融合全局与局部信息的形状轮廓特征分析与匹配
|
摘要
形状是一种高层次的视觉特征,在计算机视觉、图像分析与理解等领域中常用于表达目标物体。形状的关键性和重要性,使得形状表示和形状匹配成为计算机视觉领域中的基础性问题。虽然由于日常生活中同类物体形状的复杂多变性,使得形状匹配面临着许多困难,但长期以来在学者们的不懈研究下,已产生出一大批经典的形状表示技术和形状匹配算法。到目前为止,形状匹配仍然是计算机视觉和图像分析领域的前沿和热点问题。
本文考察了形状匹配技术的发展历程,并发现：目前已有的形状描述子均未能简单有效的将局部与全局形状信息结合起来。针对这一问题,本文分别从局部特征和全局特征的定义出发丌展研究,并提出了一种能够将这两者有机结合起来的框架,定义了性能上更为优越的轮廓描述子。本文的研究成果主要有：
(1)提出了有效的局部特征
局部特征是定义形状描述子的基础,它不仅需要准确的描述形状的特性,而且要在线性变换(平移、旋转、尺度缩放)下保持不变。本文从轮廓点的相对几何关系出发,从不同的角度分别定义了数种有效的局部特征,如特征三角形、高度函数等。这些局部特征都能够较为准确的表示形状,并且能够在线性变换下保持不变性,从而为定义有效的形状描述子打下了坚实的基础。
(2)提出了有效的全局特征
全局特征是形状描述子所蕴含的重要信息,它直接关系到描述子对噪声或局部形变等因素的抵御能力。本文通过借鉴形状匹配算法的经验,创造性的将轮廓的顺序关系定义为全局形状特征,并将它与局部特征有机结合起来。本文是轮廓的顺序关系首次作为形状特征在形状描述子中得到使用和体现。事实证明,轮廓的顺序关系不仅能够作为约束条件应用于形状匹配算法中,也完全可以作为形状特征融合在形状描述子中,并能显著提高描述子的描述性能。
(3)提出了局部与全局形状特征的有机结合框架
只有将局部与全局形状特征相结合,才能使所定义的描述子兼具有刻画形状的准确性和对抗噪声的稳定性。本文提出一种新的描述子定义框架,该框架能够将局部与全局特征有机结合在一起。我们发现,利用轮廓的顺序关系对局部特征进行处理,将局部特征根据轮廓顺序关系排列成一个序列,能够自然的将这两种性质不同的特征有机结合起来。与多尺度描述子和多方面描述子相比,本文所定义的描述子能够有效克服已有描述子不易使用或信息不全等问题,本文方法同时含有局部与全局信息,且简单易用。
(4)提出了三种新型的有效的形状描述子
在特征三角形、形状上下文、高度函数等有效的局部特征基础上,结合轮廓的顺序关系,构造了三种新的轮廓描述子。实验结果表明,这些方法均能取得较高的形状检索准确率,特别是基于高度函数的轮廓描述子,该方法能够取得到目前为止所有描述子中国际上最高的形状检索准确率(在标准测试集MPEG-7数据库上,仅靠描述子的检索精度可达90.35%,结合图转导算法后检索精度可达96.45%)。同时,这些描述子几何意义明确,易于计算、维度低,其综合性能超越了常用的轮廓描述算法。
本文对基于轮廓的形状表示技术展丌了深入研究,敏锐的抓住了轮廓的顺序关系这一核心而本质的全局形状特征,通过将不同的局部特征与轮廓顺序信息相结合的方式,提出了数种几何意义明确、描述性强、表达准确、计算复杂度适中的轮廓描述子,在形状匹配这一计算机视觉领域的关键问题上取得了进展,相关成果已经得到了大量的实验证明。本文所提出的算法对于其它视觉理论及应用也有一定的启发性。
Shape, as a high-level visual characteristic, has been frequently used to represent the properties of objects in Computer Vision, Image Analysis and Understanding. Shape is a kind of critical and fundamental feature, and shape representation/matching has become one basic problem in the field of Computer Vision. Because of serious intra-class variances among object shapes in our life, there are a lot of difficulties when performing shape matching. However, a huge number of classical shape representation technologies and shape matching algorithms have appeared by hard works of researchers. Shape matching is still one of the leading and hot topics in Computer Vision and Image Analysis so far.
In this thesis, the development of shape matching technologies is reviewed, and it is found that none of current descriptors is able to combine local and global features effectively and efficiently. Accordingly, some researches are performed on how to define local and global features, and a framework to naturally combine these two issues is presented, resulting in some novel descriptors with better performances. The main contributions of this thesis are summarized as follows:
First, some effective local features are proposed. Local features are fundamental for defining shape descriptors. Local features should give a precise description for shape contours, and remain unchanged under linear transformations (translation, rotation, and scaling). Based on the geometric relationship between contour points, several local features, such as feature triangle and height functions, are defined to represent different aspects of shape contours. These local features are able to represent shapes exactly, and achieve linear transformation invariance. They provide a solid basis for presenting effective shape descriptors.
Second, some effective global feature is proposed. Global features are important issues contained in shape descriptors. They directly determine the robustness of shape descriptors to noise and local deformations. Based on the experience of shape matching algorithms, the order sequential information of contours is creatively defined as the global feature. This is the first time for contour order information to be treated as shape feature used in shape descriptors. It is proved that the contour order information can be used not only as constraints in shape matching algorithms but also as shape features in shape descriptors. It is able to help significantly improve the performance of descriptors.
Third, a new framework to combine local and global shape features is presented. Shape descriptors will never become not only description precisely but also robust to noise until both local and global features are combined together. It is discovered that after local features are rearranged according to the contour order information, the local and global features are naturally combined. Compared with current multi-scale or multi-aspect descriptors, the proposed methods are able to overcome the problems of usage difficulties and lack of shape information. The proposed descriptors include both local and global shape information, and they are easy to use and compute as well.
Fourth, three novel shape descriptors are presented. Based on the local features of feature triangles, shape contexts and height functions, combined with contour order information, three novel shape descriptors are constructed correspondingly. The experimental results show that the proposed methods are all able to achieve excellent shape retrieval rates. Especially for height functions, it is able to get the highest accuracy rate of shape retrieval among all descriptors all over the world. It achieves on the well-known MPEG-7 shape benchmark the best ever high rate of 90.35% only by the descriptor and 96.45% when combing with the graph transduction algorithm. What is more, each of these descriptors has a definite geometric meaning, is efficient to compute, and has a low feature dimension. The general performances of them outperform other widely used shape description algorithms.
In this thesis, contour based shape representation is carefully studied and the contour sequential information (a kind of global feature) is regarded as the core and fundamental shape characteristic. Several contour descriptors with clear geometric meaning, high discriminative power, precise representation and moderate computational complexity are presented by combining the sequential information with different local shape features. Some successes are obtained for shape matching, which is one of the key problems in the field of Computer Vision, and these successes are already confirmed by extensive experimentations. Some vision theories and applications can also benefit from the studies and algorithms proposed in this thesis.
本文考察了形状匹配技术的发展历程,并发现：目前已有的形状描述子均未能简单有效的将局部与全局形状信息结合起来。针对这一问题,本文分别从局部特征和全局特征的定义出发丌展研究,并提出了一种能够将这两者有机结合起来的框架,定义了性能上更为优越的轮廓描述子。本文的研究成果主要有：
(1)提出了有效的局部特征
局部特征是定义形状描述子的基础,它不仅需要准确的描述形状的特性,而且要在线性变换(平移、旋转、尺度缩放)下保持不变。本文从轮廓点的相对几何关系出发,从不同的角度分别定义了数种有效的局部特征,如特征三角形、高度函数等。这些局部特征都能够较为准确的表示形状,并且能够在线性变换下保持不变性,从而为定义有效的形状描述子打下了坚实的基础。
(2)提出了有效的全局特征
全局特征是形状描述子所蕴含的重要信息,它直接关系到描述子对噪声或局部形变等因素的抵御能力。本文通过借鉴形状匹配算法的经验,创造性的将轮廓的顺序关系定义为全局形状特征,并将它与局部特征有机结合起来。本文是轮廓的顺序关系首次作为形状特征在形状描述子中得到使用和体现。事实证明,轮廓的顺序关系不仅能够作为约束条件应用于形状匹配算法中,也完全可以作为形状特征融合在形状描述子中,并能显著提高描述子的描述性能。
(3)提出了局部与全局形状特征的有机结合框架
只有将局部与全局形状特征相结合,才能使所定义的描述子兼具有刻画形状的准确性和对抗噪声的稳定性。本文提出一种新的描述子定义框架,该框架能够将局部与全局特征有机结合在一起。我们发现,利用轮廓的顺序关系对局部特征进行处理,将局部特征根据轮廓顺序关系排列成一个序列,能够自然的将这两种性质不同的特征有机结合起来。与多尺度描述子和多方面描述子相比,本文所定义的描述子能够有效克服已有描述子不易使用或信息不全等问题,本文方法同时含有局部与全局信息,且简单易用。
(4)提出了三种新型的有效的形状描述子
在特征三角形、形状上下文、高度函数等有效的局部特征基础上,结合轮廓的顺序关系,构造了三种新的轮廓描述子。实验结果表明,这些方法均能取得较高的形状检索准确率,特别是基于高度函数的轮廓描述子,该方法能够取得到目前为止所有描述子中国际上最高的形状检索准确率(在标准测试集MPEG-7数据库上,仅靠描述子的检索精度可达90.35%,结合图转导算法后检索精度可达96.45%)。同时,这些描述子几何意义明确,易于计算、维度低,其综合性能超越了常用的轮廓描述算法。
本文对基于轮廓的形状表示技术展丌了深入研究,敏锐的抓住了轮廓的顺序关系这一核心而本质的全局形状特征,通过将不同的局部特征与轮廓顺序信息相结合的方式,提出了数种几何意义明确、描述性强、表达准确、计算复杂度适中的轮廓描述子,在形状匹配这一计算机视觉领域的关键问题上取得了进展,相关成果已经得到了大量的实验证明。本文所提出的算法对于其它视觉理论及应用也有一定的启发性。
Shape, as a high-level visual characteristic, has been frequently used to represent the properties of objects in Computer Vision, Image Analysis and Understanding. Shape is a kind of critical and fundamental feature, and shape representation/matching has become one basic problem in the field of Computer Vision. Because of serious intra-class variances among object shapes in our life, there are a lot of difficulties when performing shape matching. However, a huge number of classical shape representation technologies and shape matching algorithms have appeared by hard works of researchers. Shape matching is still one of the leading and hot topics in Computer Vision and Image Analysis so far.
In this thesis, the development of shape matching technologies is reviewed, and it is found that none of current descriptors is able to combine local and global features effectively and efficiently. Accordingly, some researches are performed on how to define local and global features, and a framework to naturally combine these two issues is presented, resulting in some novel descriptors with better performances. The main contributions of this thesis are summarized as follows:
First, some effective local features are proposed. Local features are fundamental for defining shape descriptors. Local features should give a precise description for shape contours, and remain unchanged under linear transformations (translation, rotation, and scaling). Based on the geometric relationship between contour points, several local features, such as feature triangle and height functions, are defined to represent different aspects of shape contours. These local features are able to represent shapes exactly, and achieve linear transformation invariance. They provide a solid basis for presenting effective shape descriptors.
Second, some effective global feature is proposed. Global features are important issues contained in shape descriptors. They directly determine the robustness of shape descriptors to noise and local deformations. Based on the experience of shape matching algorithms, the order sequential information of contours is creatively defined as the global feature. This is the first time for contour order information to be treated as shape feature used in shape descriptors. It is proved that the contour order information can be used not only as constraints in shape matching algorithms but also as shape features in shape descriptors. It is able to help significantly improve the performance of descriptors.
Third, a new framework to combine local and global shape features is presented. Shape descriptors will never become not only description precisely but also robust to noise until both local and global features are combined together. It is discovered that after local features are rearranged according to the contour order information, the local and global features are naturally combined. Compared with current multi-scale or multi-aspect descriptors, the proposed methods are able to overcome the problems of usage difficulties and lack of shape information. The proposed descriptors include both local and global shape information, and they are easy to use and compute as well.
Fourth, three novel shape descriptors are presented. Based on the local features of feature triangles, shape contexts and height functions, combined with contour order information, three novel shape descriptors are constructed correspondingly. The experimental results show that the proposed methods are all able to achieve excellent shape retrieval rates. Especially for height functions, it is able to get the highest accuracy rate of shape retrieval among all descriptors all over the world. It achieves on the well-known MPEG-7 shape benchmark the best ever high rate of 90.35% only by the descriptor and 96.45% when combing with the graph transduction algorithm. What is more, each of these descriptors has a definite geometric meaning, is efficient to compute, and has a low feature dimension. The general performances of them outperform other widely used shape description algorithms.
In this thesis, contour based shape representation is carefully studied and the contour sequential information (a kind of global feature) is regarded as the core and fundamental shape characteristic. Several contour descriptors with clear geometric meaning, high discriminative power, precise representation and moderate computational complexity are presented by combining the sequential information with different local shape features. Some successes are obtained for shape matching, which is one of the key problems in the field of Computer Vision, and these successes are already confirmed by extensive experimentations. Some vision theories and applications can also benefit from the studies and algorithms proposed in this thesis.
引文
[1]章毓晋编著.图象工程(上册)图象处理和分析.清华大学出版社,北京,1999.
[2]Biederman I, Ju G. Surface versus edge-based determinants of visual recognition. Cognitive Psychology,1988,20(1):38-64.
[3]Sebastian T B, Klein P N, Kimia B B. Recognition of shapes by editing their shock graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence,2004, 26(5):550-571.
[4]丁险峰,吴洪,张宏江等.形状匹配综述.自动化学报,2001,27(5)：678-694.
[5]Zhang D S, Lu G J. Review of shape representation and description techniques. Pattern Recognition,2004,37(1):1-19.
[6]Kim W Y, Kim Y S. A region-based shape descriptor using Zernike moments. Signal Processing:Image Communication,2000,16(1):95-102.
[7]Zhang D S, Lu G. Generic Fourier descriptor for shape-based image retrieval. In: ICME:IEEE International Conference on Multimedia and Expo, Lausanne, Switzerland, August 2002,425-428.
[8]Direkoglu C, Nixon M S. Shape classification using multiscale Fourier-based description in 2-D space. In:ICSP:IEEE International Conference on Signal Processing, Leipzig, Germany, May 2008,820-823.
[9]Blum H. Biological shape and visual science (Part I). Journal of Theoretical Biology, 1973,38:205-287.
[10]Bai X, Latecki L J, Liu W Y. Skeleton pruning by contour partitioning with discrete curve evolution. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007,29(3):449-462.
[11]Bai X, Latecki L J. Path similarity skeleton graph matching. IEEE Transactions on Pattern Analysis and Machine Intelligence,2008,30(7):1282-1292.
[12]Latecki L J, Lakaemper R. Shape similarity measure based on correspondence of visual parts. IEEE Transactions on Pattern Analysis and Machine Intelligence,2000, 22(10):1185-1190.
[13]McNeill G, Vijayakumar S. Hierarchical procrustes matching for shape retrieval. In: CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, New York, USA, June 2006,885-894.
[14]Felzenszwalb P F, Schwartz J. Hierarchical matching of deformable shapes. In: CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Minneapolis, Minnesota, USA, June 2007,1-8.
[15]Latecki L J, Lakamper R. Convexity rule for shape decompostion based on discrete curve evolution. Computer Vision and Image Understanding,1999,73:441-454.
[16]Latecki L J, Lakamper R. Polygon evolution by vertex deletion. In:Proceedings of International Conference on Scale-Space, Corfu, Greece, September 1999,398-409.
[17]Mokhtarian F, Abbasi S, Kittler J. Efficient and robust retrieval by shape content through curvature scale space. In:Smeulders, A.W.M., Jain, R. (Eds.) Image Databases and Multi-Media Search,1997,51-58.
[18]Adamek T, OConnor N E. A multiscale representation method for nonrigid shapes with a single closed contour. IEEE Transactions on Circuits and Systems for Video Technology.2004,14(5):742-753.
[19]Alajlan N, Rube I E, Kamel M S, et al. Shape retrieval using triangle area representation and dynamic space warping. Pattern Recognition,2007,40(7): 1911-1920.
[20]Alajlan N, Kamel M S, Freeman G. Geometry-based image retrieval in binary image databases. IEEE Transactions on Pattern Analysis and Machine Intelligence,2008, 30(6):1003-1013.
[21]Manay S, Cremers D, Hong B W, et al. Integral invariants for shape matching. IEEE Transactions on Pattern Analysis and Machine Intelligence,2006,28(10): 1602-1618.
[22]Xu C, Liu J, Tang X.2D shape matching by contour flexibility. IEEE Transactions on Pattern Analysis and Machine Intelligence,2009,31(1):180-186.
[23]Belongie S, Malik J, Puzicha J. Shape matching and object recognition using shape contexts. IEEE Transactions on Pattern Analysis and Machine Intelligence,2002, 24(4):509-522.
[24]Ling H, Jacobs D. Shape classification using the inner-distance. IEEE Transactions on Pattern Analysis and Machine Intelligence,2007,29(2):286-299.
[25]Bai X, Liu W Y, Tu Z W. Integrating contour and skeleton for shape classification. In: ICCVW:Workshop on NORDIA (in conjunction with ICCV2009), Kyoto, Japan, September-October 2009,360-367.
[26]Yang M Q, Kpalma K, Ronsin J. Shape matching and object recognition using chord contexts. International Conference on Information Visualisation, London, UK, July 2008,63-69.
[27]Ebrahim Y, Ahmed M, Abdelsalam W, et al. Shape representation and description using the Hilbert curve. Pattern Recognition Letters,2009,30:348-358.
[28]Kuhn H W. Hungarian method for the assignment problem. Naval Research Logistics Quarterly,1955,2(1):83-97.
[29]Cormen T H, Leiserson C E, Rivest R L, et al. Introduction to Algorithms, second edition, MIT Press,2001.
[30]Latecki L J, Lakamper R, Eckhardt U. Shape descriptors for non-rigid shapes with a single closed contour. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Hilton Head, SC, USA, June 2000,1424-1429.
[31]Bai X, Wang B, Wang X G, et al. Co-transduction for shape retrieval. In:ECCV: European Conference on Computer Vision, Crete, Greece, September 2010, 328-341.
[32]Besl P J, Mckay N D. A method for registration of 3-D shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence,1992,14(2):239-256.
[33]Chui H L, Rangarajan A. A new point matching algorithm for non-rigid registration. Computer Vision and Image Understanding,2003,89:114-141.
[34]Zheng Y F, Doermann D. Robust point matching for nonrigid shapes by preserving local neighborhood structures. IEEE Transactions on Pattern Analysis and Machine Intelligence,2006,28(4):643-649.
[35]Lee J H, Won C H. Topology preserving relaxation labeling for nonrigid point matching. IEEE Transactions on Pattern Analysis and Machine Intelligence,2011, 33(2):427-432.
[36]Yang X W, Bai X, Latecki L J, et al. Improving shape retrieval by learning graph transduction. In:ECCV:European Conference on Computer Vision, Marseille, France, October 2008,328-341.
[37]Bai X, Yang X W, Latecki L J, et al. Learning context sensitive shape similarity by graph transduction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010,32(5):861-874.
[38]Yang X, Koknar-Tezel S, Latecki L J. Locally constrained diffusion process on locally densified distance spaces with applications to shape retrieval. In:CVPR: IEEE International Conference on Computer Vision and Pattern Recognition, June 2009,357-364.
[39]Peter K, Michael D, Horst B. Beyond pairwise shape similarity analysis. In:ACCV: Asian Conference on Computer Vision, Xi'an, China, September 2009,655-666.
[40]Egozi A, Keller Y, Guterman H. Improving shape retrieval by spectral matching and meta similarity. IEEE Transactions on Image Processing,2010,19(5):1319-1327.
[41]Chen J, Zhou Y, Wang B, et al. Rapid shape retrieval using improved graph transduction. In:ICIECS:Second International Conference on Information Engineering and Computer Science, Wuhan, China, December 2009,1-4.
[42]Chen J, Zhou Y, Yao Z J, et al. Unsupervised clustering using graph transduction. In: ICBECS:International Conference on Biomedical Engineering and Computer Science, Wuhan, China, April 2010,1-4.
[43]Wang J, Li Y, Bai X, et al. Learning context-sensitive similarity by shortest path propagation. Pattern Recognition,2011,44(10-11):2367-2374.
[44]Bai X, Wang B, Yao C, et al. Co-transduction for shape retrieval. IEEE Transactions on Image Processing,2012, accepted.
[45]Ling H, Yang X, Latecki L J. Balancing deformability and discriminability for shape matching. In:ECCV:European Conference on Computer Vision, Crete, Greece, September 2010,411-424.
[46]Gonzalez R C, Woods R E. Digital Image Processing, Second Edition,《数字图像处理(第二版)》,电子工业出版社,北京,2002.
[47]Hoppe H, DeRose T, Duchamp T, et al. Surface reconstruction from unorganized points. Computer Graphics,1992,26(2):71-78.
[48]Edelsbrunner H, Mijcke E P. Three-dimensional alpha shapes. ACM Transactions on Graphics,1994,13(1):43-72.
[49]Amenta N, Bern M, Kamvysselis M. A new Voronoi-based surface reconstruction algorithm. In:Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, Orlando, FL, USA, July 1998,415-421.
[50]Bemardini F, Mittleman J, Rushmeier H, et al. The ball-pivoting algorithm for surface reconstruction. IEEE Transactions on Visualization and Computer Graphics, 1999,5(4):349-359.
[51]Lu C E, Latecki L J, Adluru N, et al. Shape guided contour grouping with particle filters. In:ICCV:IEEE International Conference on Computer Vision, Kyoto, Japan, September-October 2009,2288-2295.
[52]Lazebnik S, Schmid C, Ponce J. Semi-local affine parts for object recognition. In: BMVC:British Machine Vision Conference, London, UK, September 2004, 779-788.
[53]Attalla E, Siy P. Robust shape similarity retrieval based on contour segmentation polygonal multiresolution and elastic matching. Pattern Recognition,2005,38(12): 2229-2241.
[54]Donoser M, Riemenschneider H, Bischof H. Efficient partial shape matching of outer contours. In:ACCV:Asian Conference on Computer Vision, Xi'an, China, September 2009,281-292.
[55]王军伟,刘文予.基于多尺度三元组描述的形状匹配方法.华中科技大学学报(自然科学版),2011,39(6)：6-9.
[56]Manjunath B S. Introduction to MPEG-7:Multimedia Content Description Interface, Wiley,2002.
[57]Wang Z, Liang M. Locally affine invariant descriptors for shape matching and retrieval. IEEE Signal Processing Letters,2010,17(9):803-806.
[58]Temlyakov A, Munsell B C, Waggoner J W, et al. Two perceptually motivated strategies for shape classification. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, San Francisco, USA, June 2010, 2289-2296.
[59]Payet N, Todorovic S. Matching hierarchies of deformable shapes. In:GbR: Proceedings of IAPR-TC-15 Workshop on Graph-based Representations in Pattern Recognition, Venice, Italy, May 2009,1-10.
[60]Daliri M R, Torre V. Robust symbolic representation for shape recognition and retrieval. Pattern Recognition,2008,41(5):1782-1798.
[61]Tu Z W, Yuille A L. Shape matching and recognition using generative models and informative features. In:ECCV:European Conference on Computer Vision, Slovansky ostrov, Prague 1, Czech Republic, May 2004,195-209.
[62]Super B. Retrieval from shape databases using chance probability functions and fixed correspondence. International Journal of Pattern Recognition and Artificial Intelligence,2006,20(8):1117-1138.
[63]Nasreddine K, Benzinou A, Fablet R. Variational shape matching for shape classification and retrieval. Pattern Recognition Letters,2010,31(12):1650-1657.
[64]Sun K, Super B. Classification of contour shapes using class segment sets. In:CVPR: IEEE International Conference on Computer Vision and Pattern Recognition, New York, USA, June 2006,727-733.
[65]Aslan C, Erdem A, Erdem E E, et al. Disconnected skeleton:shape at its absolute scale. IEEE Transactions on Pattern Analysis and Machine Intelligence,2008, 30(12):2188-2203.
[66]Yang S, Wang Y Y. Rotation invariant shape contexts based on feature-space Fourier transformation. In:ICIG:IEEE International Conference on Image and Graphics, Chengdu, China, August 2007,575-579.
[67]Yang S. Symbol recognition via statistical integration of pixel-level constraint histograms:a new descriptor. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(2):278-281.
[68]Liu D, Chen T. Soft shape context for iterative closest point registration. In:ICIP: IEEE International Conference on Image Processing, Singapore, October 2004, 1081-1084.
[69]韩敏,郑丹晨.基于模糊形状上下文特征的形状识别算法.自动化学报,2012,38(1)：68-75.
[70]Ling H B, Okada K. An efficient earth mover's distance algorithm for robust histogram comparison. IEEE Transactions on Pattern Analysis and Machine Intelligence,2007,29(5):840-853.
[71]Mori G, Belongie S, Malik J. Efficient shape matching using shape contexts. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(11): 1832-1837.
[72]Roman-Rangel E, Pallan C, Odobez J M, et al. Analyzing ancient Maya glyph collections with contextual shape descriptors. International Journal of Computer Vision,2011,94(1):101-117.
[73]Lowe D G. Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision,2004,60(2):91-110.
[74]Zhou Y, Wang J W, Zhou Q, et al. Shape matching using co-occurrence pattern. In: ICIG:Sixth International Conference on Image and Graphics, Hefei, China, August 2011,344-349.
[75]Kirkegaard J, Moeslund T B. Bin-picking based on harmonic shape contexts and graph-based matching. In:ICPR:IEEE International Conference on Pattern Recognition, Hong Kong, China, September 2006,581-584.
[76]Huang K S, Trivedi M M.3D shape context based gesture analysis integrated with tracking using omni video array. In:CVPRW:IEEE International Conference on Computer Vision and Pattern Recognition Workshops, San Diego, CA, USA, June 2005,80-80.
[77]Grundmann M, Meier F, Essa I.3D shape context and distance transform for action recognition. In:ICPR:IEEE International Conference on Pattern Recognition, Tampa, Florida, USA, December 2008,1-4.
[78]Kholgade N, Savakis A. Human activity recognition using the 4D spatiotemporal shape context descriptor. In:ISVC:International Symposium on Visual Computing, Las Vegas, NV, USA, November-December 2009.357-366.
[79]Zhang H, Malik J. Learning a discriminative classifier using shape context distances. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Madison, WI, USA, June 2003,242-247.
[80]Gonzalez-Jimenez D, Alba-Castro J L. Shape contexts and Gabor features for face description and authentication. In:1CIP:IEEE International Conference on Image Processing, Genoa, Italy, September 2005,11-14.
[81]Wang J G, Li J, Yau W Y, et al. Boosting dense SIFT descriptors and shape contexts for face images for gender recognition. In:CVPRW:IEEE International Conference on Computer Vision and Pattern Recognition Workshops, San Francisco, USA, June 2010,96-102.
[82]Rusinol M, Noorbakhsh F, Karatzas D, et al. Perceptual image retrieval by adding color information to the shape context descriptor. In:ICPR:IEEE International Conference on Pattern Recognition, Istanbul, Turkey, August 2010,1594-1597.
[83]Hsiao P C, Chen C S, Chang L W. Human action recognition using temporal-state shape contexts. In:ICPR:IEEE International Conference on Pattern Recognition, Tampa, Florida, USA, December 2008,1-4.
[84]Zhang Y Y, Yang N Q, Li W, et al. Gait recognition using procrustes shape analysis and shape context. In:ACCV:Asian Conference on Computer Vision, Xi'an, China, September 2009,256-265.
[85]Tepper M, Gomez F, Muse P, et al. Morphological shape context:Semi-locality and robust matching in shape recognition. In:CIARP:Ibero American Congress on Pattern Recognition, Guadalajara, Jalisco, Mexico, August 2009,129-136.
[86]Thayananthan A, Stenger B, Torr P H S, et al. Shape context and chamfer matching in cluttered scenes. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Madison, WI, USA, June 2003,1-7.
[87]Liu Z, Shen H, Feng G Y, et al. Tracking objects using shape context matching. Neurocomputing,2012,83:47-55.
[88]Bohg J, Kragic D. Learning grasping points with shape context. Robotics and Autonomous Systems,2010,58(4):362-377.
[89]Lu C E, Adluru N, Ling H B, et al. Contour based object detection using part bundles. Computer Vision and Image Understanding,2010,114(7):827-834.
[90]Yang X W, Liu H R, Latecki L J. Contour-based object detection as dominant set computation. Pattern Recognition,2012, accepted.
[91]Lv X D, Wang Z J. Shape context based image hashing using local feature points. In: ICIP:IEEE International Conference on Image Processing, Brussels, Belgium, September 2011,2541-2544.
[92]Lv X D, Wang Z J. Perceptual image hashing based on shape contexts and local feature points. IEEE Transactions on Information Forensics and Security,2012, accepted.
[93]Granlund G. Fourier preprocessing for hand print character recognition. IEEE Transactions on Computers,1972,21(2):195-201.
[94]Richard C, Hemami H. Identification of three-dimensional objects using Fourier descriptors of the boundary curve. IEEE Transactions on Systems, Man, and Cybernetics,1974,4(4):371-378.
[95]Persoon E, Fu K. Shape discrimination using Fourier descriptors. IEEE Transactions on Systems, Man, and Cybernetics,1977,7(3):170-179.
[96]Zahn C, Roskies R. Fourier descriptors for plane closed curves. IEEE Transactions on Computers,1972,21(3):269-281.
[97]Bennett J, Mac Donald J. On the measurement of curvature in a quantized environment. IEEE Transactions on Computers,1975,24(8):803-820.
[98]刘海容.形状的曲率表示与分解[博士学位论文].武汉：华中科技大学电子与信息工程系,2009.
[99]Wang S, Chen P, Lin W. Invariant pattern recognition by moment Fourier descriptor. Pattern Recognition,1994,27(12):1735-1742.
[100]Otterloo P, Delft T U. A contour-oriented approach to digital shape analysis. P J van Otterloo,1988.
[101]Davies E. Machine vision:theory, algorithms, practicalities. Academic Press, New York,1997,171-191.
[102]Liu H R, Latecki L J, Liu W Y, et al. Visual curvature. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Minneapolis, Minnesota, USA, June 2007,1-8.
[103]Liu H R, Latecki L J, Liu W Y. A unified curvature definition for regular, polygonal, and digital planar curves. International Journal of Computer Vision,2008,80: 104-124.
[104]Leibe B, Schiele B. Analyzing appearance and contour based methods for object categorization. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Madison, WI, USA, June 2003,409-415.
[105]Lin L, Zeng K, Liu X, et al. Layered graph matching by composite cluster sampling with collaborative and competitive interactions. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Miami, Florida, USA, June 2009,1351-1358.
[106]Schmidt F R, Toeppe E, Cremers D. Efficient planar graph cuts with applications in computer vision. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Miami, Florida, USA, June 2009,351-356.
[107]Xie J, Heng P, Shah M. Shape matching and modeling using skeletal context. Pattern Recognition,2008,41(5):1756-1767.
[108]Grigorescu C, Petkov N. Distance sets for shape filters and shape recognition. IEEE Transactions on Image Processing,2003,12(7):729-739.
[109]http://www.dabi.temple.edu/-hbling/code data.htm.
[110]Latecki L J, Lakaemper R, Wolter D. Optimal partial shape similarity. Image and Vision Computing,2005,23(2):227-236.
[111]Bai X, Wang X G, Latecki L J, et al. Active skeleton for non-rigid object detection. In:ICCV:IEEE International Conference on Computer Vision, Kyoto, Japan, September-October 2009,575-582.
[112]Bai X, Li Q N, Latecki L J, et al. Shape band:a deformable object detection approach. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Miami, Florida, USA, June 2009,1335-1342.
[113]Wang B, Bai X, Wang X G, et al. Object recognition using junctions. In:ECCV: European Conference on Computer Vision, Crete, Greece, September 2010,15-28.
[114]Wang X G, Bai X, Liu W Y, et al. Feature context for image classification and object detection. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Colorado Springs, Colorado, USA, June 2011,961-968.
[115]Wang X G, Bai X, Ma T Y, et al. Fan shape model for object detection. In:CVPR: IEEE International Conference on Computer Vision and Pattern Recognition,2012, accepted.
[2]Biederman I, Ju G. Surface versus edge-based determinants of visual recognition. Cognitive Psychology,1988,20(1):38-64.
[3]Sebastian T B, Klein P N, Kimia B B. Recognition of shapes by editing their shock graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence,2004, 26(5):550-571.
[4]丁险峰,吴洪,张宏江等.形状匹配综述.自动化学报,2001,27(5)：678-694.
[5]Zhang D S, Lu G J. Review of shape representation and description techniques. Pattern Recognition,2004,37(1):1-19.
[6]Kim W Y, Kim Y S. A region-based shape descriptor using Zernike moments. Signal Processing:Image Communication,2000,16(1):95-102.
[7]Zhang D S, Lu G. Generic Fourier descriptor for shape-based image retrieval. In: ICME:IEEE International Conference on Multimedia and Expo, Lausanne, Switzerland, August 2002,425-428.
[8]Direkoglu C, Nixon M S. Shape classification using multiscale Fourier-based description in 2-D space. In:ICSP:IEEE International Conference on Signal Processing, Leipzig, Germany, May 2008,820-823.
[9]Blum H. Biological shape and visual science (Part I). Journal of Theoretical Biology, 1973,38:205-287.
[10]Bai X, Latecki L J, Liu W Y. Skeleton pruning by contour partitioning with discrete curve evolution. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007,29(3):449-462.
[11]Bai X, Latecki L J. Path similarity skeleton graph matching. IEEE Transactions on Pattern Analysis and Machine Intelligence,2008,30(7):1282-1292.
[12]Latecki L J, Lakaemper R. Shape similarity measure based on correspondence of visual parts. IEEE Transactions on Pattern Analysis and Machine Intelligence,2000, 22(10):1185-1190.
[13]McNeill G, Vijayakumar S. Hierarchical procrustes matching for shape retrieval. In: CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, New York, USA, June 2006,885-894.
[14]Felzenszwalb P F, Schwartz J. Hierarchical matching of deformable shapes. In: CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Minneapolis, Minnesota, USA, June 2007,1-8.
[15]Latecki L J, Lakamper R. Convexity rule for shape decompostion based on discrete curve evolution. Computer Vision and Image Understanding,1999,73:441-454.
[16]Latecki L J, Lakamper R. Polygon evolution by vertex deletion. In:Proceedings of International Conference on Scale-Space, Corfu, Greece, September 1999,398-409.
[17]Mokhtarian F, Abbasi S, Kittler J. Efficient and robust retrieval by shape content through curvature scale space. In:Smeulders, A.W.M., Jain, R. (Eds.) Image Databases and Multi-Media Search,1997,51-58.
[18]Adamek T, OConnor N E. A multiscale representation method for nonrigid shapes with a single closed contour. IEEE Transactions on Circuits and Systems for Video Technology.2004,14(5):742-753.
[19]Alajlan N, Rube I E, Kamel M S, et al. Shape retrieval using triangle area representation and dynamic space warping. Pattern Recognition,2007,40(7): 1911-1920.
[20]Alajlan N, Kamel M S, Freeman G. Geometry-based image retrieval in binary image databases. IEEE Transactions on Pattern Analysis and Machine Intelligence,2008, 30(6):1003-1013.
[21]Manay S, Cremers D, Hong B W, et al. Integral invariants for shape matching. IEEE Transactions on Pattern Analysis and Machine Intelligence,2006,28(10): 1602-1618.
[22]Xu C, Liu J, Tang X.2D shape matching by contour flexibility. IEEE Transactions on Pattern Analysis and Machine Intelligence,2009,31(1):180-186.
[23]Belongie S, Malik J, Puzicha J. Shape matching and object recognition using shape contexts. IEEE Transactions on Pattern Analysis and Machine Intelligence,2002, 24(4):509-522.
[24]Ling H, Jacobs D. Shape classification using the inner-distance. IEEE Transactions on Pattern Analysis and Machine Intelligence,2007,29(2):286-299.
[25]Bai X, Liu W Y, Tu Z W. Integrating contour and skeleton for shape classification. In: ICCVW:Workshop on NORDIA (in conjunction with ICCV2009), Kyoto, Japan, September-October 2009,360-367.
[26]Yang M Q, Kpalma K, Ronsin J. Shape matching and object recognition using chord contexts. International Conference on Information Visualisation, London, UK, July 2008,63-69.
[27]Ebrahim Y, Ahmed M, Abdelsalam W, et al. Shape representation and description using the Hilbert curve. Pattern Recognition Letters,2009,30:348-358.
[28]Kuhn H W. Hungarian method for the assignment problem. Naval Research Logistics Quarterly,1955,2(1):83-97.
[29]Cormen T H, Leiserson C E, Rivest R L, et al. Introduction to Algorithms, second edition, MIT Press,2001.
[30]Latecki L J, Lakamper R, Eckhardt U. Shape descriptors for non-rigid shapes with a single closed contour. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Hilton Head, SC, USA, June 2000,1424-1429.
[31]Bai X, Wang B, Wang X G, et al. Co-transduction for shape retrieval. In:ECCV: European Conference on Computer Vision, Crete, Greece, September 2010, 328-341.
[32]Besl P J, Mckay N D. A method for registration of 3-D shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence,1992,14(2):239-256.
[33]Chui H L, Rangarajan A. A new point matching algorithm for non-rigid registration. Computer Vision and Image Understanding,2003,89:114-141.
[34]Zheng Y F, Doermann D. Robust point matching for nonrigid shapes by preserving local neighborhood structures. IEEE Transactions on Pattern Analysis and Machine Intelligence,2006,28(4):643-649.
[35]Lee J H, Won C H. Topology preserving relaxation labeling for nonrigid point matching. IEEE Transactions on Pattern Analysis and Machine Intelligence,2011, 33(2):427-432.
[36]Yang X W, Bai X, Latecki L J, et al. Improving shape retrieval by learning graph transduction. In:ECCV:European Conference on Computer Vision, Marseille, France, October 2008,328-341.
[37]Bai X, Yang X W, Latecki L J, et al. Learning context sensitive shape similarity by graph transduction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010,32(5):861-874.
[38]Yang X, Koknar-Tezel S, Latecki L J. Locally constrained diffusion process on locally densified distance spaces with applications to shape retrieval. In:CVPR: IEEE International Conference on Computer Vision and Pattern Recognition, June 2009,357-364.
[39]Peter K, Michael D, Horst B. Beyond pairwise shape similarity analysis. In:ACCV: Asian Conference on Computer Vision, Xi'an, China, September 2009,655-666.
[40]Egozi A, Keller Y, Guterman H. Improving shape retrieval by spectral matching and meta similarity. IEEE Transactions on Image Processing,2010,19(5):1319-1327.
[41]Chen J, Zhou Y, Wang B, et al. Rapid shape retrieval using improved graph transduction. In:ICIECS:Second International Conference on Information Engineering and Computer Science, Wuhan, China, December 2009,1-4.
[42]Chen J, Zhou Y, Yao Z J, et al. Unsupervised clustering using graph transduction. In: ICBECS:International Conference on Biomedical Engineering and Computer Science, Wuhan, China, April 2010,1-4.
[43]Wang J, Li Y, Bai X, et al. Learning context-sensitive similarity by shortest path propagation. Pattern Recognition,2011,44(10-11):2367-2374.
[44]Bai X, Wang B, Yao C, et al. Co-transduction for shape retrieval. IEEE Transactions on Image Processing,2012, accepted.
[45]Ling H, Yang X, Latecki L J. Balancing deformability and discriminability for shape matching. In:ECCV:European Conference on Computer Vision, Crete, Greece, September 2010,411-424.
[46]Gonzalez R C, Woods R E. Digital Image Processing, Second Edition,《数字图像处理(第二版)》,电子工业出版社,北京,2002.
[47]Hoppe H, DeRose T, Duchamp T, et al. Surface reconstruction from unorganized points. Computer Graphics,1992,26(2):71-78.
[48]Edelsbrunner H, Mijcke E P. Three-dimensional alpha shapes. ACM Transactions on Graphics,1994,13(1):43-72.
[49]Amenta N, Bern M, Kamvysselis M. A new Voronoi-based surface reconstruction algorithm. In:Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, Orlando, FL, USA, July 1998,415-421.
[50]Bemardini F, Mittleman J, Rushmeier H, et al. The ball-pivoting algorithm for surface reconstruction. IEEE Transactions on Visualization and Computer Graphics, 1999,5(4):349-359.
[51]Lu C E, Latecki L J, Adluru N, et al. Shape guided contour grouping with particle filters. In:ICCV:IEEE International Conference on Computer Vision, Kyoto, Japan, September-October 2009,2288-2295.
[52]Lazebnik S, Schmid C, Ponce J. Semi-local affine parts for object recognition. In: BMVC:British Machine Vision Conference, London, UK, September 2004, 779-788.
[53]Attalla E, Siy P. Robust shape similarity retrieval based on contour segmentation polygonal multiresolution and elastic matching. Pattern Recognition,2005,38(12): 2229-2241.
[54]Donoser M, Riemenschneider H, Bischof H. Efficient partial shape matching of outer contours. In:ACCV:Asian Conference on Computer Vision, Xi'an, China, September 2009,281-292.
[55]王军伟,刘文予.基于多尺度三元组描述的形状匹配方法.华中科技大学学报(自然科学版),2011,39(6)：6-9.
[56]Manjunath B S. Introduction to MPEG-7:Multimedia Content Description Interface, Wiley,2002.
[57]Wang Z, Liang M. Locally affine invariant descriptors for shape matching and retrieval. IEEE Signal Processing Letters,2010,17(9):803-806.
[58]Temlyakov A, Munsell B C, Waggoner J W, et al. Two perceptually motivated strategies for shape classification. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, San Francisco, USA, June 2010, 2289-2296.
[59]Payet N, Todorovic S. Matching hierarchies of deformable shapes. In:GbR: Proceedings of IAPR-TC-15 Workshop on Graph-based Representations in Pattern Recognition, Venice, Italy, May 2009,1-10.
[60]Daliri M R, Torre V. Robust symbolic representation for shape recognition and retrieval. Pattern Recognition,2008,41(5):1782-1798.
[61]Tu Z W, Yuille A L. Shape matching and recognition using generative models and informative features. In:ECCV:European Conference on Computer Vision, Slovansky ostrov, Prague 1, Czech Republic, May 2004,195-209.
[62]Super B. Retrieval from shape databases using chance probability functions and fixed correspondence. International Journal of Pattern Recognition and Artificial Intelligence,2006,20(8):1117-1138.
[63]Nasreddine K, Benzinou A, Fablet R. Variational shape matching for shape classification and retrieval. Pattern Recognition Letters,2010,31(12):1650-1657.
[64]Sun K, Super B. Classification of contour shapes using class segment sets. In:CVPR: IEEE International Conference on Computer Vision and Pattern Recognition, New York, USA, June 2006,727-733.
[65]Aslan C, Erdem A, Erdem E E, et al. Disconnected skeleton:shape at its absolute scale. IEEE Transactions on Pattern Analysis and Machine Intelligence,2008, 30(12):2188-2203.
[66]Yang S, Wang Y Y. Rotation invariant shape contexts based on feature-space Fourier transformation. In:ICIG:IEEE International Conference on Image and Graphics, Chengdu, China, August 2007,575-579.
[67]Yang S. Symbol recognition via statistical integration of pixel-level constraint histograms:a new descriptor. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(2):278-281.
[68]Liu D, Chen T. Soft shape context for iterative closest point registration. In:ICIP: IEEE International Conference on Image Processing, Singapore, October 2004, 1081-1084.
[69]韩敏,郑丹晨.基于模糊形状上下文特征的形状识别算法.自动化学报,2012,38(1)：68-75.
[70]Ling H B, Okada K. An efficient earth mover's distance algorithm for robust histogram comparison. IEEE Transactions on Pattern Analysis and Machine Intelligence,2007,29(5):840-853.
[71]Mori G, Belongie S, Malik J. Efficient shape matching using shape contexts. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005,27(11): 1832-1837.
[72]Roman-Rangel E, Pallan C, Odobez J M, et al. Analyzing ancient Maya glyph collections with contextual shape descriptors. International Journal of Computer Vision,2011,94(1):101-117.
[73]Lowe D G. Distinctive image features from scale-invariant keypoints. International Journal of Computer Vision,2004,60(2):91-110.
[74]Zhou Y, Wang J W, Zhou Q, et al. Shape matching using co-occurrence pattern. In: ICIG:Sixth International Conference on Image and Graphics, Hefei, China, August 2011,344-349.
[75]Kirkegaard J, Moeslund T B. Bin-picking based on harmonic shape contexts and graph-based matching. In:ICPR:IEEE International Conference on Pattern Recognition, Hong Kong, China, September 2006,581-584.
[76]Huang K S, Trivedi M M.3D shape context based gesture analysis integrated with tracking using omni video array. In:CVPRW:IEEE International Conference on Computer Vision and Pattern Recognition Workshops, San Diego, CA, USA, June 2005,80-80.
[77]Grundmann M, Meier F, Essa I.3D shape context and distance transform for action recognition. In:ICPR:IEEE International Conference on Pattern Recognition, Tampa, Florida, USA, December 2008,1-4.
[78]Kholgade N, Savakis A. Human activity recognition using the 4D spatiotemporal shape context descriptor. In:ISVC:International Symposium on Visual Computing, Las Vegas, NV, USA, November-December 2009.357-366.
[79]Zhang H, Malik J. Learning a discriminative classifier using shape context distances. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Madison, WI, USA, June 2003,242-247.
[80]Gonzalez-Jimenez D, Alba-Castro J L. Shape contexts and Gabor features for face description and authentication. In:1CIP:IEEE International Conference on Image Processing, Genoa, Italy, September 2005,11-14.
[81]Wang J G, Li J, Yau W Y, et al. Boosting dense SIFT descriptors and shape contexts for face images for gender recognition. In:CVPRW:IEEE International Conference on Computer Vision and Pattern Recognition Workshops, San Francisco, USA, June 2010,96-102.
[82]Rusinol M, Noorbakhsh F, Karatzas D, et al. Perceptual image retrieval by adding color information to the shape context descriptor. In:ICPR:IEEE International Conference on Pattern Recognition, Istanbul, Turkey, August 2010,1594-1597.
[83]Hsiao P C, Chen C S, Chang L W. Human action recognition using temporal-state shape contexts. In:ICPR:IEEE International Conference on Pattern Recognition, Tampa, Florida, USA, December 2008,1-4.
[84]Zhang Y Y, Yang N Q, Li W, et al. Gait recognition using procrustes shape analysis and shape context. In:ACCV:Asian Conference on Computer Vision, Xi'an, China, September 2009,256-265.
[85]Tepper M, Gomez F, Muse P, et al. Morphological shape context:Semi-locality and robust matching in shape recognition. In:CIARP:Ibero American Congress on Pattern Recognition, Guadalajara, Jalisco, Mexico, August 2009,129-136.
[86]Thayananthan A, Stenger B, Torr P H S, et al. Shape context and chamfer matching in cluttered scenes. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Madison, WI, USA, June 2003,1-7.
[87]Liu Z, Shen H, Feng G Y, et al. Tracking objects using shape context matching. Neurocomputing,2012,83:47-55.
[88]Bohg J, Kragic D. Learning grasping points with shape context. Robotics and Autonomous Systems,2010,58(4):362-377.
[89]Lu C E, Adluru N, Ling H B, et al. Contour based object detection using part bundles. Computer Vision and Image Understanding,2010,114(7):827-834.
[90]Yang X W, Liu H R, Latecki L J. Contour-based object detection as dominant set computation. Pattern Recognition,2012, accepted.
[91]Lv X D, Wang Z J. Shape context based image hashing using local feature points. In: ICIP:IEEE International Conference on Image Processing, Brussels, Belgium, September 2011,2541-2544.
[92]Lv X D, Wang Z J. Perceptual image hashing based on shape contexts and local feature points. IEEE Transactions on Information Forensics and Security,2012, accepted.
[93]Granlund G. Fourier preprocessing for hand print character recognition. IEEE Transactions on Computers,1972,21(2):195-201.
[94]Richard C, Hemami H. Identification of three-dimensional objects using Fourier descriptors of the boundary curve. IEEE Transactions on Systems, Man, and Cybernetics,1974,4(4):371-378.
[95]Persoon E, Fu K. Shape discrimination using Fourier descriptors. IEEE Transactions on Systems, Man, and Cybernetics,1977,7(3):170-179.
[96]Zahn C, Roskies R. Fourier descriptors for plane closed curves. IEEE Transactions on Computers,1972,21(3):269-281.
[97]Bennett J, Mac Donald J. On the measurement of curvature in a quantized environment. IEEE Transactions on Computers,1975,24(8):803-820.
[98]刘海容.形状的曲率表示与分解[博士学位论文].武汉：华中科技大学电子与信息工程系,2009.
[99]Wang S, Chen P, Lin W. Invariant pattern recognition by moment Fourier descriptor. Pattern Recognition,1994,27(12):1735-1742.
[100]Otterloo P, Delft T U. A contour-oriented approach to digital shape analysis. P J van Otterloo,1988.
[101]Davies E. Machine vision:theory, algorithms, practicalities. Academic Press, New York,1997,171-191.
[102]Liu H R, Latecki L J, Liu W Y, et al. Visual curvature. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Minneapolis, Minnesota, USA, June 2007,1-8.
[103]Liu H R, Latecki L J, Liu W Y. A unified curvature definition for regular, polygonal, and digital planar curves. International Journal of Computer Vision,2008,80: 104-124.
[104]Leibe B, Schiele B. Analyzing appearance and contour based methods for object categorization. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Madison, WI, USA, June 2003,409-415.
[105]Lin L, Zeng K, Liu X, et al. Layered graph matching by composite cluster sampling with collaborative and competitive interactions. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Miami, Florida, USA, June 2009,1351-1358.
[106]Schmidt F R, Toeppe E, Cremers D. Efficient planar graph cuts with applications in computer vision. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Miami, Florida, USA, June 2009,351-356.
[107]Xie J, Heng P, Shah M. Shape matching and modeling using skeletal context. Pattern Recognition,2008,41(5):1756-1767.
[108]Grigorescu C, Petkov N. Distance sets for shape filters and shape recognition. IEEE Transactions on Image Processing,2003,12(7):729-739.
[109]http://www.dabi.temple.edu/-hbling/code data.htm.
[110]Latecki L J, Lakaemper R, Wolter D. Optimal partial shape similarity. Image and Vision Computing,2005,23(2):227-236.
[111]Bai X, Wang X G, Latecki L J, et al. Active skeleton for non-rigid object detection. In:ICCV:IEEE International Conference on Computer Vision, Kyoto, Japan, September-October 2009,575-582.
[112]Bai X, Li Q N, Latecki L J, et al. Shape band:a deformable object detection approach. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Miami, Florida, USA, June 2009,1335-1342.
[113]Wang B, Bai X, Wang X G, et al. Object recognition using junctions. In:ECCV: European Conference on Computer Vision, Crete, Greece, September 2010,15-28.
[114]Wang X G, Bai X, Liu W Y, et al. Feature context for image classification and object detection. In:CVPR:IEEE International Conference on Computer Vision and Pattern Recognition, Colorado Springs, Colorado, USA, June 2011,961-968.
[115]Wang X G, Bai X, Ma T Y, et al. Fan shape model for object detection. In:CVPR: IEEE International Conference on Computer Vision and Pattern Recognition,2012, accepted.