人脸识别特征提取算法研究
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摘要
人脸识别作为当前生物特征识别技术领域的热门研究课题,其实现方法多种多样。如何准确、高效地实现人脸识别是人脸识别研究的一大难点。一个完整的人脸识别系统一般包含人脸图像的获取、人脸检测与定位、人脸特征提取和特征比对四个主要环节。其中,如何快速、准确地进行人脸检测,如何准确地对检测到的人脸进行特征提取,直接影响到整个人脸识别系统的性能。本文对现有经典的人脸检测和人脸特征提取算法进行分析、研究和实现,同时针对实验过程中遇到的问题,结合数字图像处理和模式识别相关知识,对经典算法进行了一定的改进,在一定程度上提高了算法的性能。
本文所做的主要研究工作如下:
1.详细阐述了目前最具实用价值的基于AdaBoost算法的人脸检测方法,主要研究了Haar-like特征提取、分类器设计以及多尺度变换三个方面的问题。同时为了进一步降低误检率,对AdaBoost算法的检测结果进行肤色校验,从而实现有效地去除误检人脸区域。
2.研究实现了基于主动形状模型(ASM)的人脸特征点提取算法。详细分析了经典ASM方法的模型建立和匹配搜索算法,同时针对传统方法在人脸含有表情情况下遇到的困难,设计了将人脸区域按变化相关度进行划分、建模的改进型ASM算法。改进后的方法对人脸面部存在表情或人在说话的情况下能更准确地进行特征点的定位。另外,还尝试研究了将核主成分分析替换主成分分析以提高小角度偏转情况下人脸特征点定位的准确性。
3.研究实现了基于主动表观模型(AAM)的人脸特征点提取算法。详细分析了经典AAM方法的模型建立和匹配搜索算法,研究了反向合成算法在AAM匹配过程中的应用。为降低全局光照的干扰,将纹理归一化操作融合到反向合成算法中,提高了模型生成实例的准确性。
4.利用OpenCV对本文的人脸检测和人脸特征提取算法进行了实现,并借助MFC搭建了一个完整的人脸识别演示程序。
Face recognition is a hot research field in biometrics identification technology, and there are many ways to realize it. How to implement it accurately and efficiently is one of the major difficulties in face recognition. Generally, a complete face recognition system consists of four main areas: the acquisition of face images, face detection, facial feature extraction and feature matching. In these areas, how to detect face fast and accurately, and how to extract facial feature accurately will affect the performance of the system directly. In this paper, we select the existing classic face detection and facial feature extraction algorithm to analyze, research and implementation. To solve the problems found during the experiment, we improved the classical algorithm combining with knowledge of digital image processing and pattern recognition. The performance of these algorithms has been improved to a certain degree.
The major research work is as follows:
1. Described a face detection method based on the AdaBoost algorithm, which has the most practical value at present. Researched on how to extract Haar-like features, how to design classifiers and how to solve the problem on multi-scale transform. Meanwhile, in order to further reduce the false detection rate, we took skin color calibration on the results of AdaBoost algorithm to remove the false face areas effectively.
2. Studied and implemented the facial feature extraction algorithm base on active shape model (ASM). Analyzed the model building and matching search algorithm of the classical ASM in detail. To solve the difficulties encountered in the traditional method with expression in the face, we proposed an improved ASM algorithm: divide face region by change-related degree and model and search independently. The improved algorithm can achieve a more accurate feature point location with the existence of human facial expressions or in the case of talking. In addition, we also tried to replace principal component analysis with kernel principal component analysis to improve the location accuracy under the situation of face with small-angle deflection.
3. Researched and implemented facial feature extraction algorithm based on Active Appearance Model (AAM). Analyzed the modeling and matching search algorithm of the classical AAM in detail. Studied how to using Inverse Compositional Algorithm in the matching searches process. To reduce the interference taking by global illumination, we took the texture normalized operation into the inverse compositional algorithm integrated, and achieved an improvement on the accuracy of the model instance.
4. Achieved the face detection and facial feature extraction algorithm proposed in this paper with OpenCV, and built a complete face recognition demo using MFC.
本文所做的主要研究工作如下:
1.详细阐述了目前最具实用价值的基于AdaBoost算法的人脸检测方法,主要研究了Haar-like特征提取、分类器设计以及多尺度变换三个方面的问题。同时为了进一步降低误检率,对AdaBoost算法的检测结果进行肤色校验,从而实现有效地去除误检人脸区域。
2.研究实现了基于主动形状模型(ASM)的人脸特征点提取算法。详细分析了经典ASM方法的模型建立和匹配搜索算法,同时针对传统方法在人脸含有表情情况下遇到的困难,设计了将人脸区域按变化相关度进行划分、建模的改进型ASM算法。改进后的方法对人脸面部存在表情或人在说话的情况下能更准确地进行特征点的定位。另外,还尝试研究了将核主成分分析替换主成分分析以提高小角度偏转情况下人脸特征点定位的准确性。
3.研究实现了基于主动表观模型(AAM)的人脸特征点提取算法。详细分析了经典AAM方法的模型建立和匹配搜索算法,研究了反向合成算法在AAM匹配过程中的应用。为降低全局光照的干扰,将纹理归一化操作融合到反向合成算法中,提高了模型生成实例的准确性。
4.利用OpenCV对本文的人脸检测和人脸特征提取算法进行了实现,并借助MFC搭建了一个完整的人脸识别演示程序。
Face recognition is a hot research field in biometrics identification technology, and there are many ways to realize it. How to implement it accurately and efficiently is one of the major difficulties in face recognition. Generally, a complete face recognition system consists of four main areas: the acquisition of face images, face detection, facial feature extraction and feature matching. In these areas, how to detect face fast and accurately, and how to extract facial feature accurately will affect the performance of the system directly. In this paper, we select the existing classic face detection and facial feature extraction algorithm to analyze, research and implementation. To solve the problems found during the experiment, we improved the classical algorithm combining with knowledge of digital image processing and pattern recognition. The performance of these algorithms has been improved to a certain degree.
The major research work is as follows:
1. Described a face detection method based on the AdaBoost algorithm, which has the most practical value at present. Researched on how to extract Haar-like features, how to design classifiers and how to solve the problem on multi-scale transform. Meanwhile, in order to further reduce the false detection rate, we took skin color calibration on the results of AdaBoost algorithm to remove the false face areas effectively.
2. Studied and implemented the facial feature extraction algorithm base on active shape model (ASM). Analyzed the model building and matching search algorithm of the classical ASM in detail. To solve the difficulties encountered in the traditional method with expression in the face, we proposed an improved ASM algorithm: divide face region by change-related degree and model and search independently. The improved algorithm can achieve a more accurate feature point location with the existence of human facial expressions or in the case of talking. In addition, we also tried to replace principal component analysis with kernel principal component analysis to improve the location accuracy under the situation of face with small-angle deflection.
3. Researched and implemented facial feature extraction algorithm based on Active Appearance Model (AAM). Analyzed the modeling and matching search algorithm of the classical AAM in detail. Studied how to using Inverse Compositional Algorithm in the matching searches process. To reduce the interference taking by global illumination, we took the texture normalized operation into the inverse compositional algorithm integrated, and achieved an improvement on the accuracy of the model instance.
4. Achieved the face detection and facial feature extraction algorithm proposed in this paper with OpenCV, and built a complete face recognition demo using MFC.
引文
[1]王映辉.人脸识别-原理、方法与技术.北京:科学出版社, 2010, 3-4
[2]田捷,杨鑫.生物特征识别技术理论与应用.北京:电子工业出版社, 2005, 6-8
[3]雷玉堂.面相识别与其他生物识别技术的比较.第十一届中国国际公共安全博览会-行业应用, 2007, 128-134
[4] Biometrics market and industry report 2009. http://www.ibgweb.com/reports/public/ma-rket_report.php
[5] M.A. Turk, A.P. Pentland. Face recognition using eigenfaces. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1991, 586-591
[6] A.M. Martinez, A.C. Kak. PCA versus LDA. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 228-233
[7] H.A. Rowley, S. Baluja, T. Kanade. Neural network-based face detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1998, 23-38
[8] A.V. Nefian, M.H. Hayes. Face detection and recognition using hidden Markov models. International Conference on Image Processing, 1998, Vol. 1:141-145
[9] E. Osuna, R. Freund, F. Gorosi. Training support vector machines: an application to face detection. IEEE Conference on Computer Vision and Pattern Recognition, 1997, 130-136
[10] P. Viola, M. Jones. Rapid object detection using a boosted cascade of simple features. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2001, 511-518
[11] B. Moghaddam, T. Jebara, A. Pentland. Bayesian face recognition. Pattern Recognition, 2000, 33(11):1771-1782
[12] T.F. Cootes, C.J. Taylor. Active shape models-smart snakes. Proceeding of the British Vision Conference, September, 1992, 266-275
[13] T.F. Cootes, C.J. Taylor. Active shape models-their training and application. [J]. Computer Vision and Image Understanding, 1995, 61(1):38-59
[14] A. Hill, T.F. Cootes, C.J. Taylor. active shape models and the shape approximation problem. Image and Vision Computing, 1996, Vol. 14:601-607
[15] G.J. Edwards, T.F. Cootes, C.J. Taylor. Face recognition using active appearance models. Proceedings of the 5th European Conference on Computer Vision, 1998, Vol. 2:581-595
[16] T.F. Cootes, G.J. Edwards, C.J. Taylor. Active appearance models [J]. Pattern Analysis and Machine Intelligence, 2001, 23(6):681-685
[17] T.F. Cootes, C.J. Taylor. Statistical models of appearance for computer vision. World Wide Web Publication, 2001, 69-73
[18] Xiaoming Liu. Discriminative face alignment. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31(11), 1941-1954
[19] A.S. Georghiades, P.N. Belhumeur, D.J. Keiegman. From few to many: illuminition cone models for face recognition under variable lighting and poses. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(6):643-660
[20] A. Shashua, T. Riklin Raviv. The quotient image: class based re-rendering and recognition with varying illuminations. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(2):129-139
[21] R. Basria, D. Jacobs. Lambertian reflectance and linear subspaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(2):218-233
[22] Rainer Lienhart, Jochen Maydt. An extended set of haar-like features for rapid object detection. The International Conference on Image Processing, 2002, Vol. 1:900-903
[23] P. Viola, M. Jones. Robust real-time object detection. Proceeding of 2nd International Workshop on Statistical and Computational Theories of Vision-Modeling, Learning, Computing and Sampling, 2001, 1-15
[24] P. Viola, M. Jones. Robust real-time face detection. International Journal of Computer Vision, 2004, 57(2):137–154
[25] Y. Freund, R.E. Schapire. A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 1997, 55(1):119-139
[26] Y. Freund, R.E. Schapire. Game theory, on-line prediction and boosting. Proceeding of the Ninth Annual Conference on Computational Learning Theory, 1996, 325–332
[27] R.E. Schapire, Y. Singer. Improved boosting algorithms using confidence-rated predictions. Machine Learning, 37(3):297-336
[28] Jerome Friedman, Trevor Hastie and Robert Tibshirani. Additive logistic regression: A tatistical view of boosting. The Annals of Statistics, 2000, 38(2):337–374
[29] R.E. Schapire. The strength of weak learnability. Journal of Machine Learning, 1990, 5(2):197-227
[30] Cheo Hun Han, Kwee-Bo Sim. Real-time face detection using adaboot algorithm.International Conference on Control Automation and Systems, 2008, 1893-1895
[31] C.N.R. Kumar, A. Bindu. An efficient skin illumination compensation model for efficient face detection. IEEE 32nd Annual Conference on Industrial Electronics, 2006, 3444–3449
[32] Rafael C. Gonzalez, Richard E. Woods (著).阮秋琦等(译).数字图像处理(第二版).北京:电子工业出版社, 2003, 228-239
[33] Ming-Hsuan Yang, Ahuja, N. Detecting human faces in color images. International Conference on Image Processing, 1998, Vol. 1:127-139
[34] R.L. Hsu, M. Abdel-Mottaleb, A.K. Jain. Face detection in color images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(5):696-706
[35] M. Kass, A.Witkin, D. Terzopdulos. Active contour models. International Journal of Computer Vision, 1988, 1(4):321-331
[36] L. Wiskott, J.M. Fellous, N. Krüger, et al. Face recognition by elastic bunch graph matching. 7th International Conference on Computer Analysis of Images and Patterns, 1997, 456-463
[37] Volker Blanz, Thomas Vetter. A morphable model for the synthesis of 3D faces. 26th Annual Conference on Computer Graphics and Interactive Techniques, 1999, 187-194
[38] Michael M. Nordstrim, Mads Larsen, Janusz Sierakowski, et al. The IMM face database. http://www2.imm.dtu.dk/pubdb/views/publication_details.php?id=3160
[39] Procrustes analysis. http://en.wikipedia.org/wiki/Procrustes_analysis
[40] Xu hua, Ma zheng. An improved active shape model for facial feature location. 2nd International Symposium on Intelligent Information Technology Application, 2008, 114-118
[41]范玉华,马建伟. ASM及其改进的人脸面部特征定位算法.计算机辅助设计与图形学学报, 2007, 19(11):1411-1415
[42]李嵩,刘党辉,沈兰荪.基于ASM和线段Hausdorff距离的人脸识别.计算机应用, 2008, 28(5):1217-1220
[43]庄连生,张浩,杨俊安等.基于ASM的人脸特征点自动标定.电路与系统学报, 2006, 11(3):101-105
[44] Yunlong Wei, Mei Xie. An improved active shape model for facial feature location. International Symposium on Computer Network and Multimedia Technology, 2009, Vol. 1:453-456
[45] Kwok-Wai Wan, Kin-Man Lam, Kit-Chong Ng. An accurate active shape model for facial feature extraction. Pattern Recognition Letters, 2005, Vol. 26:2409-2423
[46]魏云龙,解梅.一种基于KPCA的3视角非线性ASM人脸特征提取方法.电子科技大学研究生学报, 2010, No.74:75-79
[47] Bernhard Scholkopf, Alexander Smola, and Klaus-Robert Müller. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 1998, 10(5):1299-1319
[48] M. Jordan, J. Kleinberg, B. Scholkopf. Pattern recognition and machine learning. Springer Science+Business Media, LLC, 2006, 586-590
[49]袁艳.基于KPCA的人脸识别中核函数参数的研究[硕士学位论文].大连:大连海事大学, 2008, 14-19
[50] Sami Romdhani, Shaogang Gong, Alexandra Psarrou. A Multi-View Nonlinear Active Shape Model Using Kernel PCA. British Machine Vision Conference, 1999, 483-492.
[51] B. Delaunay. Sur la sphère vide, Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskikh i Estestvennykh Nauk, 1934, Vol. 7:793-800
[52] T.F. Cootes, C.J. Twining, V. Petrovic, et al. Groupwise construction of appearance models using piece-wise affine deformations. British Machine Vision Conference, 2005, Vol. 2: 879-888
[53] Donald Hearn, M. Pauline Baker (著).蔡世杰等(译).计算机图形学(第三版).北京:电子工业出版社, 2005, 504-509
[54] Mikkel Bille Stegmann. Active appearance models theory, extensions & cases. Technical University of Denmark, 2000, 70-71
[55] Iain Matthews, Simon Baker. Active appearance models revisited. International Journal of Computer Vision. 2004, 60(2):135-164
[56] S. Baker, I. Matthews. Lucas-Kanade 20 years on: a unifying framework. International Journal of Computer Vision, 2003, 56(3):221-255
[57]张培,吴亚锋. AAM反向合成匹配算法及其性能分析.计算机工程与应用, 2007, 43(18):47-50
[58] Fan Xiao-Jiu, Peng Qiang, Chen Jim X, et al. An improved AAM fast localization method for human facial features. Dianzi Yu Xinxi Xuebao/Journal of Electronics and Information Technology, 2009, Vol. 31:1354-1358
[59] Zhao Xinbo, Zou Xiaochun. Improving convergence of AAM (active appearance model) fitting algorithm based on orthogonal projection. Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University, 2008, Vol. 26:168-172
[60] OpenCV中文网站. http://www.opencv.org.cn/index.php/%E9%A6%96%E9%A1%B5, 2011
[2]田捷,杨鑫.生物特征识别技术理论与应用.北京:电子工业出版社, 2005, 6-8
[3]雷玉堂.面相识别与其他生物识别技术的比较.第十一届中国国际公共安全博览会-行业应用, 2007, 128-134
[4] Biometrics market and industry report 2009. http://www.ibgweb.com/reports/public/ma-rket_report.php
[5] M.A. Turk, A.P. Pentland. Face recognition using eigenfaces. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1991, 586-591
[6] A.M. Martinez, A.C. Kak. PCA versus LDA. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 228-233
[7] H.A. Rowley, S. Baluja, T. Kanade. Neural network-based face detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1998, 23-38
[8] A.V. Nefian, M.H. Hayes. Face detection and recognition using hidden Markov models. International Conference on Image Processing, 1998, Vol. 1:141-145
[9] E. Osuna, R. Freund, F. Gorosi. Training support vector machines: an application to face detection. IEEE Conference on Computer Vision and Pattern Recognition, 1997, 130-136
[10] P. Viola, M. Jones. Rapid object detection using a boosted cascade of simple features. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2001, 511-518
[11] B. Moghaddam, T. Jebara, A. Pentland. Bayesian face recognition. Pattern Recognition, 2000, 33(11):1771-1782
[12] T.F. Cootes, C.J. Taylor. Active shape models-smart snakes. Proceeding of the British Vision Conference, September, 1992, 266-275
[13] T.F. Cootes, C.J. Taylor. Active shape models-their training and application. [J]. Computer Vision and Image Understanding, 1995, 61(1):38-59
[14] A. Hill, T.F. Cootes, C.J. Taylor. active shape models and the shape approximation problem. Image and Vision Computing, 1996, Vol. 14:601-607
[15] G.J. Edwards, T.F. Cootes, C.J. Taylor. Face recognition using active appearance models. Proceedings of the 5th European Conference on Computer Vision, 1998, Vol. 2:581-595
[16] T.F. Cootes, G.J. Edwards, C.J. Taylor. Active appearance models [J]. Pattern Analysis and Machine Intelligence, 2001, 23(6):681-685
[17] T.F. Cootes, C.J. Taylor. Statistical models of appearance for computer vision. World Wide Web Publication, 2001, 69-73
[18] Xiaoming Liu. Discriminative face alignment. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31(11), 1941-1954
[19] A.S. Georghiades, P.N. Belhumeur, D.J. Keiegman. From few to many: illuminition cone models for face recognition under variable lighting and poses. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(6):643-660
[20] A. Shashua, T. Riklin Raviv. The quotient image: class based re-rendering and recognition with varying illuminations. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(2):129-139
[21] R. Basria, D. Jacobs. Lambertian reflectance and linear subspaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(2):218-233
[22] Rainer Lienhart, Jochen Maydt. An extended set of haar-like features for rapid object detection. The International Conference on Image Processing, 2002, Vol. 1:900-903
[23] P. Viola, M. Jones. Robust real-time object detection. Proceeding of 2nd International Workshop on Statistical and Computational Theories of Vision-Modeling, Learning, Computing and Sampling, 2001, 1-15
[24] P. Viola, M. Jones. Robust real-time face detection. International Journal of Computer Vision, 2004, 57(2):137–154
[25] Y. Freund, R.E. Schapire. A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 1997, 55(1):119-139
[26] Y. Freund, R.E. Schapire. Game theory, on-line prediction and boosting. Proceeding of the Ninth Annual Conference on Computational Learning Theory, 1996, 325–332
[27] R.E. Schapire, Y. Singer. Improved boosting algorithms using confidence-rated predictions. Machine Learning, 37(3):297-336
[28] Jerome Friedman, Trevor Hastie and Robert Tibshirani. Additive logistic regression: A tatistical view of boosting. The Annals of Statistics, 2000, 38(2):337–374
[29] R.E. Schapire. The strength of weak learnability. Journal of Machine Learning, 1990, 5(2):197-227
[30] Cheo Hun Han, Kwee-Bo Sim. Real-time face detection using adaboot algorithm.International Conference on Control Automation and Systems, 2008, 1893-1895
[31] C.N.R. Kumar, A. Bindu. An efficient skin illumination compensation model for efficient face detection. IEEE 32nd Annual Conference on Industrial Electronics, 2006, 3444–3449
[32] Rafael C. Gonzalez, Richard E. Woods (著).阮秋琦等(译).数字图像处理(第二版).北京:电子工业出版社, 2003, 228-239
[33] Ming-Hsuan Yang, Ahuja, N. Detecting human faces in color images. International Conference on Image Processing, 1998, Vol. 1:127-139
[34] R.L. Hsu, M. Abdel-Mottaleb, A.K. Jain. Face detection in color images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24(5):696-706
[35] M. Kass, A.Witkin, D. Terzopdulos. Active contour models. International Journal of Computer Vision, 1988, 1(4):321-331
[36] L. Wiskott, J.M. Fellous, N. Krüger, et al. Face recognition by elastic bunch graph matching. 7th International Conference on Computer Analysis of Images and Patterns, 1997, 456-463
[37] Volker Blanz, Thomas Vetter. A morphable model for the synthesis of 3D faces. 26th Annual Conference on Computer Graphics and Interactive Techniques, 1999, 187-194
[38] Michael M. Nordstrim, Mads Larsen, Janusz Sierakowski, et al. The IMM face database. http://www2.imm.dtu.dk/pubdb/views/publication_details.php?id=3160
[39] Procrustes analysis. http://en.wikipedia.org/wiki/Procrustes_analysis
[40] Xu hua, Ma zheng. An improved active shape model for facial feature location. 2nd International Symposium on Intelligent Information Technology Application, 2008, 114-118
[41]范玉华,马建伟. ASM及其改进的人脸面部特征定位算法.计算机辅助设计与图形学学报, 2007, 19(11):1411-1415
[42]李嵩,刘党辉,沈兰荪.基于ASM和线段Hausdorff距离的人脸识别.计算机应用, 2008, 28(5):1217-1220
[43]庄连生,张浩,杨俊安等.基于ASM的人脸特征点自动标定.电路与系统学报, 2006, 11(3):101-105
[44] Yunlong Wei, Mei Xie. An improved active shape model for facial feature location. International Symposium on Computer Network and Multimedia Technology, 2009, Vol. 1:453-456
[45] Kwok-Wai Wan, Kin-Man Lam, Kit-Chong Ng. An accurate active shape model for facial feature extraction. Pattern Recognition Letters, 2005, Vol. 26:2409-2423
[46]魏云龙,解梅.一种基于KPCA的3视角非线性ASM人脸特征提取方法.电子科技大学研究生学报, 2010, No.74:75-79
[47] Bernhard Scholkopf, Alexander Smola, and Klaus-Robert Müller. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 1998, 10(5):1299-1319
[48] M. Jordan, J. Kleinberg, B. Scholkopf. Pattern recognition and machine learning. Springer Science+Business Media, LLC, 2006, 586-590
[49]袁艳.基于KPCA的人脸识别中核函数参数的研究[硕士学位论文].大连:大连海事大学, 2008, 14-19
[50] Sami Romdhani, Shaogang Gong, Alexandra Psarrou. A Multi-View Nonlinear Active Shape Model Using Kernel PCA. British Machine Vision Conference, 1999, 483-492.
[51] B. Delaunay. Sur la sphère vide, Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskikh i Estestvennykh Nauk, 1934, Vol. 7:793-800
[52] T.F. Cootes, C.J. Twining, V. Petrovic, et al. Groupwise construction of appearance models using piece-wise affine deformations. British Machine Vision Conference, 2005, Vol. 2: 879-888
[53] Donald Hearn, M. Pauline Baker (著).蔡世杰等(译).计算机图形学(第三版).北京:电子工业出版社, 2005, 504-509
[54] Mikkel Bille Stegmann. Active appearance models theory, extensions & cases. Technical University of Denmark, 2000, 70-71
[55] Iain Matthews, Simon Baker. Active appearance models revisited. International Journal of Computer Vision. 2004, 60(2):135-164
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