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研究生:李易俊
研究生(外文):Yi-ChunLee
論文名稱:基於Gabor水平與垂直特徵之人臉判別
論文名稱(外文):A Gabor Feature Based Horizontal and Vertical Discriminant for Face Verification
指導教授:陳進興陳進興引用關係
指導教授(外文):Chin-Hsing Chen
學位類別:博士
校院名稱:國立成功大學
系所名稱:電腦與通信工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:89
中文關鍵詞:Gabor 費雪分類器費雪線性判別增強型費雪模型Gabor 濾波器
外文關鍵詞:Gabor Fisher classifier (GFC)Fisher linear discriminant (FLD)enhanced Fisher linear discriminant model (EFM)Gabor Filters
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本論文針對人臉辨識提出三種不同的新判別方法。第一種方法利用曲線波轉換來萃取人臉特徵。在方法中,原始影像使用六個與方向、尺度變化相關的Gabor濾波器製造出六個Gabor影像特徵,再將Gabor影像特徵作脊波轉換分析,並緊接著使用二維主軸分析(2DPCA)方法計算出脊波轉換之共變異矩陣的特徵向量。實驗結果顯示,此方法在人臉辨識度可達到95.5%。
第二種方法利用Gabor特徵萃取並採用二維局部保留投影 (2DLPP)。首先在特徵萃取中,將原始影像使用與方向、尺度變化相關的Gabor濾波器製作出影像特徵,再利用2DPCA方法直接對二維Gabor影像特徵矩陣降低維度,而2DLPP則利用偵測本身的紋理來保留影像空間的局部結構。使用ORL人臉資料庫的實驗結果顯示此方法有較高辨識率並且可達到95.5%。
最後一種方法,首先將水平與垂直二維主軸分析(HV-2DPCA)直接應用於Gabor影像特徵來降低其資訊維度並有效保留雙方向特性,接著採用增強型費雪線性判別模型來產生低維度的特徵表示與判別能力的增強並將不同類別的訓練樣本在投影空間上的距離拉得更開,而相同類別的訓練樣本在投影空間上的距離則是拉得更近,我們稱此法為基於Gabor水平與垂直特徵之人臉判別(HV-EGF)。在使用各種特徵維度以及各種訓練樣本數中,實驗數據證明我們提出的HV-EGF方法跟費雪線性判別(FLD)方法、EFM方法及Gabor費雪分類器(GFC)相比較,HV-EGF具有較高的辨識率。在ORL與Yale人臉資料庫中,HV-EGF方法在使用38382與10102的特徵維度下分別可以達到99.0%與97.7%的辨識率。

This thesis proposes three different approaches for face recognition. In the first approach, a novel feature extraction method for face recognition is proposed. The digital curvelet transform is used to extract the face features. In the method, an original image is convolved with 6 Gabor filters corresponding to various orientations and scales to give its Gabor representation. Then, the Gabor representation is analyzed by the ridgelet transform followed by the two-dimensional principal component analysis (2DPCA) which computes the eigenvectors of the ridgelet image covariance matrix. Experiments showed that the correct recognition rate of our method is up to 95.5%.
For the second approach, a new method of the two-dimensional locality preserving projections (2DLPP) was proposed to extract Gabor features for face recognition. The 2DPCA is first utilized for dimensionality reduction of Gabor feature space, which is implemented directly from 2D image matrices. The objective of 2DLPP is to preserve the local structure of the image space by detecting the intrinsic manifold structure. In the method, an original image is convolved with Gabor filters corresponding to various orientations and scales to give its Gabor representation. Experiments are conducted on the ORL face database, which shows higher recognition performance of the proposed method. The top recognition rate can reach 95.5%.
In the last approach, a novel discriminant analysis method for a Gabor-based image feature extraction and representation is proposed and then implemented. The horizontal and vertical two-dimensional principal component analysis (HV-2DPCA) is directly applied to a Gabor face to reduce the redundant information and preserves a bi-directional characteristic as well. It is followed by an enhanced Fisher linear discriminant model (EFM) generating a low-dimensional feature representation with enhanced discrimination power. By the most discriminant features, different types of classes of training samples are made widely apart and the same category classes are made as compact as possible. This novel algorithm is designated as the horizontal and vertical enhanced Gabor Fisher discriminant (HV-EGF). By use of various dimensions of features as well as various numbers of training samples, our experiments indicate that the proposed HV-EGF method provides a superior recognition accuracy relative to those by the Fisher linear discriminant (FLD), the EFM and the Gabor Fisher classifier (GFC) methods. In our proposal, the recognition accuracies up to 99.0% and 97.7% are reached with images of features dimensions and on the ORL and the Yale databases, respectively.

摘要 I
Abstract III
致謝 V
Contents VI
List of Tables IX
List of Figures X

Chapter 1 Introduction
1.1 Motivation 1
1.2 Related Research 1
1.3 The Proposed Approach 5
1.4 Organization of the Thesis 7
Chapter 2 Technology of Image Preprocessing
2.1 Introduction 8
2.2 Wavelet Theory 8
2.3 Gabor Filtering 13
2.4 Gabor Representation 18
Chapter 3 Image Analysis for Feature Discriminant
3.1 Introduction 22
3.2 Principal Component Analysis 22
3.2.1 The Basic Concept of Principal Component Analysis 22
3.2.2 Two-Dimensional Principal Component Analysis 25
3.2.3 Horizontal 2DPCA 25
3.2.4 Vertical 2DPCA 27
3.2.5 Properties 29
3.3 Two-Dimensional Fisher Linear Discriminant 30
3.3.1 Notations 33
3.3.2 One-Dimensional FLD (1DFLD) 34
3.3.3 Two-Dimensional FLD (2DFLD) 34
3.4 The Enhanced Fisher Linear Discriminant Model (EFM) 36
3.4.1 Dimensionality Reduction (PCA) 36
3.4.2 Enhanced FLD Model (EFM) 38
3.5 Digital Curvelet Transform 39
3.5.1 Two-Dimensional Wavelet Transform 40
3.5.2 Ridgelet Transform 41
3.6 Two-Dimensional Locality Preserving Projections (2DLPP) 43
Chapter 4 Experimental Results on Digital Curvelet Transform Approach
4.1 Introduction 47
4.2 The Proposed method 48
4.3 Experiments 49
Chapter 5 Experimental Results on Two-Dimensional Locality Preserving Projection Approach
5.1 Introduction 52
5.2 The Proposed method 53
5.3 Experiments 54

Chapter 6 Experimental Results on Gabor Feature Based Horizontal and Vertical Discriminant Approach
6.1 Introduction 57
6.2 The Proposed method 58
6.3 Experiments on ORL Database 59
6.3.1 Gabor Feature Representation 60
6.3.2 Experiments with different dimensions of feature space 61
6.3.3 Experiments of some fixed training samples 64
6.4 Experimental Results on Yale Database 68
6.4.1 Gabor Feature Representation 69
6.4.2 Experiments with different dimensions of feature space 71
6.4.3 Experiments of some fixed training samples 73
6.5 Summary 78
Chapter 7 Conclusion
7.1 Conclusion 80
References 82

[1] M. Alwakeel and Z. Shaaban, “Face Recognition Based on Haar Wavelet Transform and Principal Component Analysis via Levenberg-Marquardt Backpropagation Neural Network, European Journal of Scientific Research ISSN 1450-216X, Vol. 42, No. 1, pp. 25-31, 2010.
[2] M. Antonini, M. Barlaud and I. Daubechies, “Image Coding using Wavelet Transform, IEEE Trans. On Image Processing Vol. 1, No. 2, pp. 205-220, April 1992.
[3] M. Bahoura and J. Rouat, “Wavelet Speech Enhancement using the Teager Energy Operator, IEEE Signal Processing Letters, Vol. 8, No. 1, pp. 10-12, January 2001.
[4] P. N. Belhumeur, J. P. Hespanha and D. J. Kriegman, “Eigenfaces vs. Fisherfaces: Recognition using Class Specific Linear Projection, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 19, No. 7, pp. 711-720, 1997.
[5] M. Belkin and P. Niyogi, “Laplacian Eigenmaps for Dimensionality Reduction and Data Representation, Neural Computation, Vol. 15, No. 6, pp. 1373-1396, 2003.
[6] G. Beylkin, “On the Representation of Operators in Bases of Compactly Supported Wavelets, SIAM J. Numer. Anal., Dec. 1992.
[7] A. C. Bovik, M. Clark and W. S. Geisler, “Multichannel Texture Analysis using Localized Spatial Fillters, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 12, No. 1, pp. 55-73, 1990.
[8] C. S. Burrus, R. A. Gopinath, and H. Guo. Introduction to Wavelets and Wavelet Transforms: A Primer. Prentice Hall, Upper Saddle River, New Jersey 07458, 1998.
[9] E. J. Candès, “Harmonic Analysis of Neural Networks, Applied and Computational Harmonic Analysis, pp. 197-218, 1999.
[10] E. J. Candès, L. Demanet, D. L. Donoho, L. Ying, “Fast Discrete Curvelet Transform, SIAM Multiscale Model, Simul. 2006.
[11] E. J. Candès and D. Donoho, “Curvelets - A Surprisingly Effective Nonadaptive Representation for Objects with Edges, In: A. Cohen, C. Rabut and L. Schumaker, Editors, Curves and Surface Fitting: Saint-Malo 1999, Vanderbilt University Press, Nashville, pp. 105-120, 2000.
[12] S. Chang, Y. Kwon and S. Yang, “Speech Feature Extracted from Adaptive Wavelet for Speech Recognition, Electron. Lett., Vol. 34, No. 23, pp. 2211-2213, 1998.
[13] S. Chen, H. Zhao, M. Kong, B. Luo, “2DLPP: A Two-dimensional Extension of Locality Preserving Projections, Neurocomputing, Vol. 70, pp.912-921, 2007.
[14] I. Dagher and R. Nachar, “Face Recognition using IPCA-ICA Algorithm, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 28, pp. 996-1000, 2006.
[15] I. Daubechies, “The Wavelet Transform, Time-Frequency Localization and Signal Analysis, IEEE Trans. Inf. Theory, Vol. 36, pp. 961-1005, 1990.
[16] J. G. Daugman, “Two-dimensional Spectral Analysis of Cortical Receptive Field Profiles, Vision Research, Vol. 20, pp. 847-856, 1980.
[17] J. G. Daugman, “Uncertainty Relation for Resolution in Space, Spatial Frequency, and Orientation Optimized by Two-dimensional Visual Cortical Filters, Journal of Optical America A, Vol. 2, No. 7, pp. 1160-1169, 1985.
[18] J. G. Daugman, “Complete Discrete 2D Gabor Transforms by Neural Networks for Image Analysis and Compression, IEEE Trans. Acoustic Speech and Signal Proc., Vol. 36, No. 7, pp. 1169-1179, 1988.
[19] M. N. Do and M. Vetterli, “The Finite Ridgelet Transform for Image Representation, IEEE Transactions on Image Processing, Vol. 12, No. 1, pp. 16-28, 2003.
[20] M. N. Do and M. Vetterli, “The Contourlet Transform: An Efficient Directional Multiresolution Image Representation, IEEE Transactions on Image Processing, Vol. 14, No. 12, 2091-2106, 2005.
[21] D. L. Dohono and M. R. Duncan, “Digital Curvelet Transform Strategy, Implementation and Experiments, Available at http://www-stat.stanford.edu/ ~beamlab/.
[22] R. Duda and P. Hart, “Pattern Classification and Scene Analysis, (Wiley, New York) 1973.
[23] S. Edelman, “Representation and Recognition in Vision, (MIT Press, Cambridge, MA), 1999.
[24] K. Etemad and R. Chellappa, “Discriminant Analysis for Recognition of Human Face Images, Jl. Optical Society of America, Vol. 14, pp. 1724-1733, 1997.
[25] G. Y. Feng, D. W. Hu and Z. T. Zhou, “A Direct Locality Preserving Projections (DLPP) Algorithm for Image Recognition, Neural Processing Letters, Vol. 27, No. 3, pp. 247-255, 2005.
[26] C. Garcia, G. Zikos, G. Tziritas, “Wavelet Packet Analysis for Face Recognition,“ Image and Vision Computing, Vol. 18, pp. 289-297, 2000.
[27] R. C. Gonzalez and R. E. Woods, “Digital Image Processing, Second Edition, Prentice Hall, NJ, 2002.
[28] A. L. Graps, “An Introduction to Wavelets, IEEE Computational Sciences and Engineering, Vol. 2, No. 2, pp. 50-61, 1995.
[29] J. H. Guo, “Wavelet Bookmark, Department of Mathematics National Central University (http://www.math.ncu.edu.tw/~guo/ wavelet_bookmark/index.html).
[30] X. He, D. Cai, S. C. Yan and H. J. Zhang, “Neighborhood Preserving Embedding, IEEE International Conference on Computer Vision, Vol. 2, pp. 1208-1213, 2005.
[31] X. He and P. Niyogi, Locality Preserving Projections, Proceedings of the Conference on Advances in Neural Information Processing System, pp. 135-160, 2003.
[32] X. He, S. Yan, Y. Hu, P. Niyogi and H. Zhang, “Face Recognition using Laplicanfaces, IEEE Trans. Pattern Anal. Mach. Intell, Vol. 27, No. 3, pp.328-340, 2005.
[33] D. Hu, G. Feng and Z. Zhou, “Two-dimensional Locality Preserving Projections (2DLPP) with its Application to Palmprint Recognition, Pattern Recognition, Vol. 40, pp. 339-342, 2007.
[34] A. Hyvrinen, “Fast and Robust Fixed-Point Algorithms for Independent Component Analysis,“ Neural Computing Surveys, Vol. 2, pp. 94-128, 1999.
[35] Y. Jian and L. Chengjun, “Horizontal and Vertical 2DPCA-based Discriminant Analysis for Face Verification on A Large-Scale Database, IEEE Transactions on Information Forensics and Security, Vol. 2, No. 4, pp. 781-792, 2007.
[36] J. Jones and L. Palmer, “An Evaluation of the Two-dimensional Gabor Filter Model of Simple Receptive Fields in Cat Striate Cortex, J. Neurophysiol, pp. 1233-1258, 1987.
[37] S. Kadambe and G. F. Boudreaux-Bartels, “Application of the Wavelet Transform for Pitch Detection of Speech Signals, IEEE Trans. Inform. Theory, Vol. 38, No. 2, pp. 917-924, Mar. 1992.
[38] S. N. Kakarwal, S. D. Sapkal, P. J. Ahire, Dr. D. S. Bormane, “Analysis of Facial Image Classification using Discrete Wavelet Transform, in Proc. International Conference ICSCI, pp. 700-705, 2007.
[39] M. Kirby and M. Sirovich, “Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 12, No. 1, pp. 103-108, 1990.
[40] H. Kong, L. Wang, E. K. Teoh, X. Li and J. G. Wang et al., “Generalized 2D Principal Component Analysis for Face Image Representation and Recognition, Neural Netw., Vol. 18, No. 5-6, pp. 585-594, 2005.
[41] M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. von der Malsburg, R. R. Wurtz and W. Konen, “Distortion Invariant Object Recognition in the Dynamic Link Architecture, IEEE Trans. Computers, Vol. 42, pp. 300-311, 1993.
[42] M. Li and B. Yuan, “2D-LDA: A Statistical Linear Discriminant Analysis for Image Matrix, Pattern Recognition Letters, Vol. 26, No. 5, pp. 527-532, 2005.
[43] S. D. Lin, J. H. Lin and C. C. Chiang, “Using Gradient Features from Scale-Invariant Keypoints on Face Recognition, International Journal of Innovative Computing, Information and Control (IJICIC), Vol. 7, No. 4, pp. 1639-1649, 2011.
[44] C. J. Lin, J. G. Wang, and S. M. Chen, “2D/3D Face Recognition Using Neural Network Based on Hybrid Taguchi-Particle Swarm Optimization, International Journal of Innovative Computing, Information and Control (IJICIC), Vol. 7, No. 2, pp. 537-553, 2011.
[45] C. Liu and H. Wechsler, “Robust Coding Schemes for Indexing and Retrieval from Large Face Databases, IEEE Trans. Image Process., Vol. 9, No. 1, pp. 132-137, 2000.
[46] C. Liu and H. Wechsler, “A Shape and Texture Based Enhanced Fisher Classifier for Face Recognition, IEEE Trans. Image Process., Vol. 10, No. 4, pp. 598-608, 2001.
[47] C. Liu and H. Wechsler, “A Gabor Feature Classifier for Face Recognition, Eighth IEEE International Conference on Computer Vision, pp. 9-12, 2001.
[48] C. Liu and H. Wechsler, “Gabor Feature Based Classification using the Enhanced Fisher Linear Discriminant Model for Face Recognition, IEEE Trans. Image Processing, Vol. 11, No. 4, pp. 467-476, 2002.
[49] C. Liu and H. Wechsler, “Independent Component Analysis of Gabor Features for Face Recognition, IEEE Trans. Neural Networks, Vol. 14, No. 4, pp. 919-928, 2003.
[50] S. G. Mallat, Multiresolution Approach to Wavelets in Computer Vision, 2nd Edition, Springer, New York, 1989.
[51] L. S. Qiao, S. C. Chen and X. Y. Tan, “Sparsity Preserving Projections with Applications to Face Recognition, Pattern Recognition, Vol. 43, No. 1, pp. 331-341, 2010.
[52] S. T. Roweis and L. K. Saul, Nonlinear Dimensionality Reduction by Locally Linear Embedding, Science, Vol. 290, No.5500, pp. 2323-2326, 2000.
[53] A. H. Sahoolizadeh, B. Z. Heidari and C. H. Dehghani, “A New Face Recognition Method using PCA, LDA and Neural Network, International Journal of Computer Science and Engineering, 2008.
[54] K. Sandberg, “The Haar Wavelet Transform, (http://amath.colora do.edu/courses/4720/2000Spr/Labs/Haar/haar.html). Online, April 1, 2000.
[55] J. L. Starck, E. J. Candès and D. L. Dohono, “The Curvelet Transform for Image Denoising, IEEE Trans. Image Processing, Vol. 11, pp. 670-683, 2002.
[56] J. L. Starck, F. Murtagh, E. J. Candès and D. L. Dohono, “Gray and Color Image Contrast Enhancement by the Curvelet Transform, IEEE Trans. Image Processing, Vol. 12 , pp.706-717, 2003.
[57] I. Sumana, M. Islam, D. S. Zhang and G. Lu, “Content Based Image Retrieval Using Curvlet Transform, In Proc.of IEEE International Workshop on multimedia signal processing, Cairs, Queensland, Australia, pp.111-16, October 8-10, 2008.
[58] D. L. Swets and J. Weng, “Using Discriminant Eigenfeatures for Image Retrieval, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 18, No. 8, pp. 831-836, 1996.
[59] D. M. Tsai and B. Hsiao, “Automatic Surface Inspection using Wavelet Reconstruction, Pattern Recognition, Vol. 34, pp. 1285-1305, 2001.
[60] M. Turk and A. Pentland, “Eigenfaces for Recognition, J. Cognitive Neuroscience, Vol. 3, No. 1, 1991.
[61] N. Vaswani and R. Chellappa, “Principal Components Null Space Analysis for Image and Video Classification, IEEE Trans. Image Process., Vol. 15, pp. 1816-1830, 2006.
[62] M. Visani, C. Garcia and C. Laurent, “Comparing Robustness of Two-dimensional PCA and Eigenfaces for Face Recognition, Lecture Notes Comput. Sci., Vol. 3212, pp. 717-724, 2004.
[63] L. W. Wang, X. Wang and J. F. Feng, “On Image Matrix Based Feature Extraction Algorithms, IEEE Trans. Syst., Man, Cybern. B, Vol. 36, No. 1, pp. 194-197, Feb. 2006.
[64] X. Wei, C. Zhou and Q. Zhang, “ICA-based Features Fusion for Face Recognition, International Journal of Innovative Computing, Information and Control (IJICIC), Vol. 6, No. 10, pp. 4651-4661, 2010.
[65] L. G. Weiss, R. K. Young, and L. H. Sibul, “Wide-band Processing of Acoustic-signals using Wavelet Transforms 1: Theory, J. Acoust. Soc. Amer., Vol. 96, pp. 850-856, 1994.
[66] R. Wilson, A. D. Calway and E. R. S. Pearson, “A Generalized Wavelet Transform for Fourier Analysis: The Multiresolution Fourier Transform and its Application to Image and Audio Signal Analysis, IEEE Trans. Inf. Theory, Vol. 38, No. 2, pp. 674-690, 1992.
[67] J. Xie, “Face Recognition Based on Curvelet Transform and LS-SVM, Proceedings of the 2009 International Symposium on Information Processing (ISIP’09), Huangshan, P. R. China, August 21-23, pp. 140-143, 2009.
[68] X. Xie and K. Lam, “Gabor-based Kernel PCA with Doubly Nonlinear Mapping for Face Recognition with A Single Face Image, IEEE Trans. Image Process., Vol. 15, pp. 2481-2492, 2006.

[69] H. Xiong, M. N. S. Swamy and M. O. Ahmad, “Two Dimensional FLD for Face Recognition, Pattern Recognition, Vol. 38, No. 7, pp. 1121-1124, 2005.
[70] J. Yang, D. Zhang, A. Frangi and J. Yang. “Two-dimensional PCA: A New Approach to Appearance-based Face Representation and Recognition, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 26, pp. 131-137, 2004.
[71] J. Ye, “Generalized Low Rank Approximations of Matrices, Mach. Learn., Vol. 61, No. 1-3, pp. 167-191, 2005.
[72] B. Yu, L. F. Jin and P. Chen, Normalized LDA Method for Face Recognition, Chinese Journal of Computer-aided Design and Computer Graphics, Vol. 15, No. 3, pp. 302-306, 2003.
[73] H. Yu and J. Yang, “A Direct LDA Algorithm for High-dimensional Data with Application to Face Recognition, Pattern Recognition, Vol. 34, No. 11, pp. 2067-2070, 2001.
[74] Y. Zeng and D. Feng, “The Face Recognition Method of the Two-directional Variation of 2DPCA, JDCTA: International Journal of Digital Content Technology and its Applications, Vol. 5, No. 2, pp. 216-223, 2011.
[75] B. Zhang, W. Gao, S. Shan and W. Wang, “Constraint Shape Model using Edge Constraint and Gabor Wavelet Based Search, AVBPA, pp. 52-61, 2003.
[76] D. Q. Zhang and Z. H. Zhou, “(2D)(2)PCA: Two-directional Two-dimensional PCA for Efficient Face Representation and Recognition, Neurocomput., Vol. 69, No. 1-3, pp. 224-231, 2005.
[77] Q. Zhang, C. Zhou and J. Zhao, “Face Recognition Based on FLDA, CPCA and Improved HMM, International Journal of Innovative Computing, Information and Control (IJICIC), Vol. 6, No. 2, pp. 801-807, 2010.
[78] Z. Zheng, F. Yang, W. Tan, J. Jia and J. Yang, Gabor Feature-based Face Recognition Using Supervised Locality Preserving Projection, Signal Processing, pp. 2473-2483, 2007.
[79] R. Zhi and Q. Ruan, “Facial Expression Recognition using Fuzzy Laplacianface, International Journal of Innovative Computing, Information and Control (IJICIC), Vol. 6, No. 5, pp. 1999-2011, 2010.
[80] W. M. Zuo, D. Zhang and K. Wang, “An Assembled Matrix Distance Metric for 2DPCA-based Image Recognition, Pattern Recognit. Lett., Vol. 27, No. 3, pp. 210-216, 2006.

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