ofpoints, which is priority considering global topological property of the set of points.
The traditional point set matching methods are difficult to deal with consistent andlarge deformation shape. To solve this problem, we first transform the shape into agraph, and then propose the concept,“weighted pseudo common path”, which can ef-fectively measure the global topology similarity of the two shapes; On this basis, we analysis the traditional point set matching algorithm based on the optimization of theenergy function, and summarize the conclusion that the point set matching explicitlyor implicitly containing a set of points of space transformation and local adjacency in-formation; And thus design an energy function balanced global topological similarityand local shape similarity, which can be used the available dynamic programming tosolve. The energy function can not only find the corresponding relationship of pointsset of the deformed shape, but also can be able to estimate the similarity except theglobal deformation influence. Comparing to the classic point set matching algorithm,the experimental results show that the proposed model in this paper can consider theglobal topological property of point set, which can maintain the global topology of thedeformable shape invariance in the matching process, thus it will not failure in the largedeformation case.
2. A contour length estimation algorithm for shape is proposed based on the cubicspline interpolation and the pixel gray information.
First using cubic spline fits the local contour gray silhouette image edge, and thearc length of the spline function is approximated by the Taylor series. The whole cal-culation process avoids the specific parameters of the calculated spline fitting shapecontour, and only use four columns around the estimated position and the pixel valueof certain row. The method has linear computational complexity. The theoretical er-ror analysis shows that, in different resolutions, the relative error ceiling exponentiallyreduced with the reduction of the pixel convergence quantization step. The experimen-tal result shows that, comparing with the classical algorithm, the relative error on theclassic artificial data sets is lower, and has the same order of magnitude relative erroron the simulation of the actual data set and on the manual data. And with respect tothe classic B-spline estimation algorithm, the algorithm with the improvement of imageresolution, the relative error stable reduced.
3. Proposed a shape Classification algorithm based on sub-shape.
For deformation shape classification, application sub-shape method describing thedeformable shape or class can get rid of containing the effects of shielding shape. Wepropose sub-shape description based on optimal public distance. This algorithm canbe used not only shape matching, but also can be combined with other image point set feature recognition or matching images; Propose the definition of “request shapeclasses”; Proposethenotionof“separationabilityof2classes”withMutualInformationwhich can distinguish shapes to2classes; And a shape classification algorithm basedon the sub-shape class is presented. The algorithm improves the retrieval rate of theclassic data set on the deformed shape class.
4. A Similarity algorithm based on sub-shape shape is proposed.
For the sub-shapes can fullyreflect the invariance characteristics of the local shapeofthedeformedshape, thesimilaritymeasurealgorithmbasedonthecontoursub-shapeis given in this paper. For the local shape of the joint deformation, the shape of the sub-region-basedsimilaritymeasurementalgorithmispresented. Andweproposealgorithmcombinedwiththeshapeofthetwosub-metrics: toreducetheimpactofthedeformationof shape similarity, in the contour and regional, measure the shapes of the part of thealgorithmcorrespondingtotheapplicationofmeasurementalgorithm,respectively. Thealgorithm can significantly improve the retrieval rate on the classic data set of deformedshape.
形状是一种高级的视觉特征,是计算机视觉、图像理解等研究领域中最主要的研究内容之一。形状特征最重要的特点就是形状的可变形特性。为了解决形变大的形状匹配难的问题,本文主要从形状拓扑特性和形状的局部“子形状”两个层面入手,对可变形形状的点集对应关系、分类和相似性这几个方面进行了深入的研究,提出了全局拓扑信息的度量算法、灰度图像中计算形状轮廓长度的算法、基于子形状的形状分类以及基于子形状的形状相似度度量算法。
本文的主要研究工作如下：
1.提出了一种优先考虑整体拓扑性质的点集对应关系匹配算法。
传统点集匹配中难以处理拓扑一致而变形较大的形状,针对这一问题,先把形状转化为图,然后提出了能有效度量两个形状全局拓扑相似性的“加权伪公共路径”的概念；在此基础上,分析了传统基于优化的点集匹配算法的能量函数,总结得出点集匹配中都显式或隐式的含有点集的空间变换和局部邻接两种信息的结论；并由此设计了一种平衡全局拓扑相似性和局部形状相似性且可用动态规划求解的能量函数,该能量函数不仅能找到可变形形状的点集对应关系,还能估计可变形状除去整体形变影响下的相似度。实验结果表明相比于经典的点集匹配算法,考虑整体拓扑性质的模型能在点集匹配过程中保持可变形形状的整体拓扑不变性,不会因为形状形变大而失效。
2.提出了一种基于三次样条插值和像素灰度信息的形状轮廓长度估计算法。
应用三次样条拟合灰度剪影图像中局部轮廓边缘,再通过泰勒级数近似估计样条函数的弧长；整个计算过程避免了计算拟合形状轮廓的样条曲线的具体参数,仅用到了估计位置周围4列、若干行的像素值,具有线性计算复杂度；理论的误差分析表明在不同分辨率,随着像素收敛量化阶的降低,相对误差上限成指数级降低。实验结果表明,该算法相对于经典算法,在经典人工数据集上的相对误差更低；在模拟实际数据集上具有和人工数据上同数量级的相对误差；而且相对于经典B样条的估计算法,该算法随着图像分辨率的提高,相对误差稳定降低。
3.提出了一种基于子形状的形状分类算法。
针对可变形状的分类问题,应用子形状方法描述可变形形状或形状类,能排除含有遮蔽形状的影响。提出了基于最优公共部分距离的子形状描述算法,该算法不仅能用于形状匹配,还可以结合其他图像点集特征识别或匹配图像；提出“频繁形状类”的定义,应用互信息的方法,给出度量子形状类表示形状类能力的“二类区分度”定义；并提出了一种基于子形状类的形状分类算法。该算法提高了经典数据集上的可变形形状的按类检索率。
4.提出了一种基于子形状的形状相似度算法。
针对子形状能充分体现可变形形状的局部形状不变性的特点,提出了基于轮廓的子形状相似性度量算法；针对局部形状的关节变形问题,提出了基于区域的子形状相似性度量算法；并提出了结合两种子形状度量的算法：分别在适用于轮廓、区域的度量算法的形状部分应用对应的度量算法,以减小形变对形状相似度的“影响。该算法可以明显提高在经典数据集上可变形形状的检索率。
The related research of computer vision, image understanding aims to make themachine “see” the world. The research is the interdisciplinary of neurobiology, signalprocessing, image processing, machine learning, and is an important area of artificialintelligence. Theassociatedtechnologicalachievementscangreatlychangetheproduc-tion of human life, which can be widely used in aerospace, industrial and agriculturalproduction, militarydefense, household, healthcare, transportation, navigationandoth-er aspects.
Shape is an advanced visual feature, which is one of the most important research-es in the field of computer vision, image understanding. The most important featureof the shape is the deformation characteristics. In order to solve the difficulty defor-mation matching problem, in this paper, two levels start from the shape topologicalcharacteristics and the local sub-shape. The corresponding relationship, classificationand similarity of the set of points about the deformed shape are carried out in-depthresearch. We present the global topology information measure algorithm, the algorithmof calculating the contour length of shape in the gray-scale image, the shape classifica-tion method based on the sub-shape and the similarity measure algorithm based on thesub-shape.
The main works of this paper are as follows:
1. We propose a novel corresponding relationship matching method for the set ofpoints, which is priority considering global topological property of the set of points.
The traditional point set matching methods are difficult to deal with consistent andlarge deformation shape. To solve this problem, we first transform the shape into agraph, and then propose the concept,“weighted pseudo common path”, which can ef-fectively measure the global topology similarity of the two shapes; On this basis, we analysis the traditional point set matching algorithm based on the optimization of theenergy function, and summarize the conclusion that the point set matching explicitlyor implicitly containing a set of points of space transformation and local adjacency in-formation; And thus design an energy function balanced global topological similarityand local shape similarity, which can be used the available dynamic programming tosolve. The energy function can not only find the corresponding relationship of pointsset of the deformed shape, but also can be able to estimate the similarity except theglobal deformation influence. Comparing to the classic point set matching algorithm,the experimental results show that the proposed model in this paper can consider theglobal topological property of point set, which can maintain the global topology of thedeformable shape invariance in the matching process, thus it will not failure in the largedeformation case.
2. A contour length estimation algorithm for shape is proposed based on the cubicspline interpolation and the pixel gray information.
First using cubic spline fits the local contour gray silhouette image edge, and thearc length of the spline function is approximated by the Taylor series. The whole cal-culation process avoids the specific parameters of the calculated spline fitting shapecontour, and only use four columns around the estimated position and the pixel valueof certain row. The method has linear computational complexity. The theoretical er-ror analysis shows that, in different resolutions, the relative error ceiling exponentiallyreduced with the reduction of the pixel convergence quantization step. The experimen-tal result shows that, comparing with the classical algorithm, the relative error on theclassic artificial data sets is lower, and has the same order of magnitude relative erroron the simulation of the actual data set and on the manual data. And with respect tothe classic B-spline estimation algorithm, the algorithm with the improvement of imageresolution, the relative error stable reduced.
3. Proposed a shape Classification algorithm based on sub-shape.
For deformation shape classification, application sub-shape method describing thedeformable shape or class can get rid of containing the effects of shielding shape. Wepropose sub-shape description based on optimal public distance. This algorithm canbe used not only shape matching, but also can be combined with other image point set feature recognition or matching images; Propose the definition of “request shapeclasses”; Proposethenotionof“separationabilityof2classes”withMutualInformationwhich can distinguish shapes to2classes; And a shape classification algorithm basedon the sub-shape class is presented. The algorithm improves the retrieval rate of theclassic data set on the deformed shape class.
4. A Similarity algorithm based on sub-shape shape is proposed.
For the sub-shapes can fullyreflect the invariance characteristics of the local shapeofthedeformedshape, thesimilaritymeasurealgorithmbasedonthecontoursub-shapeis given in this paper. For the local shape of the joint deformation, the shape of the sub-region-basedsimilaritymeasurementalgorithmispresented. Andweproposealgorithmcombinedwiththeshapeofthetwosub-metrics: toreducetheimpactofthedeformationof shape similarity, in the contour and regional, measure the shapes of the part of thealgorithmcorrespondingtotheapplicationofmeasurementalgorithm,respectively. Thealgorithm can significantly improve the retrieval rate on the classic data set of deformedshape.
引文
[1] Haralock R M, Shapiro L G. Computer and robot vision[M]. Addison-WesleyLongman Publishing Co., Inc.,1991.
[2] Nixon M, Aguado A S. Feature Extraction&Image Processing for ComputerVision[M]. Waltham: Academic Press,2012.
[3] Chatterji G, Menon P, Sridhar B. GPS/machine vision navigation system foraircraft[J]. Aerospace and Electronic Systems, IEEE Transactions on,1997,33(3):1012–1025.
[4] Su T H, Zhang T W, Guan D J, et al. Off-line recognition of realistic Chi-nese handwriting using segmentation-free strategy[J]. Pattern Recognition,2009,42(1):167–182.
[5] Meyer E A, Castellano R K, Diederich F. Interactions with aromatic rings inchemical and biological recognition[J]. Angewandte Chemie International Edi-tion,2003,42(11):1210–1250.
[6] Jarrett K, Kavukcuoglu K, Ranzato M, et al. What is the best multi-stage architec-ture for object recognition?[C]. Computer Vision,2009IEEE12th InternationalConference on. New York: IEEE:2146–2153.
[7] Torres R d S, Falc o A X, Gon alves M A, et al. A genetic programmingframework for content-based image retrieval[J]. Pattern Recognition,2009,42(2):283–292.
[8] Ke Y, Sukthankar R, Hebert M. Volumetric features for video event detection[J].International journal of computer vision,2010,88(3):339–362.
[9] Dhawan A P. Medical image analysis[M]. Wiley-IEEE Press,2011.
[10] Berg R, Kato K, Brown K, et al. Anti-Missile system and method: WIPO Patent2008108860[P].2008-9-13.
[11] Richards J A. Remote sensing digital image analysis: an introduction[M]. Berlin:Springer,2012.
[12] Datta R, Joshi D, Li J, et al. Image retrieval: Ideas, influences, and trends of thenew age[J]. ACM Computing Surveys (CSUR),2008,40(2):5.
[13] Smeulders A W M, Worring M, Santini S, et al. Content-based image retrievalat the end of the early years[J]. Pattern Analysis and Machine Intelligence, IEEETransactions on,2000,22(12):1349–1380.
[14] Rui Y, Huang T S, Chang S F. Image retrieval: Current techniques, promisingdirections, and open issues[J]. Journal of visual communication and image repre-sentation,1999,10(1):39–62.
[15] Shotton J, Blake A, Cipolla R. Multi-Scale categorical object recognition usingcontour fragments[J]. Pattern Analysis and Machine Intelligence, IEEE Transac-tions on,2008,30(7):1270–1281.
[16] Silson E H, McKeefry D J, Rodgers J, et al. Specialized and independent pro-cessing of orientation and shape in visual field maps LO1and LO2[J]. Natureneuroscience,2013.
[17] Moon H, Chellappa R, Rosenfeld A. Optimal edge-based shape detection[J]. Im-age Processing, IEEE Transactions on,2002,11(11):1209–1227.
[18] Haralick R M, Shapiro L G. Image segmentation techniques[J]. Computer vision,graphics, and image processing,1985,29(1):100–132.
[19] Shi J, Malik J. Normalized cuts and image segmentation[J]. Pattern Analysis andMachine Intelligence, IEEE Transactions on,2000,22(8):888–905.
[20] Freeman H. On the encoding of arbitrary geometric configurations[J]. ElectronicComputers, IRE Transactions on,1961(2):260–268.
[21] Iivarinen J, Visa A J E. Shape recognition of irregular objects[C]//PhotonicsEast’96. International Society for Optics and Photonics,1996:25-32.
[22] Grosky W I, Mehrotra R. Index-based object recognition in pictorial da-ta management[J]. Computer Vision, Graphics, and Image Processing,1990,52(3):416–436.
[23] Grosky W I, Neo P, Mehrotra R. A pictorial index mechanism for model-basedmatching[J]. Data&knowledge engineering,1992,8(4):309–327.
[24] Berretti S, Del Bimbo A, Pala P. Retrieval by shape similarity with perceptu-al distance and effective indexing[J]. Multimedia, IEEE Transactions on,2000,2(4):225–239.
[25] Cohen F S, Huang Z, Yang Z. Invariant matching and identification of curvesusing B-splines curve representation[J]. IEEE Transactions on Image Processing,1995,4(1):1–10.
[26] Cao F. A theory of shape identification[M]. Springer Verlag,2008.
[27] Belongie S, Malik J, Puzicha J. Shape Matching and Object Recognition UsingShape Contexts[J]. IEEE Transactions on Pattern Analysis and Machine Intelli-gence,2002,24(24):509–522.
[28] Sundar H, Silver D, Gagvani N, et al. Skeleton based shape matching and re-trieval[C]. Shape Modeling International,2003. New York: IEEE:130–139.
[29] Ling H, Jacobs D W. Shape classification using the inner-distance[J]. PatternAnalysis and Machine Intelligence, IEEE Transactions on,2007,29(2):286–299.
[30] Zhang D, Lu G. Review of shape representation and description techniques[J].Pattern recognition,2004,37(1):1–19.
[31] BlakeA,RotherC,BrownM,etal.Interactiveimagesegmentationusinganadap-tive GMMRF model[J]. Computer Vision-ECCV2004,2004:428–441.
[32] Mai F, Chang C Q, Hung Y S. Affine-invariant shape matching and recognitionunderpartialocclusion[C].ImageProcessing(ICIP),201017thIEEEInternation-al Conference on. New York: IEEE,2010:4605-4608.
[33] Young I T, Walker J E, Bowie J E. An analysis technique for biological shape.I[J]. Information and control,1974,25(4):357–370.
[34] Peura M, Iivarinen J. Efficiency of simple shape descriptors[C]. Proceedings ofthe third international workshop on visual form.1997:443-451.
[35] Freeman H. Shape description via the use of critical points[J]. Pattern Recogni-tion,1978,10(3):159–166.
[36] Parui S, Dutta Majumder D. Symmetry analysis by computer[J]. Pattern Recog-nition,1983,16(1):63–67.
[37] MehrotraR,GaryJE.Similar-shaperetrievalinshapedatamanagement[J].Com-puter,1995,28(9):57–62.
[38] Klette R, Kovalevsky V V, Yip B. Length estimation of digital curves[C]. SPIE’sInternational Symposium on Optical Science, Engineering, and Instrumentation.International Society for Optics and Photonics:117–128.
[39] Fu K. Syntactic image modeling using stochastic tree grammars[J]. ComputerGraphics and Image Processing,1980,12(2):136–152.
[40] Zhang D. Image retrieval based on shape[D]. Melbourne: Monash University,2002.
[41] Chetverikov D, Khenokh Y. Matching for shape defect detection[C]. ComputerAnalysis of Images and Patterns. Springer Berlin Heidelberg,1999:367-374.
[42] Babaud J, Witkin A P, Baudin M, et al. Uniqueness of the Gaussian kernel forscale-space filtering[J]. Pattern Analysis and Machine Intelligence, IEEE Trans-actions on,1986,8(1):26–33.
[43] Mokhtarian F, Mackworth A K. A theory of multiscale, curvature-based shaperepresentation for planar curves[J]. IEEE Transactions on Pattern Analysis andMachine Intelligence,1992,14(8):789–805.
[44] Mokhtarian F, Abbasi S, Kittler J. Efficient and robust retrieval by shape contentthrough curvature scale space[J]. Series on Software Engineering and KnowledgeEngineering,1997,8:51–58.
[45] Attalla E, Siy P. Robust shape similarity retrieval based on contour segmentationpolygonal multiresolution and elastic matching[J]. Pattern Recognition,2005,38(12):2229–2241.
[46] Bartolini I, Ciaccia P, Patella M. Warp: Accurate retrieval of shapes using phaseoffourierdescriptorsandtimewarpingdistance[J].PatternAnalysisandMachineIntelligence, IEEE Transactions on,2005,27(1):142–147.
[47] Peter A M, Rangarajan A. Maximum likelihood wavelet density estimation withapplications to image and shape matching[J]. Image Processing, IEEE Transac-tions on,2008,17(4):458–468.
[48] Peter A, Rangarajan A, Ho J. Shape L Ane rouge: Sliding wavelets for indexingand retrieval[C]. Computer Vision and Pattern Recognition,2008. CVPR2008.IEEE Conference on. New York: IEEE:1–8.
[49] Kashyap R, Chellappa R. Stochastic models for closed boundary analysis: Repre-sentationandreconstruction[J].InformationTheory, IEEETransactionson,1981,27(5):627–637.
[50] Davies E R. Machine vision: theory, algorithms, practicalities[M]. Morgan Kauf-mann,2004.
[51] VanOtterlooPJ.Acontour-orientedapproachtoshapeanalysis[M].PrenticeHallInternational (UK) Ltd.,1991.
[52] Amanatiadis A, Kaburlasos V G, Gasteratos A, et al. A comparative study of in-variantdescriptorsforshaperetrieval[C].ImagingSystemsandTechniques,2009.IST’09. IEEE International Workshop on. IEEE,2009:391-394.
[53] Rodrigues J J, Aguiar P, Xavier J. Ansig an analytic signature for permutation-invariant two-dimensional shape representation[C]. Computer Vision and PatternRecognition,2008. CVPR2008. IEEE Conference on. New York: IEEE:1–8.
[54] Xu C, Liu J, Tang X.2D Shape Matching by Contour Flexibility[J]. IEEE Trans-actions on Pattern Analysis and Machine Intelligence,2009,31(1):180–186.
[55] Mori G, Belongie S, Malik J. Efficient shape matching using shape con-texts[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2005,27(11):1832–1837.
[56] Wang J, Bai X, You X, et al. Shape matching and classification using height func-tions[J]. Pattern Recognition Letters,2011.
[57] Blum H. Biological shape and visual science (Part I)[J]. Journal of theoreticalBiology,1973,38(2):205–287.
[58] Gorelick L, Galun M, Sharon E, et al. Shape representation and classificationusing the poisson equation[J]. Pattern Analysis and Machine Intelligence, IEEETransactions on,2006,28(12):1991–2005.
[59] HlavacV,SonkaM,BoyleR.ImageProcessing, AnalysisandMachineVision[J].Brooks/Cole Thompson,1993,2.
[60] TeagueMR.Imageanalysisviathegeneraltheoryofmoments[J].OpticalSocietyof America, Journal,1980,70(8):920–930.
[61] Shapiro L G, Macdonald R S, Sternberg S R. Ordered structural shape matchingwith primitive extraction by mathematical morphology[J]. Pattern Recognition,1987,20(1):75–90.
[62] Latecki L J, Lakamper R, Eckhardt T. Shape descriptors for non-rigid shapes witha single closed contour[C]. Computer Vision and Pattern Recognition,2000. Pro-ceedings. IEEE Conference on. New York: IEEE1:424–429.
[63] S derkvist O. Computer vision classification of leaves from swedish trees[D].Link ping: Link ping University,2001.
[64] Leibe B, Schiele B. Analyzing appearance and contour based methods for objectcategorization[C]. Computer Vision and Pattern Recognition,2003. Proceedings.2003IEEE Computer Society Conference on. New York: IEEE2:II–409–15vol.2.
[65] Sebastian T B, Klein P N, Kimia B B. Recognition of shapes by editing theirshock graphs[J]. Pattern Analysis and Machine Intelligence, IEEE Transactionson,2004,26(5):550–571.
[66] Baseski E, Erdem A, Tari S. Dissimilarity between two skeletal trees in a contex-t[J]. Pattern Recognition,2009,42(3):370–385.
[67] Huang X, Paragios N, Metaxas D N. Shape registration in implicit spaces usinginformation theory and free form deformations[J]. Pattern Analysis and MachineIntelligence, IEEE Transactions on,2006,28(8):1303–1318.
[68] Besl P J, Mckay N D. A Method for Registration of3-D Shapes[J]. IEEE Trans-actions on Pattern Analysis and Machine Intelligence,1992,14(2):239–256.
[69] Li H, Shen T, Huang X. Approximately Global Optimization for Robust Align-ment of Generalized Shapes[J]. IEEE Transactions on Pattern Analysis and Ma-chine Intelligence,2011,33(6):1116–1130.
[70] Sebastian T B, Klein P N, Kimia B B. On Aligning Curves[J]. IEEE Transactionson Pattern Analysis and Machine Intelligence,2003,25(1):116–124.
[71] Chui H, Rangarajan A. A new algorithm for non-rigid point matching[C]. Com-puter Vision and Pattern Recognition,2000. Proceedings. IEEE Conference on.IEEE,2000,2:44-51.
[72] Chui H, Rangarajan A. A New Point Matching Algorithm for Non-rigid Regis-tration[J]. Computer Vision and Image Understanding,2003,89(2-3):114–141.
[73] ZhengY,DoermannD.RobustPointMatchingforNonrigidShapesbyPreservingLocal Neighborhood Structures[J]. IEEE Transactions on Pattern Analysis andMachine Intelligence,2006,28(4):643–649.
[74] Hibbard L S, Hawkins R A. Objective image alignment for three-dimensional re-constructionofdigitalautoradiograms[J].Journalofneurosciencemethods,1988,26(1):55–74.
[75] Ballard D H. Generalizing the Hough transform to detect arbitrary shapes[J]. Pat-tern recognition,1981,13(2):111–122.
[76] StockmanG.Objectrecognitionandlocalizationviaposeclustering[J].ComputerVision, Graphics, and Image Processing,1987,40(3):361–387.
[77] Huttenlocher D P, Klanderman G A, Rucklidge W J. Comparing images using theHausdorff distance[J]. Pattern Analysis and Machine Intelligence, IEEE Transac-tions on,1993,15(9):850–863.
[78] Baird H S. Model-based image matching using location[J].1985.
[79] Grimson W E L, Lozano-Perez T. Localizing overlapping parts by searching theinterpretation tree[J]. Pattern Analysis and Machine Intelligence, IEEE Transac-tions on,1987,9(4):469–482.
[80] Hummel R, Wolfson H. Affine invariant matching[C]. Science Applications In-ternational Corp, Proceedings: Image Understanding Workshop,.1988,1.
[81] Lamdan Y, Schwartz J T, Wolfson H J. Object recognition by affine invari-ant matching[C]. Computer Vision and Pattern Recognition,1988. ProceedingsCVPR’88., Computer Society Conference on. New York: IEEE:335–344.
[82] Metaxas D, Koh E, Badler N I. Multi-level shape representation using global de-formations and locally adaptive finite elements[J]. International journal of com-puter vision,1997,25(1):49–61.
[83] Sclaroff S, Pentland A P. Modal matching for correspondence and recogni-tion[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1995,17(6):545–561.
[84] Feldmar J, Ayache N. Rigid, affine and locally affine registration of free-formsurfaces[J]. International journal of computer vision,1996,18(2):99–119.
[85] Szeliski R, Lavallée S. Matching3-D anatomical surfaces with non-rigid defor-mations using octree-splines[J]. International journal of computer vision,1996,18(2):171–186.
[86] TagareHD,O’SheaD,RangarajanA.Ageometriccriterionforshape-basednon-rigidcorrespondence[C].ComputerVision,1995.Proceedings.,FifthInternation-al Conference on. New York: IEEE:434–439.
[87] Cootes T F, Taylor C J, Cooper D H, et al. Active shape models-their training andapplication[J]. Computer vision and image understanding,1995,61(1):38–59.
[88] Scott G L, Longuet-Higgins H C. An algorithm for associating the features oftwo images[J]. Proceedings of the Royal Society of London. Series B: BiologicalSciences,1991,244(1309):21–26.
[89] Shapiro L S, Michael Brady J. Feature-based correspondence: an eigenvectorapproach[J]. Image and vision computing,1992,10(5):283–288.
[90] Lohmann G, Von Cramon D Y. Automatic labelling of the human cortical surfaceusing sulcal basins[J]. Medical Image Analysis,2000,4(3):179.
[91] Cross A D J, Hancock E R. Graph matching with a dual-step EM algorith-m[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1998,20(11):1236–1253.
[92] Amit Y, Kong A. Graphical templates for model registration[J]. Pattern Analysisand Machine Intelligence, IEEE Transactions on,1996,18(3):225–236.
[93] Brown L G. A survey of image registration techniques[J]. ACM computing sur-veys (CSUR),1992,24(4):325–376.
[94] Chui H, Rambo J, Duncan J, et al. Registration of cortical anatomical structuresvia robust3D point matching[C]. Information Processing in Medical Imaging.Springer Berlin Heidelberg,1999:168-181.
[95] Rangarajan A, Chui H, Bookstein F. The softassign procrustes matching algorith-m[C]. Information Processing in Medical Imaging. Berlin: Springer:29–42.
[96] Widrow B. The “rubber-mask” technique I. Pattern measurement and analy-sis[J]. Pattern Recognition,1973,5(3):175–197.
[97] Chen L. Topological Structure in Visual Perception[J]. Science,1982,218(4573):699–700.
[98] Elzinga C H, Wang H. Kernels for Acyclic Digraphs[J]. Pattern Recognition Let-ters,2012,33(16).
[99] Chen L. The Topological Approach to perceptual organization[J]. Visual Cogni-tion,2005,12(4):553–637.
[100] Datta S, Limaye N, Nimbhorkar P, et al. Planar graph isomorphism is in log-space[C]. Computational Complexity,2009. CCC’09.24th Annual IEEE Confer-ence on. IEEE,2009:203-214.
[101] Cormen T H, Leiserson C E, Rivest R L, et al. Introduction to Algorithms[J].2009.
[102] Diestel R. Graph Theory.4rd[M]. Graduate Texts in Mathematics. Heidelberg:Springer-Verlag,2010.
[103] Coeurjolly D, Klette R. A comparative evaluation of length estimators of digi-tal curves[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2004,26(2):252–258.
[104] Sladoje N, Lindblad J. High-precision boundary length estimation by utiliz-ing gray-level information[J]. Pattern Analysis and Machine Intelligence, IEEETransactions on,2009,31(2):357–363.
[105] Hübler A, Klette R, Voss K. Determination of the convex hull of a finite set ofplanar points within linear time[J]. Elektronische Informationsverarbeitung undKybernetik,1981,17(2/3):121–139.
[106] Sloboda F, Zatko B. On one-dimensional grid continua in R2[R]. Technical re-port, Institute of Control Theory and Robotics, Slovak Academy of Sciences,Bratislava, Slovakia,1996.
[107] Wu L D. On the chain code of a line[J]. Pattern Analysis and Machine Intelli-gence, IEEE Transactions on,1982,4(3):347–353.
[108] Koplowitz J, Bruckstein A M. Design of perimeter estimators for digitized pla-nar shapes[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1989,11(6):611–622.
[109] Dorst L, Smeulders A W. Discrete straight line segments: parameters, primitivesand properties[J]. Ser. Contemp. Maths,1991,119:45–62.
[110] Debled-Rennesson I, Reveillès J P. A linear algorithm for segmentation of digitalcurves[J]. International Journal of Pattern Recognition and Artificial Intelligence,1995,9(04):635–662.
[111] Sloboda F, Zatko B, Stoer J. On approximation of planar one-dimensional con-tinua[J]. Advances in Digital and Computational Geometry,1998:113–160.
[112] Borgefors G. Distance transformations in digital images[J]. Computer vision,graphics, and image processing,1986,34(3):344–371.
[113] Dorst L, Smeulders A W. Length estimators for digitized contours[J]. ComputerVision, Graphics, and Image Processing,1987,40(3):311–333.
[114] Verwer B J. Local distances for distance transformations in two and three dimen-sions[J]. Pattern Recognition Letters,1991,12(11):671–682.
[115] Vossepoel A, Smeulders A. Vector code probability and metrication error in therepresentation of straight lines of finite length[J]. Computer Graphics and ImageProcessing,1982,20(4):347–364.
[116] Suhadolnik A, Petri i J, Kosel F. Digital Curve Length Calculation by UsingB-spline[J]. Journal of Mathematical Imaging and Vision,2010,38(2):132–138.
[117] Klette R, Rosenfeld A. Digital geometry: geometric methods for digital pictureanalysis[M]. Burlington: Morgan Kaufmann,2004.
[118] Farin G E. Curves and surfaces for CAGD: a practical guide[M]. Morgan Kauf-mann,2001.
[119] KletteR,YipB.Thelengthofdigitalcurves[R].Auckland: CITR,TheUniversityof Auckland, New Zealand,1999.
[120] Latecki L J, Lakaemper R, Wolter D. Optimal partial shape similarity[J]. Imageand Vision Computing,2005,23(2):227–236.
[121] Chen L, Feris R, Turk M. Efficient partial shape matching using smith-watermanalgorithm[C]. Computer Vision and Pattern Recognition Workshops,2008.CVPRW’08. IEEE Computer Society Conference on. IEEE,2008:1-6.
[122] Lakaemper R, Sobel M. Correspondences between parts of shapes with particlefilters[C]. Computer Vision and Pattern Recognition,2008. CVPR2008. IEEEConference on. New York: IEEE:1–8.
[123] Tanase M, Veltkamp R. Part-based shape retrieval with relevance feedback[C].MultimediaandExpo,2005.ICME2005.IEEEInternationalConferenceon.NewYork: IEEE:936–939.
[124] Saber E, Xu Y, Murat Tekalp A. Partial shape recognition by sub-matrix match-ing for partial matching guided image labeling[J]. Pattern Recognition,2005,38(10):1560–1573.
[125] Bai X, Yang X, Latecki L J. Detection and recognition of contour parts based onshape similarity[J]. Pattern Recognition,2008,41(7):2189–2199.
[126],,.研究[J].学,2012,38(6):889–910.
[127] Lowe D G. Object recognition from local scale-invariant features[C]. ComputerVision,1999. The Proceedings of the Seventh IEEE International Conference on.New York: IEEE2:1150–1157.
[128] Lowe D G. Distinctive image features from scale-invariant keypoints[J]. Inter-national journal of computer vision,2004,60(2):91–110.
[129] May M, Turner M, Morris T. Analysing false positives and3d structure to createintelligent thresholding and weighting functions for SIFT features[J]. Advancesin Image and Video Technology,2012:190–201.
[130] Han J, Kamber M, Pei J. Data Mining: Concepts and Techniques, Third Edi-tion[J].2011.
[131] Latecki L J, Lak mper R. Convexity rule for shape decomposition based on dis-crete contour evolution[J]. Computer Vision and Image Understanding,1999,73(3):441–454.
[132] SunKB,SuperBJ.Classificationofcontourshapesusingclasssegmentsets[C].Computer Vision and Pattern Recognition,2005. CVPR2005. IEEE ComputerSociety Conference on. New York: IEEE2:727–733.
[133] Egozi A, Keller Y, Guterman H. Improving shape retrieval by spectral match-ing and meta similarity[J]. Image Processing, IEEE Transactions on,2010,19(5):1319–1327.
[134] Bai X, Wang B, Yao C, et al. Co-transduction for shape retrieval[J]. Image Pro-cessing, IEEE Transactions on,2012,21(5):2747–2757.
[135] Yang X, Koknar-Tezel S, Latecki L J. Locally constrained diffusion process onlocally densified distance spaces with applications to shape retrieval[C]. Comput-er Vision and Pattern Recognition,2009. CVPR2009. IEEE Conference on. NewYork: IEEE:357–364.
[136] Lafon S, Lee A B. Diffusion maps and coarse-graining: A unified frame-work for dimensionality reduction, graph partitioning, and data set parameteriza-tion[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2006,28(9):1393–1403.
[137] Matousek J. Lectures on discrete geometry[M]. Vol.212. Berlin: Springer,2002.
[138] Jaakkola M S T. Partially labeled classification with Markov random walks[C].Advances in Neural Information Processing Systems14: Proceedings of the2002Conference. Cambridge: MIT Press2:945.
[139] Kontschieder P, Donoser M, Bischof H. Beyond pairwise shape similarity anal-ysis[J]. Computer Vision–ACCV2009,2010:655–666.
[140] Zhu X, Lafferty J, Rosenfeld R. Semi-supervised learning with graphs[D].Carnegie Mellon University, Language Technologies Institute, School of Com-puter Science,2005.
[141] Bai X, Yang X, Latecki L J, et al. Learning context-sensitive shape similarity bygraph transduction[J]. Pattern Analysis and Machine Intelligence, IEEE Transac-tions on,2010,32(5):861–874.
[142] Hein M, Maier M. Manifold denoising[J]. Advances in neural information pro-cessing systems,2007,19:561.
[143] Wang F, Zhang C, Shen H C, et al. Semi-supervised classification using linearneighborhood propagation[C]. Computer Vision and Pattern Recognition,2006IEEE Computer Society Conference on. New York: IEEE1:160–167.
[144] Lawrence N D, Jordan M I. Semi-supervised learning via Gaussian processes[J].Advances in neural information processing systems,2005,17:753–760.
[145] Vleugels J, Veltkamp R C. Efficient image retrieval through vantage objects[J].Pattern Recognition,2002,35(1):69–80.
[2] Nixon M, Aguado A S. Feature Extraction&Image Processing for ComputerVision[M]. Waltham: Academic Press,2012.
[3] Chatterji G, Menon P, Sridhar B. GPS/machine vision navigation system foraircraft[J]. Aerospace and Electronic Systems, IEEE Transactions on,1997,33(3):1012–1025.
[4] Su T H, Zhang T W, Guan D J, et al. Off-line recognition of realistic Chi-nese handwriting using segmentation-free strategy[J]. Pattern Recognition,2009,42(1):167–182.
[5] Meyer E A, Castellano R K, Diederich F. Interactions with aromatic rings inchemical and biological recognition[J]. Angewandte Chemie International Edi-tion,2003,42(11):1210–1250.
[6] Jarrett K, Kavukcuoglu K, Ranzato M, et al. What is the best multi-stage architec-ture for object recognition?[C]. Computer Vision,2009IEEE12th InternationalConference on. New York: IEEE:2146–2153.
[7] Torres R d S, Falc o A X, Gon alves M A, et al. A genetic programmingframework for content-based image retrieval[J]. Pattern Recognition,2009,42(2):283–292.
[8] Ke Y, Sukthankar R, Hebert M. Volumetric features for video event detection[J].International journal of computer vision,2010,88(3):339–362.
[9] Dhawan A P. Medical image analysis[M]. Wiley-IEEE Press,2011.
[10] Berg R, Kato K, Brown K, et al. Anti-Missile system and method: WIPO Patent2008108860[P].2008-9-13.
[11] Richards J A. Remote sensing digital image analysis: an introduction[M]. Berlin:Springer,2012.
[12] Datta R, Joshi D, Li J, et al. Image retrieval: Ideas, influences, and trends of thenew age[J]. ACM Computing Surveys (CSUR),2008,40(2):5.
[13] Smeulders A W M, Worring M, Santini S, et al. Content-based image retrievalat the end of the early years[J]. Pattern Analysis and Machine Intelligence, IEEETransactions on,2000,22(12):1349–1380.
[14] Rui Y, Huang T S, Chang S F. Image retrieval: Current techniques, promisingdirections, and open issues[J]. Journal of visual communication and image repre-sentation,1999,10(1):39–62.
[15] Shotton J, Blake A, Cipolla R. Multi-Scale categorical object recognition usingcontour fragments[J]. Pattern Analysis and Machine Intelligence, IEEE Transac-tions on,2008,30(7):1270–1281.
[16] Silson E H, McKeefry D J, Rodgers J, et al. Specialized and independent pro-cessing of orientation and shape in visual field maps LO1and LO2[J]. Natureneuroscience,2013.
[17] Moon H, Chellappa R, Rosenfeld A. Optimal edge-based shape detection[J]. Im-age Processing, IEEE Transactions on,2002,11(11):1209–1227.
[18] Haralick R M, Shapiro L G. Image segmentation techniques[J]. Computer vision,graphics, and image processing,1985,29(1):100–132.
[19] Shi J, Malik J. Normalized cuts and image segmentation[J]. Pattern Analysis andMachine Intelligence, IEEE Transactions on,2000,22(8):888–905.
[20] Freeman H. On the encoding of arbitrary geometric configurations[J]. ElectronicComputers, IRE Transactions on,1961(2):260–268.
[21] Iivarinen J, Visa A J E. Shape recognition of irregular objects[C]//PhotonicsEast’96. International Society for Optics and Photonics,1996:25-32.
[22] Grosky W I, Mehrotra R. Index-based object recognition in pictorial da-ta management[J]. Computer Vision, Graphics, and Image Processing,1990,52(3):416–436.
[23] Grosky W I, Neo P, Mehrotra R. A pictorial index mechanism for model-basedmatching[J]. Data&knowledge engineering,1992,8(4):309–327.
[24] Berretti S, Del Bimbo A, Pala P. Retrieval by shape similarity with perceptu-al distance and effective indexing[J]. Multimedia, IEEE Transactions on,2000,2(4):225–239.
[25] Cohen F S, Huang Z, Yang Z. Invariant matching and identification of curvesusing B-splines curve representation[J]. IEEE Transactions on Image Processing,1995,4(1):1–10.
[26] Cao F. A theory of shape identification[M]. Springer Verlag,2008.
[27] Belongie S, Malik J, Puzicha J. Shape Matching and Object Recognition UsingShape Contexts[J]. IEEE Transactions on Pattern Analysis and Machine Intelli-gence,2002,24(24):509–522.
[28] Sundar H, Silver D, Gagvani N, et al. Skeleton based shape matching and re-trieval[C]. Shape Modeling International,2003. New York: IEEE:130–139.
[29] Ling H, Jacobs D W. Shape classification using the inner-distance[J]. PatternAnalysis and Machine Intelligence, IEEE Transactions on,2007,29(2):286–299.
[30] Zhang D, Lu G. Review of shape representation and description techniques[J].Pattern recognition,2004,37(1):1–19.
[31] BlakeA,RotherC,BrownM,etal.Interactiveimagesegmentationusinganadap-tive GMMRF model[J]. Computer Vision-ECCV2004,2004:428–441.
[32] Mai F, Chang C Q, Hung Y S. Affine-invariant shape matching and recognitionunderpartialocclusion[C].ImageProcessing(ICIP),201017thIEEEInternation-al Conference on. New York: IEEE,2010:4605-4608.
[33] Young I T, Walker J E, Bowie J E. An analysis technique for biological shape.I[J]. Information and control,1974,25(4):357–370.
[34] Peura M, Iivarinen J. Efficiency of simple shape descriptors[C]. Proceedings ofthe third international workshop on visual form.1997:443-451.
[35] Freeman H. Shape description via the use of critical points[J]. Pattern Recogni-tion,1978,10(3):159–166.
[36] Parui S, Dutta Majumder D. Symmetry analysis by computer[J]. Pattern Recog-nition,1983,16(1):63–67.
[37] MehrotraR,GaryJE.Similar-shaperetrievalinshapedatamanagement[J].Com-puter,1995,28(9):57–62.
[38] Klette R, Kovalevsky V V, Yip B. Length estimation of digital curves[C]. SPIE’sInternational Symposium on Optical Science, Engineering, and Instrumentation.International Society for Optics and Photonics:117–128.
[39] Fu K. Syntactic image modeling using stochastic tree grammars[J]. ComputerGraphics and Image Processing,1980,12(2):136–152.
[40] Zhang D. Image retrieval based on shape[D]. Melbourne: Monash University,2002.
[41] Chetverikov D, Khenokh Y. Matching for shape defect detection[C]. ComputerAnalysis of Images and Patterns. Springer Berlin Heidelberg,1999:367-374.
[42] Babaud J, Witkin A P, Baudin M, et al. Uniqueness of the Gaussian kernel forscale-space filtering[J]. Pattern Analysis and Machine Intelligence, IEEE Trans-actions on,1986,8(1):26–33.
[43] Mokhtarian F, Mackworth A K. A theory of multiscale, curvature-based shaperepresentation for planar curves[J]. IEEE Transactions on Pattern Analysis andMachine Intelligence,1992,14(8):789–805.
[44] Mokhtarian F, Abbasi S, Kittler J. Efficient and robust retrieval by shape contentthrough curvature scale space[J]. Series on Software Engineering and KnowledgeEngineering,1997,8:51–58.
[45] Attalla E, Siy P. Robust shape similarity retrieval based on contour segmentationpolygonal multiresolution and elastic matching[J]. Pattern Recognition,2005,38(12):2229–2241.
[46] Bartolini I, Ciaccia P, Patella M. Warp: Accurate retrieval of shapes using phaseoffourierdescriptorsandtimewarpingdistance[J].PatternAnalysisandMachineIntelligence, IEEE Transactions on,2005,27(1):142–147.
[47] Peter A M, Rangarajan A. Maximum likelihood wavelet density estimation withapplications to image and shape matching[J]. Image Processing, IEEE Transac-tions on,2008,17(4):458–468.
[48] Peter A, Rangarajan A, Ho J. Shape L Ane rouge: Sliding wavelets for indexingand retrieval[C]. Computer Vision and Pattern Recognition,2008. CVPR2008.IEEE Conference on. New York: IEEE:1–8.
[49] Kashyap R, Chellappa R. Stochastic models for closed boundary analysis: Repre-sentationandreconstruction[J].InformationTheory, IEEETransactionson,1981,27(5):627–637.
[50] Davies E R. Machine vision: theory, algorithms, practicalities[M]. Morgan Kauf-mann,2004.
[51] VanOtterlooPJ.Acontour-orientedapproachtoshapeanalysis[M].PrenticeHallInternational (UK) Ltd.,1991.
[52] Amanatiadis A, Kaburlasos V G, Gasteratos A, et al. A comparative study of in-variantdescriptorsforshaperetrieval[C].ImagingSystemsandTechniques,2009.IST’09. IEEE International Workshop on. IEEE,2009:391-394.
[53] Rodrigues J J, Aguiar P, Xavier J. Ansig an analytic signature for permutation-invariant two-dimensional shape representation[C]. Computer Vision and PatternRecognition,2008. CVPR2008. IEEE Conference on. New York: IEEE:1–8.
[54] Xu C, Liu J, Tang X.2D Shape Matching by Contour Flexibility[J]. IEEE Trans-actions on Pattern Analysis and Machine Intelligence,2009,31(1):180–186.
[55] Mori G, Belongie S, Malik J. Efficient shape matching using shape con-texts[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2005,27(11):1832–1837.
[56] Wang J, Bai X, You X, et al. Shape matching and classification using height func-tions[J]. Pattern Recognition Letters,2011.
[57] Blum H. Biological shape and visual science (Part I)[J]. Journal of theoreticalBiology,1973,38(2):205–287.
[58] Gorelick L, Galun M, Sharon E, et al. Shape representation and classificationusing the poisson equation[J]. Pattern Analysis and Machine Intelligence, IEEETransactions on,2006,28(12):1991–2005.
[59] HlavacV,SonkaM,BoyleR.ImageProcessing, AnalysisandMachineVision[J].Brooks/Cole Thompson,1993,2.
[60] TeagueMR.Imageanalysisviathegeneraltheoryofmoments[J].OpticalSocietyof America, Journal,1980,70(8):920–930.
[61] Shapiro L G, Macdonald R S, Sternberg S R. Ordered structural shape matchingwith primitive extraction by mathematical morphology[J]. Pattern Recognition,1987,20(1):75–90.
[62] Latecki L J, Lakamper R, Eckhardt T. Shape descriptors for non-rigid shapes witha single closed contour[C]. Computer Vision and Pattern Recognition,2000. Pro-ceedings. IEEE Conference on. New York: IEEE1:424–429.
[63] S derkvist O. Computer vision classification of leaves from swedish trees[D].Link ping: Link ping University,2001.
[64] Leibe B, Schiele B. Analyzing appearance and contour based methods for objectcategorization[C]. Computer Vision and Pattern Recognition,2003. Proceedings.2003IEEE Computer Society Conference on. New York: IEEE2:II–409–15vol.2.
[65] Sebastian T B, Klein P N, Kimia B B. Recognition of shapes by editing theirshock graphs[J]. Pattern Analysis and Machine Intelligence, IEEE Transactionson,2004,26(5):550–571.
[66] Baseski E, Erdem A, Tari S. Dissimilarity between two skeletal trees in a contex-t[J]. Pattern Recognition,2009,42(3):370–385.
[67] Huang X, Paragios N, Metaxas D N. Shape registration in implicit spaces usinginformation theory and free form deformations[J]. Pattern Analysis and MachineIntelligence, IEEE Transactions on,2006,28(8):1303–1318.
[68] Besl P J, Mckay N D. A Method for Registration of3-D Shapes[J]. IEEE Trans-actions on Pattern Analysis and Machine Intelligence,1992,14(2):239–256.
[69] Li H, Shen T, Huang X. Approximately Global Optimization for Robust Align-ment of Generalized Shapes[J]. IEEE Transactions on Pattern Analysis and Ma-chine Intelligence,2011,33(6):1116–1130.
[70] Sebastian T B, Klein P N, Kimia B B. On Aligning Curves[J]. IEEE Transactionson Pattern Analysis and Machine Intelligence,2003,25(1):116–124.
[71] Chui H, Rangarajan A. A new algorithm for non-rigid point matching[C]. Com-puter Vision and Pattern Recognition,2000. Proceedings. IEEE Conference on.IEEE,2000,2:44-51.
[72] Chui H, Rangarajan A. A New Point Matching Algorithm for Non-rigid Regis-tration[J]. Computer Vision and Image Understanding,2003,89(2-3):114–141.
[73] ZhengY,DoermannD.RobustPointMatchingforNonrigidShapesbyPreservingLocal Neighborhood Structures[J]. IEEE Transactions on Pattern Analysis andMachine Intelligence,2006,28(4):643–649.
[74] Hibbard L S, Hawkins R A. Objective image alignment for three-dimensional re-constructionofdigitalautoradiograms[J].Journalofneurosciencemethods,1988,26(1):55–74.
[75] Ballard D H. Generalizing the Hough transform to detect arbitrary shapes[J]. Pat-tern recognition,1981,13(2):111–122.
[76] StockmanG.Objectrecognitionandlocalizationviaposeclustering[J].ComputerVision, Graphics, and Image Processing,1987,40(3):361–387.
[77] Huttenlocher D P, Klanderman G A, Rucklidge W J. Comparing images using theHausdorff distance[J]. Pattern Analysis and Machine Intelligence, IEEE Transac-tions on,1993,15(9):850–863.
[78] Baird H S. Model-based image matching using location[J].1985.
[79] Grimson W E L, Lozano-Perez T. Localizing overlapping parts by searching theinterpretation tree[J]. Pattern Analysis and Machine Intelligence, IEEE Transac-tions on,1987,9(4):469–482.
[80] Hummel R, Wolfson H. Affine invariant matching[C]. Science Applications In-ternational Corp, Proceedings: Image Understanding Workshop,.1988,1.
[81] Lamdan Y, Schwartz J T, Wolfson H J. Object recognition by affine invari-ant matching[C]. Computer Vision and Pattern Recognition,1988. ProceedingsCVPR’88., Computer Society Conference on. New York: IEEE:335–344.
[82] Metaxas D, Koh E, Badler N I. Multi-level shape representation using global de-formations and locally adaptive finite elements[J]. International journal of com-puter vision,1997,25(1):49–61.
[83] Sclaroff S, Pentland A P. Modal matching for correspondence and recogni-tion[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1995,17(6):545–561.
[84] Feldmar J, Ayache N. Rigid, affine and locally affine registration of free-formsurfaces[J]. International journal of computer vision,1996,18(2):99–119.
[85] Szeliski R, Lavallée S. Matching3-D anatomical surfaces with non-rigid defor-mations using octree-splines[J]. International journal of computer vision,1996,18(2):171–186.
[86] TagareHD,O’SheaD,RangarajanA.Ageometriccriterionforshape-basednon-rigidcorrespondence[C].ComputerVision,1995.Proceedings.,FifthInternation-al Conference on. New York: IEEE:434–439.
[87] Cootes T F, Taylor C J, Cooper D H, et al. Active shape models-their training andapplication[J]. Computer vision and image understanding,1995,61(1):38–59.
[88] Scott G L, Longuet-Higgins H C. An algorithm for associating the features oftwo images[J]. Proceedings of the Royal Society of London. Series B: BiologicalSciences,1991,244(1309):21–26.
[89] Shapiro L S, Michael Brady J. Feature-based correspondence: an eigenvectorapproach[J]. Image and vision computing,1992,10(5):283–288.
[90] Lohmann G, Von Cramon D Y. Automatic labelling of the human cortical surfaceusing sulcal basins[J]. Medical Image Analysis,2000,4(3):179.
[91] Cross A D J, Hancock E R. Graph matching with a dual-step EM algorith-m[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1998,20(11):1236–1253.
[92] Amit Y, Kong A. Graphical templates for model registration[J]. Pattern Analysisand Machine Intelligence, IEEE Transactions on,1996,18(3):225–236.
[93] Brown L G. A survey of image registration techniques[J]. ACM computing sur-veys (CSUR),1992,24(4):325–376.
[94] Chui H, Rambo J, Duncan J, et al. Registration of cortical anatomical structuresvia robust3D point matching[C]. Information Processing in Medical Imaging.Springer Berlin Heidelberg,1999:168-181.
[95] Rangarajan A, Chui H, Bookstein F. The softassign procrustes matching algorith-m[C]. Information Processing in Medical Imaging. Berlin: Springer:29–42.
[96] Widrow B. The “rubber-mask” technique I. Pattern measurement and analy-sis[J]. Pattern Recognition,1973,5(3):175–197.
[97] Chen L. Topological Structure in Visual Perception[J]. Science,1982,218(4573):699–700.
[98] Elzinga C H, Wang H. Kernels for Acyclic Digraphs[J]. Pattern Recognition Let-ters,2012,33(16).
[99] Chen L. The Topological Approach to perceptual organization[J]. Visual Cogni-tion,2005,12(4):553–637.
[100] Datta S, Limaye N, Nimbhorkar P, et al. Planar graph isomorphism is in log-space[C]. Computational Complexity,2009. CCC’09.24th Annual IEEE Confer-ence on. IEEE,2009:203-214.
[101] Cormen T H, Leiserson C E, Rivest R L, et al. Introduction to Algorithms[J].2009.
[102] Diestel R. Graph Theory.4rd[M]. Graduate Texts in Mathematics. Heidelberg:Springer-Verlag,2010.
[103] Coeurjolly D, Klette R. A comparative evaluation of length estimators of digi-tal curves[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2004,26(2):252–258.
[104] Sladoje N, Lindblad J. High-precision boundary length estimation by utiliz-ing gray-level information[J]. Pattern Analysis and Machine Intelligence, IEEETransactions on,2009,31(2):357–363.
[105] Hübler A, Klette R, Voss K. Determination of the convex hull of a finite set ofplanar points within linear time[J]. Elektronische Informationsverarbeitung undKybernetik,1981,17(2/3):121–139.
[106] Sloboda F, Zatko B. On one-dimensional grid continua in R2[R]. Technical re-port, Institute of Control Theory and Robotics, Slovak Academy of Sciences,Bratislava, Slovakia,1996.
[107] Wu L D. On the chain code of a line[J]. Pattern Analysis and Machine Intelli-gence, IEEE Transactions on,1982,4(3):347–353.
[108] Koplowitz J, Bruckstein A M. Design of perimeter estimators for digitized pla-nar shapes[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1989,11(6):611–622.
[109] Dorst L, Smeulders A W. Discrete straight line segments: parameters, primitivesand properties[J]. Ser. Contemp. Maths,1991,119:45–62.
[110] Debled-Rennesson I, Reveillès J P. A linear algorithm for segmentation of digitalcurves[J]. International Journal of Pattern Recognition and Artificial Intelligence,1995,9(04):635–662.
[111] Sloboda F, Zatko B, Stoer J. On approximation of planar one-dimensional con-tinua[J]. Advances in Digital and Computational Geometry,1998:113–160.
[112] Borgefors G. Distance transformations in digital images[J]. Computer vision,graphics, and image processing,1986,34(3):344–371.
[113] Dorst L, Smeulders A W. Length estimators for digitized contours[J]. ComputerVision, Graphics, and Image Processing,1987,40(3):311–333.
[114] Verwer B J. Local distances for distance transformations in two and three dimen-sions[J]. Pattern Recognition Letters,1991,12(11):671–682.
[115] Vossepoel A, Smeulders A. Vector code probability and metrication error in therepresentation of straight lines of finite length[J]. Computer Graphics and ImageProcessing,1982,20(4):347–364.
[116] Suhadolnik A, Petri i J, Kosel F. Digital Curve Length Calculation by UsingB-spline[J]. Journal of Mathematical Imaging and Vision,2010,38(2):132–138.
[117] Klette R, Rosenfeld A. Digital geometry: geometric methods for digital pictureanalysis[M]. Burlington: Morgan Kaufmann,2004.
[118] Farin G E. Curves and surfaces for CAGD: a practical guide[M]. Morgan Kauf-mann,2001.
[119] KletteR,YipB.Thelengthofdigitalcurves[R].Auckland: CITR,TheUniversityof Auckland, New Zealand,1999.
[120] Latecki L J, Lakaemper R, Wolter D. Optimal partial shape similarity[J]. Imageand Vision Computing,2005,23(2):227–236.
[121] Chen L, Feris R, Turk M. Efficient partial shape matching using smith-watermanalgorithm[C]. Computer Vision and Pattern Recognition Workshops,2008.CVPRW’08. IEEE Computer Society Conference on. IEEE,2008:1-6.
[122] Lakaemper R, Sobel M. Correspondences between parts of shapes with particlefilters[C]. Computer Vision and Pattern Recognition,2008. CVPR2008. IEEEConference on. New York: IEEE:1–8.
[123] Tanase M, Veltkamp R. Part-based shape retrieval with relevance feedback[C].MultimediaandExpo,2005.ICME2005.IEEEInternationalConferenceon.NewYork: IEEE:936–939.
[124] Saber E, Xu Y, Murat Tekalp A. Partial shape recognition by sub-matrix match-ing for partial matching guided image labeling[J]. Pattern Recognition,2005,38(10):1560–1573.
[125] Bai X, Yang X, Latecki L J. Detection and recognition of contour parts based onshape similarity[J]. Pattern Recognition,2008,41(7):2189–2199.
[126],,.研究[J].学,2012,38(6):889–910.
[127] Lowe D G. Object recognition from local scale-invariant features[C]. ComputerVision,1999. The Proceedings of the Seventh IEEE International Conference on.New York: IEEE2:1150–1157.
[128] Lowe D G. Distinctive image features from scale-invariant keypoints[J]. Inter-national journal of computer vision,2004,60(2):91–110.
[129] May M, Turner M, Morris T. Analysing false positives and3d structure to createintelligent thresholding and weighting functions for SIFT features[J]. Advancesin Image and Video Technology,2012:190–201.
[130] Han J, Kamber M, Pei J. Data Mining: Concepts and Techniques, Third Edi-tion[J].2011.
[131] Latecki L J, Lak mper R. Convexity rule for shape decomposition based on dis-crete contour evolution[J]. Computer Vision and Image Understanding,1999,73(3):441–454.
[132] SunKB,SuperBJ.Classificationofcontourshapesusingclasssegmentsets[C].Computer Vision and Pattern Recognition,2005. CVPR2005. IEEE ComputerSociety Conference on. New York: IEEE2:727–733.
[133] Egozi A, Keller Y, Guterman H. Improving shape retrieval by spectral match-ing and meta similarity[J]. Image Processing, IEEE Transactions on,2010,19(5):1319–1327.
[134] Bai X, Wang B, Yao C, et al. Co-transduction for shape retrieval[J]. Image Pro-cessing, IEEE Transactions on,2012,21(5):2747–2757.
[135] Yang X, Koknar-Tezel S, Latecki L J. Locally constrained diffusion process onlocally densified distance spaces with applications to shape retrieval[C]. Comput-er Vision and Pattern Recognition,2009. CVPR2009. IEEE Conference on. NewYork: IEEE:357–364.
[136] Lafon S, Lee A B. Diffusion maps and coarse-graining: A unified frame-work for dimensionality reduction, graph partitioning, and data set parameteriza-tion[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2006,28(9):1393–1403.
[137] Matousek J. Lectures on discrete geometry[M]. Vol.212. Berlin: Springer,2002.
[138] Jaakkola M S T. Partially labeled classification with Markov random walks[C].Advances in Neural Information Processing Systems14: Proceedings of the2002Conference. Cambridge: MIT Press2:945.
[139] Kontschieder P, Donoser M, Bischof H. Beyond pairwise shape similarity anal-ysis[J]. Computer Vision–ACCV2009,2010:655–666.
[140] Zhu X, Lafferty J, Rosenfeld R. Semi-supervised learning with graphs[D].Carnegie Mellon University, Language Technologies Institute, School of Com-puter Science,2005.
[141] Bai X, Yang X, Latecki L J, et al. Learning context-sensitive shape similarity bygraph transduction[J]. Pattern Analysis and Machine Intelligence, IEEE Transac-tions on,2010,32(5):861–874.
[142] Hein M, Maier M. Manifold denoising[J]. Advances in neural information pro-cessing systems,2007,19:561.
[143] Wang F, Zhang C, Shen H C, et al. Semi-supervised classification using linearneighborhood propagation[C]. Computer Vision and Pattern Recognition,2006IEEE Computer Society Conference on. New York: IEEE1:160–167.
[144] Lawrence N D, Jordan M I. Semi-supervised learning via Gaussian processes[J].Advances in neural information processing systems,2005,17:753–760.
[145] Vleugels J, Veltkamp R C. Efficient image retrieval through vantage objects[J].Pattern Recognition,2002,35(1):69–80.