二维形状分析方法的研究
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摘要
形状分析是一种通过提取图像中目标的形状特征对图像进行识别和理解的方法。作为计算机视觉领域的一个重要研究问题,其在科学研究和工程技术上都有着广泛的应用。形状是物体最本质的特征,也是最难描述的特征之一。因此,如何有效准确地描述形状的特征是计算机视觉处理中的关键问题。本文将研究二维形状的分析方法。
图像中目标形状的提取是进行形状分析的前提。针对形状目标的提取过程进行了研究,通过对图像进行预处理,阈值分割和轮廓跟踪得到形状目标的区域及其轮廓,为形状的描述做准备。
形状的特征对形状分析是至关重要的。首先研究的基于区域的形状分析方法。针对传统方法识别检索能力差、计算复杂的问题,从Radon变换的性质出发,找到了一组具有平移和缩放不变性的特征,并且通过找到形状的参考方向解决了该特征的旋转不变性。实验表明这种特征具有较好的识别和检索性能,而且计算代价小,易于实现。然后研究了基于轮廓的形状分析方法。从轮廓信息的统计特性出发,在分析了边界序列矩和Chen不变矩的基础上,根据特征融合的思想,将两种方法进行融合。实验表明特征融合后的组合矩的识别和检索性能均优于边界序列矩和Chen不变矩。接下来研究了体现轮廓信息频率特性的傅里叶描述符。针对小波多尺度傅里叶描述符对起始点敏感、旋转和缩放不变性差的问题,结合高斯多尺度分析方法,将形状的轮廓序列在高斯尺度空间展开,并用其归一化的傅立叶系数来描述形状。通过对比实验表明该方法对起始点不敏感,具有较好的平移旋转缩放不变性和识别检索性能。
最后,从抗噪性能、消耗时间以及识别检索性能三个方面对这三种方法进行了综合比较,并对所做的研究工作进行了总结,提出了下一步研究工作的思路。
Shape analysis is a method which distinguishes and comprehends the images through extracting characteristics of its object's shape.As an essential issue in the field of computer vision, it has been extensively used in science research as well as engineering technology. Human's understanding of an image depends largely on the perception and distinguishment of the shape of the target image, thus shape becomes the most essential features of characterizing the object, as well as the indescribable one. Thus, how to effectively and exactly describe the characteristics of the shape is left to be the pivotal problem in computer vision operation. This article has focused on the analysis method of 2D images.
The extraction of the object's shape in the image is the premise of the shape analysis. To prepare for the shape description, Shapes and their boundary are acquired by preprocessing, threshold segmentation and contour tracing,
The description of the shape is vital to shape analysis. This article begin with a shape description method based on the regional Radon transform, which projects the 2D shape to a Radon feature space. And then features insensitive to translation, rotation and scale are obtained within Radon space. Experiments has shown that this features had a better performance.
After analyzing the Contour Sequence Moments and Chen Invariant Moment, a combination moment based on them with the ideas of feature fusion was proposed, to overcome the shortcomings of these two methods. It was found that the combination moment after the feature fusion is superior to the Contour Sequence Moment and Chen Invariant Moment.
Then a new multiscale fourier descriptors was proposed. In this method, first the contour sequence was spread in Gaussian scale space and then the contour sequences of different scales were expressed as a set of one-dimensional position function. Then its normalized Fourier coefficients are used as the shape descriptors. A good quality of the shape description of this method has been testified through experiments.
Finally, a conclusion was brought out after the comparing of these three methods in this paper. And the present research work was summarized with some guiding follow-up ideas for further research.
图像中目标形状的提取是进行形状分析的前提。针对形状目标的提取过程进行了研究,通过对图像进行预处理,阈值分割和轮廓跟踪得到形状目标的区域及其轮廓,为形状的描述做准备。
形状的特征对形状分析是至关重要的。首先研究的基于区域的形状分析方法。针对传统方法识别检索能力差、计算复杂的问题,从Radon变换的性质出发,找到了一组具有平移和缩放不变性的特征,并且通过找到形状的参考方向解决了该特征的旋转不变性。实验表明这种特征具有较好的识别和检索性能,而且计算代价小,易于实现。然后研究了基于轮廓的形状分析方法。从轮廓信息的统计特性出发,在分析了边界序列矩和Chen不变矩的基础上,根据特征融合的思想,将两种方法进行融合。实验表明特征融合后的组合矩的识别和检索性能均优于边界序列矩和Chen不变矩。接下来研究了体现轮廓信息频率特性的傅里叶描述符。针对小波多尺度傅里叶描述符对起始点敏感、旋转和缩放不变性差的问题,结合高斯多尺度分析方法,将形状的轮廓序列在高斯尺度空间展开,并用其归一化的傅立叶系数来描述形状。通过对比实验表明该方法对起始点不敏感,具有较好的平移旋转缩放不变性和识别检索性能。
最后,从抗噪性能、消耗时间以及识别检索性能三个方面对这三种方法进行了综合比较,并对所做的研究工作进行了总结,提出了下一步研究工作的思路。
Shape analysis is a method which distinguishes and comprehends the images through extracting characteristics of its object's shape.As an essential issue in the field of computer vision, it has been extensively used in science research as well as engineering technology. Human's understanding of an image depends largely on the perception and distinguishment of the shape of the target image, thus shape becomes the most essential features of characterizing the object, as well as the indescribable one. Thus, how to effectively and exactly describe the characteristics of the shape is left to be the pivotal problem in computer vision operation. This article has focused on the analysis method of 2D images.
The extraction of the object's shape in the image is the premise of the shape analysis. To prepare for the shape description, Shapes and their boundary are acquired by preprocessing, threshold segmentation and contour tracing,
The description of the shape is vital to shape analysis. This article begin with a shape description method based on the regional Radon transform, which projects the 2D shape to a Radon feature space. And then features insensitive to translation, rotation and scale are obtained within Radon space. Experiments has shown that this features had a better performance.
After analyzing the Contour Sequence Moments and Chen Invariant Moment, a combination moment based on them with the ideas of feature fusion was proposed, to overcome the shortcomings of these two methods. It was found that the combination moment after the feature fusion is superior to the Contour Sequence Moment and Chen Invariant Moment.
Then a new multiscale fourier descriptors was proposed. In this method, first the contour sequence was spread in Gaussian scale space and then the contour sequences of different scales were expressed as a set of one-dimensional position function. Then its normalized Fourier coefficients are used as the shape descriptors. A good quality of the shape description of this method has been testified through experiments.
Finally, a conclusion was brought out after the comparing of these three methods in this paper. And the present research work was summarized with some guiding follow-up ideas for further research.
引文
[1]I Young, J Walker, J Bowie. An analysis technique for biological shape[J]. Computer Graphics and Image Processing,1974,25:357-370.
[2]J R Bennet, J S McDonald. On the measurement of curvature in a quantized environment[J]. IEEE Transactions on Computers,1975,24:803-820.
[3]S Wang, P Chen, W Lin. Invariant pattern recognition by moment Fourier[J]. Pattern Recognition,1994,27:1735-1742.
[4]Aditya Vailaya. Semantic Classification In Image Databases:[博士学位论文].USA:Michigan State University,2000.
[5]Dengsheng Zhang, Guojun Lu. Review of Shape Representation and Description Techniques[J]. Pattern Recognition,2004,37:1-19.
[6]王涛,刘文印,孙家广,等.傅立叶描述子识别物体的形状[J].计算机研究与发展,2002,12(39)：1714-1719.
[7]M F Wu, H T Sheu. Contour-based correspondence using Fourier descriptors[J]. IEEE Proceedings-Vision, Image and Signal Processing,1997,144(3):150-160.
[8]K Arbter, W E Snyder, H Burkhardt. Application of affine-invariant Fourier descriptors to recognition of 3-D objects[J], IEEE Transactions on PAMI,1990, 12(7):640-647.
[9]H Kauppinen, T Seppanen, M Pietikainen. An Experimental Comparison of Autoregressive and Fourier-based Descriptors in 2D Shape Classification[J]. IEEE Transactions on PAMI,1995,17(2):201-207.
[10]Y Rui, A C She, T S Huang. A modiled Fourier descriptor for shape matching in MARS[C], Image Databases and Multimedia Search,1997:165-177.
[11]李丽宏,苗敬利.相对边界矩在模式识别中的应用[J].微计算机信息,2005,21(7)：42-43,
[12]R Kashyap, R Chellappa. Stochastic models for closed boundary analysis: Representation and reconstruction[J], IEEE Transactions on PAMI,1981,27: 627-637.
[13]S Belongie, J Malik, J Puzicha. Matching shapes[C]. Proceedings of Eighth IEEE ICCV,2001,Ⅰ:454-461.
[14]Y He, A Kundu.2-D shape classification using hidden Markov model[J]. IEEE Transactions on PAMI,1991,13:1172-1184.
[15]S Dubois, F Glanz. An autoregressive model approach to two-dimensional shape classification[J]. IEEE Transactions on PAMI,1986,8:55-66.
[16]W J Rucklidge. Efficient locating objects using Hausdorff distance[J], Int. J.Comput.Vision,1991,24(3):251-270.
[17]R L Kasyap, R Chellappa. Stochastic models for closed boundary analysis: representation andreconstruction[C]. IEEE Transactions Inform.Theory,1981, 27(5):627-637.
[18]Y Lin, J Dou, H Wang. Contour shape description based on arch height function[J]. Pattern Recogniton,1992,25:17-23.
[19]S Parui, D Majumder. Symmetry analysis by computer[J]. Pattern Recognition, 1983,16:63-67.
[20]J Iivarinen, M Peura, J Sarela. Comparison of Combined Shape Descriptors For Irregular Objects[J]. The 8th British Machine Vision Corcference,1997,2: 430-439.
[21]Jukka Iivarinen, Ari Visa. Shape recognition of irregular objects[C]. Proc. SPIE, 1996,25:25-32.
[22]A P Witkin. Scale-space filtering. Proc.8th Int'l Joint Conference on Artificial Intelligence,1983,1019-1022.
[23]H Asada, M Brady. The curvature primal sketch[J]. IEEE Transactions on PAMI, 1986,8:2-14.
[24]Mokhtarian, A K Mackworth. Scale-based description and recognition of planar curves and two-dimensional shapes[J]. IEEE Transactions on PAMI,1986,8: 34-43.
[25]H Liu, M Srinath. Partial shape classification using contour matching in distance transformation[J]. IEEE Transactions on PAMI,1990,12:1072-1079.
[26]K S Fu, T Kunii. A general (syntactic-semantic) approach to picture analysis[J]. Picture Engineering,1982:56-74.
[27]K S Fu. Syntactic image modeling using stochastic tree grammars[J]. Computer Graphics and Image Processing,1980,12:136-152.
[28]W I Groskey, P Neo, R Mehrotra. A Pictorial Index Mechanism For Model-Based Matching[J]. Date Knowledge Eng,1992,8:309-327.
[29]S Berretti, A D Bimbo, P Pala. Retrieval by shape similarity with perceptual distance and effective indexing[J]. IEEE Trans.Multimedia,2000,2(4):225-239.
[30]W I Groskey, R Mehrotra. Index-Based Object Recognition in Pictorial Data Management[J]. Computure Vision Graphics Image Process,1990,52:416-436.
[31]M K Hu. Visual Pattern Recognition by Moment Invariants[J]. IEEE Transactions Information Theory,1962,8(2):179-187.
[32]J R Prokop, A P Reeves. A survey of moment-based techniques for unoccluded object representation and recognition[J]. CVGIP:Graphical Models and Image Processing,1992,54:438-460.
[33]Y S Kim, W Y Kim. A Region-based Shape Descriptor Using Zernike Moments[J]. Image Signal Process,2000,16:95-102.
[34]S X Liao, M Pawlak. On image analysis by moments[J], IEEE Transactions on PAMI,1996,18(3):254-266.
[35]L Shapiro, R MacDonald, S Sternberg. Ordered structural shape matching with primitive extraction by mathematical morphology[J]. Pattern Recognition,1987, 20:75-80.
[36]A Loui, A Venetsans, K Smith. Two-dimensional shape representation using morphological correlation functions[C]. Proceedings of the IEEE International Conference on ASSP,1990:2165-2168.
[37]S Loncaric, A P Dhawan. A morphological signature transform for shape description[J]. Pattern Recognition,1993,26:1029-1037.
[38]N Ueda, S Suzulci. Learning Visual Models From Shape Contours Using Multiscale Convex/Concave Structure Matching[J]. IEEE Transactions on PAMI, 1993,15(4):337-352.
[39]C E Kim. Digital Concexity, Straightness and Convex Polygons[J]. IEEE Transactions on PAMI,1982,4:618-626.
[40]J H Conell, M Brady. Learning Shape Descriptions[C]. Proc. of International Joint Conference on Artificial Intelligence,1985:922-925.
[41]H Blum. A transformation for extracting new descriptors of shape[C]. In Whaten Dunn(eds), Models for the Perception of Speech and Visual Forms. MIT Press, 1967,362-380.
[42]L Calabi, W Hartnett. Shape recognition, prairie fires, convex deficiencies and skeletons[J]. The American Mathematical Monthly,1968,75:335-341.
[43]Naif Alajlan. Shape retrieval using triangle-area representation and dynamic space warping [J]. Pattern Recongnition,2007:1911-1920.
[44]Joon Woong Lee. A machine vision system for lane-departure detection[J]. Computer Vision and Image Understanding,2002,86(1):52-78.
[45]Remco Veltkamp, Michiel Hagedoorn. State of the art in shape matching[C]. Principles of visual information retrieval, London,2000:87-119.
[46]Yuan Shao, Mehmet Celenk. Higher-order spectra(HOS) invariants for shape recognition[J]. Pattern Recognition,2001,34:2097-2113.
[47]G D Sullivan, K D Baker, A D Worrall. Model-based vehicle detection and classification using orthographic approximations [J]. Image and Vision Computing,1997,15:649-654.
[48]Luminita A Vese, Tony F Chan. A muliphase level set framework for image segmentation using the mumford and shah model[J]. International Journal of Computer Vision,2002,50(3):271-293.
[49]刘贵喜,杨万海.基于多尺度对比度塔的图像融合方法及性能评价[J].光学学报,2001,21(11)：1336-1342.
[50]Junhong Li, Quan Pan, Hongcai. Image Recognition using Radon Transform[C]. Proceeding of the IEEE Conference on Intelligent Transportation Systems,2003, 1:741-744.
[51]Dattatray Jadhao, Raghunath Holambe. Feature Extraction and Dimensionality Reduction Using Radon and Fourier Transforms with Application to Face Recognition[J]. ICCIMA 2007.36:256-260.
[52]G Y Chen, B Kegl. Feature extraction using Radon, wavelet and fourier transform. ICSMC 2007:1020-1024.
[53]曹茂永,孙农亮,郁道银.用于模式识别的极半径不变矩[J].计算机学报,2004,27(6)：860-864.
[54]杨静,丘江,王岩飞.线性不变矩及其在图象识别中的应用算法研究[J].光子学报,2003,32(3)：336-339.
[55]李军宏,潘泉,程咏梅.一种基于高阶统计量的图像识别算法研究[J].系统工程与电子技术,2005,27(6)：7-10.
[56]Yuan Shao, Mehmet Celenk. Higher-order spectra(HOS) invariants for shape recognition[J]. Pattern Recognition,2001,34:2097-2113.
[57]R J Prokop, A P Reeves. A survery of moment-based techniques for unconcluded object representation and recognition[C]. Proceedings of International Conference on Automatic Face and Gesture Recognition,1992,3(2):438-460.
[58]H Kauppinen, T Seppanen, Matti Pietikainen. An Experimental Comparison of Autoregressive and Fourier-based Descriptors in 2-D Shape Classification[J]. IEEE Transactions on PAMI,1995,17:201-207.
[59]Dengsheng Zhang, Guojun Lu. A comparative study of curvature scale space and Fourier descriptors for shape-based image retrieval[J]. Journal of Visual Communication and Image Representation,2003,14(1):39-57.
[60]Iivari Kunttu, Leena Lepisto, Juhani Rauhamaa. Multiscale Fourier Descriptor for Shape-Based Image Retrieval[C]. ICIAP,2003:536-541.
[61]Babu M Mehtre, Mohan S Kankanhalli, Wing F Lee. Shape Measures for Content Based Image Retrieval:A Comparison[J]. Information Processing and Management: 1997,33(3):319-337.
[2]J R Bennet, J S McDonald. On the measurement of curvature in a quantized environment[J]. IEEE Transactions on Computers,1975,24:803-820.
[3]S Wang, P Chen, W Lin. Invariant pattern recognition by moment Fourier[J]. Pattern Recognition,1994,27:1735-1742.
[4]Aditya Vailaya. Semantic Classification In Image Databases:[博士学位论文].USA:Michigan State University,2000.
[5]Dengsheng Zhang, Guojun Lu. Review of Shape Representation and Description Techniques[J]. Pattern Recognition,2004,37:1-19.
[6]王涛,刘文印,孙家广,等.傅立叶描述子识别物体的形状[J].计算机研究与发展,2002,12(39)：1714-1719.
[7]M F Wu, H T Sheu. Contour-based correspondence using Fourier descriptors[J]. IEEE Proceedings-Vision, Image and Signal Processing,1997,144(3):150-160.
[8]K Arbter, W E Snyder, H Burkhardt. Application of affine-invariant Fourier descriptors to recognition of 3-D objects[J], IEEE Transactions on PAMI,1990, 12(7):640-647.
[9]H Kauppinen, T Seppanen, M Pietikainen. An Experimental Comparison of Autoregressive and Fourier-based Descriptors in 2D Shape Classification[J]. IEEE Transactions on PAMI,1995,17(2):201-207.
[10]Y Rui, A C She, T S Huang. A modiled Fourier descriptor for shape matching in MARS[C], Image Databases and Multimedia Search,1997:165-177.
[11]李丽宏,苗敬利.相对边界矩在模式识别中的应用[J].微计算机信息,2005,21(7)：42-43,
[12]R Kashyap, R Chellappa. Stochastic models for closed boundary analysis: Representation and reconstruction[J], IEEE Transactions on PAMI,1981,27: 627-637.
[13]S Belongie, J Malik, J Puzicha. Matching shapes[C]. Proceedings of Eighth IEEE ICCV,2001,Ⅰ:454-461.
[14]Y He, A Kundu.2-D shape classification using hidden Markov model[J]. IEEE Transactions on PAMI,1991,13:1172-1184.
[15]S Dubois, F Glanz. An autoregressive model approach to two-dimensional shape classification[J]. IEEE Transactions on PAMI,1986,8:55-66.
[16]W J Rucklidge. Efficient locating objects using Hausdorff distance[J], Int. J.Comput.Vision,1991,24(3):251-270.
[17]R L Kasyap, R Chellappa. Stochastic models for closed boundary analysis: representation andreconstruction[C]. IEEE Transactions Inform.Theory,1981, 27(5):627-637.
[18]Y Lin, J Dou, H Wang. Contour shape description based on arch height function[J]. Pattern Recogniton,1992,25:17-23.
[19]S Parui, D Majumder. Symmetry analysis by computer[J]. Pattern Recognition, 1983,16:63-67.
[20]J Iivarinen, M Peura, J Sarela. Comparison of Combined Shape Descriptors For Irregular Objects[J]. The 8th British Machine Vision Corcference,1997,2: 430-439.
[21]Jukka Iivarinen, Ari Visa. Shape recognition of irregular objects[C]. Proc. SPIE, 1996,25:25-32.
[22]A P Witkin. Scale-space filtering. Proc.8th Int'l Joint Conference on Artificial Intelligence,1983,1019-1022.
[23]H Asada, M Brady. The curvature primal sketch[J]. IEEE Transactions on PAMI, 1986,8:2-14.
[24]Mokhtarian, A K Mackworth. Scale-based description and recognition of planar curves and two-dimensional shapes[J]. IEEE Transactions on PAMI,1986,8: 34-43.
[25]H Liu, M Srinath. Partial shape classification using contour matching in distance transformation[J]. IEEE Transactions on PAMI,1990,12:1072-1079.
[26]K S Fu, T Kunii. A general (syntactic-semantic) approach to picture analysis[J]. Picture Engineering,1982:56-74.
[27]K S Fu. Syntactic image modeling using stochastic tree grammars[J]. Computer Graphics and Image Processing,1980,12:136-152.
[28]W I Groskey, P Neo, R Mehrotra. A Pictorial Index Mechanism For Model-Based Matching[J]. Date Knowledge Eng,1992,8:309-327.
[29]S Berretti, A D Bimbo, P Pala. Retrieval by shape similarity with perceptual distance and effective indexing[J]. IEEE Trans.Multimedia,2000,2(4):225-239.
[30]W I Groskey, R Mehrotra. Index-Based Object Recognition in Pictorial Data Management[J]. Computure Vision Graphics Image Process,1990,52:416-436.
[31]M K Hu. Visual Pattern Recognition by Moment Invariants[J]. IEEE Transactions Information Theory,1962,8(2):179-187.
[32]J R Prokop, A P Reeves. A survey of moment-based techniques for unoccluded object representation and recognition[J]. CVGIP:Graphical Models and Image Processing,1992,54:438-460.
[33]Y S Kim, W Y Kim. A Region-based Shape Descriptor Using Zernike Moments[J]. Image Signal Process,2000,16:95-102.
[34]S X Liao, M Pawlak. On image analysis by moments[J], IEEE Transactions on PAMI,1996,18(3):254-266.
[35]L Shapiro, R MacDonald, S Sternberg. Ordered structural shape matching with primitive extraction by mathematical morphology[J]. Pattern Recognition,1987, 20:75-80.
[36]A Loui, A Venetsans, K Smith. Two-dimensional shape representation using morphological correlation functions[C]. Proceedings of the IEEE International Conference on ASSP,1990:2165-2168.
[37]S Loncaric, A P Dhawan. A morphological signature transform for shape description[J]. Pattern Recognition,1993,26:1029-1037.
[38]N Ueda, S Suzulci. Learning Visual Models From Shape Contours Using Multiscale Convex/Concave Structure Matching[J]. IEEE Transactions on PAMI, 1993,15(4):337-352.
[39]C E Kim. Digital Concexity, Straightness and Convex Polygons[J]. IEEE Transactions on PAMI,1982,4:618-626.
[40]J H Conell, M Brady. Learning Shape Descriptions[C]. Proc. of International Joint Conference on Artificial Intelligence,1985:922-925.
[41]H Blum. A transformation for extracting new descriptors of shape[C]. In Whaten Dunn(eds), Models for the Perception of Speech and Visual Forms. MIT Press, 1967,362-380.
[42]L Calabi, W Hartnett. Shape recognition, prairie fires, convex deficiencies and skeletons[J]. The American Mathematical Monthly,1968,75:335-341.
[43]Naif Alajlan. Shape retrieval using triangle-area representation and dynamic space warping [J]. Pattern Recongnition,2007:1911-1920.
[44]Joon Woong Lee. A machine vision system for lane-departure detection[J]. Computer Vision and Image Understanding,2002,86(1):52-78.
[45]Remco Veltkamp, Michiel Hagedoorn. State of the art in shape matching[C]. Principles of visual information retrieval, London,2000:87-119.
[46]Yuan Shao, Mehmet Celenk. Higher-order spectra(HOS) invariants for shape recognition[J]. Pattern Recognition,2001,34:2097-2113.
[47]G D Sullivan, K D Baker, A D Worrall. Model-based vehicle detection and classification using orthographic approximations [J]. Image and Vision Computing,1997,15:649-654.
[48]Luminita A Vese, Tony F Chan. A muliphase level set framework for image segmentation using the mumford and shah model[J]. International Journal of Computer Vision,2002,50(3):271-293.
[49]刘贵喜,杨万海.基于多尺度对比度塔的图像融合方法及性能评价[J].光学学报,2001,21(11)：1336-1342.
[50]Junhong Li, Quan Pan, Hongcai. Image Recognition using Radon Transform[C]. Proceeding of the IEEE Conference on Intelligent Transportation Systems,2003, 1:741-744.
[51]Dattatray Jadhao, Raghunath Holambe. Feature Extraction and Dimensionality Reduction Using Radon and Fourier Transforms with Application to Face Recognition[J]. ICCIMA 2007.36:256-260.
[52]G Y Chen, B Kegl. Feature extraction using Radon, wavelet and fourier transform. ICSMC 2007:1020-1024.
[53]曹茂永,孙农亮,郁道银.用于模式识别的极半径不变矩[J].计算机学报,2004,27(6)：860-864.
[54]杨静,丘江,王岩飞.线性不变矩及其在图象识别中的应用算法研究[J].光子学报,2003,32(3)：336-339.
[55]李军宏,潘泉,程咏梅.一种基于高阶统计量的图像识别算法研究[J].系统工程与电子技术,2005,27(6)：7-10.
[56]Yuan Shao, Mehmet Celenk. Higher-order spectra(HOS) invariants for shape recognition[J]. Pattern Recognition,2001,34:2097-2113.
[57]R J Prokop, A P Reeves. A survery of moment-based techniques for unconcluded object representation and recognition[C]. Proceedings of International Conference on Automatic Face and Gesture Recognition,1992,3(2):438-460.
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