基于AAM的人脸特征点定位算法研究与改进
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摘要
自动人脸识别(AFR)主要研究如何赋予计算机通过人脸辨别人物身份的能力,作为模式识别的一个研究领域,不仅具有非常重要的科学意义并且商业应用价值巨大。经过几十年的发展,AFR在受控环境和人工配合的情况下已经达到非常高的识别率,并出现了不少实际应用的商业系统。AFR系统主要有三个部分组成:人脸检测、人脸特征点定位、人脸特征提取和特征分类。人脸特征点定位作为AFR系统最重要的组成部分,它的定位精度在很大程度上影响着AFR系统的性能,同时它也是人脸表情识别和人脸三维建模的关键步骤。主动表观模型(Active Appearance Model,简称AAM)作为人脸特征点定位最主要和最有效的方法之一,被大量的学者研究并应用于实际的AFR系统中。本文对该方法在实际应用中遇到的问题进行了深入分析和研究,对其不足提出了相应的改进方法。
主要的改进有以下三点:1)针对光照变化影响定位算法效果的问题,提出一种快速Gabor小波算法,用它提取输入图像的纹理信息用于AAM纹理建模和拟合计算。2)针对人脸某部分发生遮挡导致定位算法效果变差的问题,提出一种基于分块加权的AAM拟合算法。该方法先把人脸区域分成几个子区域,然后根据每个区域被遮挡的程度分配一个权重,在拟合过程中不断调整每个区域对应的权重从而到达消除遮挡干扰的目的。3)为了提高拟合算法的效率,提出基于多分辨率的AAM拟合算法。首先在低分辨率图像上进行拟合,因为该图像包含的纹理信息相对较少,所以拟合所需要的计算复杂度也相对较少,在该图像上得到一个相对接近人脸的模板位置后,然后在高分辨率图像上进行更精确的拟合。
后本文采用Visual Studio 2005构建了一个基于AdaBoost人脸检测和AAM人脸特征点定位的演示系统,并将本文对特征点定位算法在鲁棒性上的改进应用于该系统中。
Automatic Face Recognition (AFR) mainly studies on how to give a computer the capability of recognizing identification through people faces. As a research field of pattern recognition, it not only has very important scientific significance, but also has great commercial application values. After decades of development, AFR has reached a very high recognition rate in the controlled environment and artificial situation, lots of business systems applied practically. There are three main parts of an AFR system, face detection, facial feature points positioning, and facial feature extraction and feature classification. As the most important part of AFR system, the accuracy of facial feature points positioning extremely affects AFR systems' performance, meanwhile it is the key step of facial expression recognition and 3D face modeling. Active appearance model (AAM), as one of the most important and efficient methods of facial feature points positioning, has been studied and applied to actual AFR systems by many scholars. In this paper, the problems of the method in practical application are encountered in the deep analysis and researches, the corresponding methods for its lack are pointed out as well.
There are three main issues for improvement: 1) In terms of the accuracy of AAM under varied illumination, a fast Gabor wavelet algorithm is proposed to compute AAM Fitting and Texture Modeling; 2) For the problem of occlusion, a sub-block weighted AAM fitting algorithm is present, which first divides a region is into sub-blocks with different weights according to the proportion of occlusion. The weights of each sub-block are adjusted in the fitting process in order to eliminate occlusion influence; 3) To enhance the speed of the AAM fitting, a multi scale fitting strategy is put forward. Because lower scale image has less texture information, the speed of fitting is fast. Through the lower scale fitting which provides a better initial location, the fitting on high scale image is accelerated.
Finally, we design a demo system of face detection using AdaBoost and facial feature localization using the improved AAM proposed in this paper. The system implemented under Visual Studio 2005 by appropriate designing its functional modules.
主要的改进有以下三点:1)针对光照变化影响定位算法效果的问题,提出一种快速Gabor小波算法,用它提取输入图像的纹理信息用于AAM纹理建模和拟合计算。2)针对人脸某部分发生遮挡导致定位算法效果变差的问题,提出一种基于分块加权的AAM拟合算法。该方法先把人脸区域分成几个子区域,然后根据每个区域被遮挡的程度分配一个权重,在拟合过程中不断调整每个区域对应的权重从而到达消除遮挡干扰的目的。3)为了提高拟合算法的效率,提出基于多分辨率的AAM拟合算法。首先在低分辨率图像上进行拟合,因为该图像包含的纹理信息相对较少,所以拟合所需要的计算复杂度也相对较少,在该图像上得到一个相对接近人脸的模板位置后,然后在高分辨率图像上进行更精确的拟合。
后本文采用Visual Studio 2005构建了一个基于AdaBoost人脸检测和AAM人脸特征点定位的演示系统,并将本文对特征点定位算法在鲁棒性上的改进应用于该系统中。
Automatic Face Recognition (AFR) mainly studies on how to give a computer the capability of recognizing identification through people faces. As a research field of pattern recognition, it not only has very important scientific significance, but also has great commercial application values. After decades of development, AFR has reached a very high recognition rate in the controlled environment and artificial situation, lots of business systems applied practically. There are three main parts of an AFR system, face detection, facial feature points positioning, and facial feature extraction and feature classification. As the most important part of AFR system, the accuracy of facial feature points positioning extremely affects AFR systems' performance, meanwhile it is the key step of facial expression recognition and 3D face modeling. Active appearance model (AAM), as one of the most important and efficient methods of facial feature points positioning, has been studied and applied to actual AFR systems by many scholars. In this paper, the problems of the method in practical application are encountered in the deep analysis and researches, the corresponding methods for its lack are pointed out as well.
There are three main issues for improvement: 1) In terms of the accuracy of AAM under varied illumination, a fast Gabor wavelet algorithm is proposed to compute AAM Fitting and Texture Modeling; 2) For the problem of occlusion, a sub-block weighted AAM fitting algorithm is present, which first divides a region is into sub-blocks with different weights according to the proportion of occlusion. The weights of each sub-block are adjusted in the fitting process in order to eliminate occlusion influence; 3) To enhance the speed of the AAM fitting, a multi scale fitting strategy is put forward. Because lower scale image has less texture information, the speed of fitting is fast. Through the lower scale fitting which provides a better initial location, the fitting on high scale image is accelerated.
Finally, we design a demo system of face detection using AdaBoost and facial feature localization using the improved AAM proposed in this paper. The system implemented under Visual Studio 2005 by appropriate designing its functional modules.
引文
[1]林维训,潘纲,吴朝晖等.脸部特征定位方法[J].中国图象图形学报,2003,8(8):849-859.
[2]G Yang,T S Huang.Human face detection in a complex background[J].Pattern Recognition,1994,27(1):53-63.
[3]C Kotropoulos,I Pitas.Rule-based face detection in frontal views[C].In:Proceedings of International Conference on Acoustics,Speech and Signal Processing.Munich,Germany:IEEE,1997,2537-2540.
[4]T Kanade.Picture processing by computer complex and recognition of human face[J].Kyoto University,Japan:Deptement Information Science,1973.
[5]R Brunelli,T Poggio.Face recognition:features versus templates[J].IEEE Trasnactions on Pattern Analysis and Machine Intelligence,1993,15(10):1042-1052.
[6]G C Feng,P C Yuen.Variance projection function and its application to eye detection for human face recognition[J].Pattern Recognition Letters,1998,19(9):899-906.
[7]L M Zhang,P Lenders.Knowledge-based eye detection for human face recognition[J].In:Proceedings of Knowledge-Based Intelligent Engineering Systems and Allied Technologies.Brighton,UK:2000,117-120.
[8]范宏深,倪国强,申会堂.利用几何特性及神经网络进行人脸探测技术的研究[J].光学技术,2002,28(2):105-107.
[9]D Reisfeld,H Wolfson,Yeshurun Y.Context-free attentional operators:the generalized symmetry transform[J].International Journal of Computer Vision,1995,14(3):119-130.
[10]周杰,卢春雨,张长水等.基于方向对称变换的人脸定位方法[J].电子学报,1999,27(8):12-15.
[11]刘文予,潘峰.离散对称变换在人脸图像眼睛定位中的应用[J].红外与毫米波学报,2001,20(5):375-380.
[12]M Kass,A Witkin,D Terzopoulos.Snakes:Active contour models[J].International Journal of Computer Vision,1987,321-331.
[13]H Wu,T Yokoyama,D Pramadihanto et al.Face and facial feature extraction from color image[J].In:Proceedings of Automatic Face and Gesture Recognition.Killington VT,USA:1996,345-350.
[14]A L Yuille,D S Cohen,P W Halinan.Feature extraction from faces using deformable templates[C].In:Proceedings of IEEE Computer Soc.Conf.on computer Vision and Pattern Recognition.Washington,DC:1989,104-109.
[15]X Xie,R Sudhakar,H Zhuang.On improving eye feature extraction using deformable templates[J].Pattern Recognition,1994,27(6):791-799.
[16]T F Cootes,C J Taylor,D H Cooper et al.Active shape models-their training and application[J].Computer Vision and Image Understanding,1995,61(1):38-59.
[17]J Luettin,A N Thacker,S W Beet.Locating and tracking facial speech features[C].In:Proceedings of ICPR'96.Vienna,Austria:1996,652-656.
[18]B D Lucas,T Kanade.An iterative image registration technique with an application to stereo vision[C].In:Proceedings of International Joint Conference on Artificial Intelligence.Texas,USA:Morgan Kaufmann Publishers,1981,674-679.
[19]C Tomasi,T Kanade.Detection and tracking of feature points[R].Carnegie Melton University Technical Report CMU-CS-91-132,Pittsburgh,PA,1991,1-22.
[20]段鸿,程义明,王以孝等.基于Kanade-Lucas-Tomasi算法的人脸特征点跟踪方法[J].计算机辅助设计与图形学学报,2004,3(16):279-283.
[21]H C Fu,P S Lai,R S Lou et al.Face detection and eye localization by neural network based color segmentation[J].In:Proceedings of Neural Networks for Signal Processing.Sydney,Australia:2000,507-516.
[22]R L Hsu,M A Mottaleb,A K Jain.Face detection in color images[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(5):696-706.
[23]J Waite,J Vincent.A probabilistic framework for neural network facial feature location[J].British Telecom Technology Journal,1992,10(3):20-29.
[24]M Turk,A Pentland.Eigenfaces for recognition[J].Journal of Cognitive Neuroscience,1991,3(1):71-86.
[25]G Pan,W X Lin,Z H Wu et al.An eye detection system based on SVM filter[C].In:Proceedings of SPIE,Electronic Imaging and Multimedia Technology.Shanghai, China: 2002, 326-331.
[26]Dihua Li, I T Podolak, S W Lee. Facial component extraction and face recognition with support vector machines[C]. In: Proceedings of Automatic Face and Gesture Recognition. Washington, DC USA: 2002, 76-81.
[27]C Y Kin, R Cipolla. A probabilistic framework for perceptual grouping of features for human face detection[C]. In: Proceedings of Automatic Face and Gesture Recognition. Killington, USA: 1996,16-21.
[28]V Kruger, G Sommer. Wavelet networks for face processing[J]. Journal of Optical Society of America, 2002, 19(b): 1112-1119.
[29]R S Feris, J Gemmell, K Toyama et al. Hierarchical wavelet networks for facial feature localization[C]. In: Proceedings of Automatic Face and Gesture Recognition. Washington DC, USA: 2002,118-123.
[30]T F Cootes, G J Edwwards, C J Taylor. Active appearance models[J]. IEEE Trans, 2001, PAMI-23(6): 681-685.
[31]I Matthews, S Baker. Active appearance models revisited[J]. International Journal of Computer Vision, 2004, 60(2): 135-164.
[32]G J Edwards, C J Taylor, T F Cootes. Interpreting face images using active appearance models[C]. In: Proceedings of 3rd IEEE International Conference on AFGR. Nara, JAPAN: 1998,300-305.
[33]S Sclaroff, J Isidoro. Active blobs[C]. In: Proceedings of 6th International Conference on Computer Vision Processings. Bombay, India: 1998, 1146-1153.
[34] V Blanz, T Vetter. A morphable model for the synthesis of 3D faces[J]. In: Proceedings of 5IGGRAPH. Los Angeles, California, USA: 1999, 187-194.
[35]M Jones, T Poggio. Multidimensional morphable models: A framework for representing and matching object classes[C]. In: Proceedings of the IEEE International Conference on Computer Vision. Bombay, India: 1998, 683-688.
[36]Fatih Kahraman, Muhittin Gokmen. An active Illumination and Appearance Model for face Alignment[J]. International Journal of Computer Vision, 2007, 60(2): 135-164.
[37]Yuchi Huang, Stephen Lin, Stan Z.Li, Hanqing Lu etal. Face Alignment under variable illumination[C]. In: Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition, 2004, 272-278.
[38]Lee T S. Image representation using 2D Gabor wavelet[J]. IEEE Trans Pattern Analysis and Machine Intelligence, 1996, 18 (10):959-971.
[39]Liu D H, Lam K M, Shen L S. Optimal sampling of Gabor feature for face recognition[J]. Pattern recognition Letters, 2004,25: 267-276.
[40]R Gross, I Matthews, S Baker. Constructing and fitting active appearance models with occlusion[C]. In: Proceedings of Conference on Computer Vision and Pattern Recognition. Washington DC, USA: 2004, 72-75.
[41]T Ishikawa, I Matthews, S Baker. Efficient image alignment with outlier rejection[R]. Robotics Institute, Carnegie Mellon University, October, 2002,1-24.
[42]Schapire R E. The strength of weak learnablity[J]. Machine Learning. 1990. 5(2):197-227
[43]Kearns M, Valiant L G. Learning Boolean Formulae or Factoring[R]. MA: Havard University Aiken Computation Laboratory. 1988.
[44]Kearns M, Valiant L G.Crytographic Limitation on Learning Boolean Formulae and Finite Automata[M]. In: Proc of the 21 annual ACM Sytoposlum on Theory of Computing. New York NY: ACM press. 1989. 433- 444.
[45]Valiant L G. Atheory of the learnable[J]. Communications of the ACM .1984(1):1134- 1142.
[46]Freund Y. Boosting a weak learning algorithm by majority[J]. Information and computation, 1995, 141(2):256-285
[47]Kearns M J, Vazirani L G. Learning Boolean formulme or finite automata is as hard as coring[R]. Harvard University Aiken Computation Laboratory, Aug. 1988.
[48]Kearns M, Valiant L G. Cryptographic limitations on learning Boolean formulae and finite automata[J]. Journal of the Association for Computing Machinery, 1994, 41(1):67-95.
[49]Freund Y, Schapire R E. A decision theoretic generalization of online learning and an application to boosting[J]. Journal of Computer and System Science, 1997, 55(1):11 9-139.
[50]C Papageorgiou, M Oren, and T Poggio.A general framework for object detection[C]. In International Conference on Computer Vision,1998.
[51]P Viola,M Jones.Robust Real-Time Face Detection[J].International Journal of Computer Vision.2004,57(2):137-154.
[52]P Viola,MB Jones.Rapid Object Detection using a Boosted Cascade of Simple Features[C].In proceedings IEEE conf.on Computer Vision and Pattern Recognition,Kauai,Hawaii,USA,2001:511-518.
[53]P Viola,M Jones.Robust Real-time Object Detection[R].Cambridge Research Laboratory,Technical Report Series.CRL 2001,01.
[54]Rainer,Lienhart.An Extended Set of Haar-like Features for Rapid Object Detection[C].IEEE ICIP 2002,Vol.1,900-903.
[55]沈利明.人脸跟踪算法及其在D.AM6416平台上的实现[D].南京理工大学,2006.
[2]G Yang,T S Huang.Human face detection in a complex background[J].Pattern Recognition,1994,27(1):53-63.
[3]C Kotropoulos,I Pitas.Rule-based face detection in frontal views[C].In:Proceedings of International Conference on Acoustics,Speech and Signal Processing.Munich,Germany:IEEE,1997,2537-2540.
[4]T Kanade.Picture processing by computer complex and recognition of human face[J].Kyoto University,Japan:Deptement Information Science,1973.
[5]R Brunelli,T Poggio.Face recognition:features versus templates[J].IEEE Trasnactions on Pattern Analysis and Machine Intelligence,1993,15(10):1042-1052.
[6]G C Feng,P C Yuen.Variance projection function and its application to eye detection for human face recognition[J].Pattern Recognition Letters,1998,19(9):899-906.
[7]L M Zhang,P Lenders.Knowledge-based eye detection for human face recognition[J].In:Proceedings of Knowledge-Based Intelligent Engineering Systems and Allied Technologies.Brighton,UK:2000,117-120.
[8]范宏深,倪国强,申会堂.利用几何特性及神经网络进行人脸探测技术的研究[J].光学技术,2002,28(2):105-107.
[9]D Reisfeld,H Wolfson,Yeshurun Y.Context-free attentional operators:the generalized symmetry transform[J].International Journal of Computer Vision,1995,14(3):119-130.
[10]周杰,卢春雨,张长水等.基于方向对称变换的人脸定位方法[J].电子学报,1999,27(8):12-15.
[11]刘文予,潘峰.离散对称变换在人脸图像眼睛定位中的应用[J].红外与毫米波学报,2001,20(5):375-380.
[12]M Kass,A Witkin,D Terzopoulos.Snakes:Active contour models[J].International Journal of Computer Vision,1987,321-331.
[13]H Wu,T Yokoyama,D Pramadihanto et al.Face and facial feature extraction from color image[J].In:Proceedings of Automatic Face and Gesture Recognition.Killington VT,USA:1996,345-350.
[14]A L Yuille,D S Cohen,P W Halinan.Feature extraction from faces using deformable templates[C].In:Proceedings of IEEE Computer Soc.Conf.on computer Vision and Pattern Recognition.Washington,DC:1989,104-109.
[15]X Xie,R Sudhakar,H Zhuang.On improving eye feature extraction using deformable templates[J].Pattern Recognition,1994,27(6):791-799.
[16]T F Cootes,C J Taylor,D H Cooper et al.Active shape models-their training and application[J].Computer Vision and Image Understanding,1995,61(1):38-59.
[17]J Luettin,A N Thacker,S W Beet.Locating and tracking facial speech features[C].In:Proceedings of ICPR'96.Vienna,Austria:1996,652-656.
[18]B D Lucas,T Kanade.An iterative image registration technique with an application to stereo vision[C].In:Proceedings of International Joint Conference on Artificial Intelligence.Texas,USA:Morgan Kaufmann Publishers,1981,674-679.
[19]C Tomasi,T Kanade.Detection and tracking of feature points[R].Carnegie Melton University Technical Report CMU-CS-91-132,Pittsburgh,PA,1991,1-22.
[20]段鸿,程义明,王以孝等.基于Kanade-Lucas-Tomasi算法的人脸特征点跟踪方法[J].计算机辅助设计与图形学学报,2004,3(16):279-283.
[21]H C Fu,P S Lai,R S Lou et al.Face detection and eye localization by neural network based color segmentation[J].In:Proceedings of Neural Networks for Signal Processing.Sydney,Australia:2000,507-516.
[22]R L Hsu,M A Mottaleb,A K Jain.Face detection in color images[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2002,24(5):696-706.
[23]J Waite,J Vincent.A probabilistic framework for neural network facial feature location[J].British Telecom Technology Journal,1992,10(3):20-29.
[24]M Turk,A Pentland.Eigenfaces for recognition[J].Journal of Cognitive Neuroscience,1991,3(1):71-86.
[25]G Pan,W X Lin,Z H Wu et al.An eye detection system based on SVM filter[C].In:Proceedings of SPIE,Electronic Imaging and Multimedia Technology.Shanghai, China: 2002, 326-331.
[26]Dihua Li, I T Podolak, S W Lee. Facial component extraction and face recognition with support vector machines[C]. In: Proceedings of Automatic Face and Gesture Recognition. Washington, DC USA: 2002, 76-81.
[27]C Y Kin, R Cipolla. A probabilistic framework for perceptual grouping of features for human face detection[C]. In: Proceedings of Automatic Face and Gesture Recognition. Killington, USA: 1996,16-21.
[28]V Kruger, G Sommer. Wavelet networks for face processing[J]. Journal of Optical Society of America, 2002, 19(b): 1112-1119.
[29]R S Feris, J Gemmell, K Toyama et al. Hierarchical wavelet networks for facial feature localization[C]. In: Proceedings of Automatic Face and Gesture Recognition. Washington DC, USA: 2002,118-123.
[30]T F Cootes, G J Edwwards, C J Taylor. Active appearance models[J]. IEEE Trans, 2001, PAMI-23(6): 681-685.
[31]I Matthews, S Baker. Active appearance models revisited[J]. International Journal of Computer Vision, 2004, 60(2): 135-164.
[32]G J Edwards, C J Taylor, T F Cootes. Interpreting face images using active appearance models[C]. In: Proceedings of 3rd IEEE International Conference on AFGR. Nara, JAPAN: 1998,300-305.
[33]S Sclaroff, J Isidoro. Active blobs[C]. In: Proceedings of 6th International Conference on Computer Vision Processings. Bombay, India: 1998, 1146-1153.
[34] V Blanz, T Vetter. A morphable model for the synthesis of 3D faces[J]. In: Proceedings of 5IGGRAPH. Los Angeles, California, USA: 1999, 187-194.
[35]M Jones, T Poggio. Multidimensional morphable models: A framework for representing and matching object classes[C]. In: Proceedings of the IEEE International Conference on Computer Vision. Bombay, India: 1998, 683-688.
[36]Fatih Kahraman, Muhittin Gokmen. An active Illumination and Appearance Model for face Alignment[J]. International Journal of Computer Vision, 2007, 60(2): 135-164.
[37]Yuchi Huang, Stephen Lin, Stan Z.Li, Hanqing Lu etal. Face Alignment under variable illumination[C]. In: Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition, 2004, 272-278.
[38]Lee T S. Image representation using 2D Gabor wavelet[J]. IEEE Trans Pattern Analysis and Machine Intelligence, 1996, 18 (10):959-971.
[39]Liu D H, Lam K M, Shen L S. Optimal sampling of Gabor feature for face recognition[J]. Pattern recognition Letters, 2004,25: 267-276.
[40]R Gross, I Matthews, S Baker. Constructing and fitting active appearance models with occlusion[C]. In: Proceedings of Conference on Computer Vision and Pattern Recognition. Washington DC, USA: 2004, 72-75.
[41]T Ishikawa, I Matthews, S Baker. Efficient image alignment with outlier rejection[R]. Robotics Institute, Carnegie Mellon University, October, 2002,1-24.
[42]Schapire R E. The strength of weak learnablity[J]. Machine Learning. 1990. 5(2):197-227
[43]Kearns M, Valiant L G. Learning Boolean Formulae or Factoring[R]. MA: Havard University Aiken Computation Laboratory. 1988.
[44]Kearns M, Valiant L G.Crytographic Limitation on Learning Boolean Formulae and Finite Automata[M]. In: Proc of the 21 annual ACM Sytoposlum on Theory of Computing. New York NY: ACM press. 1989. 433- 444.
[45]Valiant L G. Atheory of the learnable[J]. Communications of the ACM .1984(1):1134- 1142.
[46]Freund Y. Boosting a weak learning algorithm by majority[J]. Information and computation, 1995, 141(2):256-285
[47]Kearns M J, Vazirani L G. Learning Boolean formulme or finite automata is as hard as coring[R]. Harvard University Aiken Computation Laboratory, Aug. 1988.
[48]Kearns M, Valiant L G. Cryptographic limitations on learning Boolean formulae and finite automata[J]. Journal of the Association for Computing Machinery, 1994, 41(1):67-95.
[49]Freund Y, Schapire R E. A decision theoretic generalization of online learning and an application to boosting[J]. Journal of Computer and System Science, 1997, 55(1):11 9-139.
[50]C Papageorgiou, M Oren, and T Poggio.A general framework for object detection[C]. In International Conference on Computer Vision,1998.
[51]P Viola,M Jones.Robust Real-Time Face Detection[J].International Journal of Computer Vision.2004,57(2):137-154.
[52]P Viola,MB Jones.Rapid Object Detection using a Boosted Cascade of Simple Features[C].In proceedings IEEE conf.on Computer Vision and Pattern Recognition,Kauai,Hawaii,USA,2001:511-518.
[53]P Viola,M Jones.Robust Real-time Object Detection[R].Cambridge Research Laboratory,Technical Report Series.CRL 2001,01.
[54]Rainer,Lienhart.An Extended Set of Haar-like Features for Rapid Object Detection[C].IEEE ICIP 2002,Vol.1,900-903.
[55]沈利明.人脸跟踪算法及其在D.AM6416平台上的实现[D].南京理工大学,2006.