歐陽明臺灣大學：資訊工程學研究所歐珮珮Ou, Pei-PeiPei-PeiOu2007-11-262018-07-052007-11-262018-07-052006http://ntur.lib.ntu.edu.tw//handle/246246/54014非負矩陣分解演算法的主要問題為，無法確保產生，對於人臉辨識很重要，具備局部強化特徵的基底。我們的目標是強化基底的局部特徵，以及將主軸分析演算法的正交特徵加在非負矩陣分解演算法上。為了降低原圖的雜訊干擾，例如臉部表情、光照變化和局部遮蔽，小波轉換被應用在基底強化非負矩陣分解演算法之前。在這篇論文中我們提出一個新的子空間投影技術，叫做小波轉換之基底強化非負矩陣分解演算法，以表示位於低頻的人臉圖像，並且產生較佳的人臉辨識正確率。最後將這些結果與主軸分析演算法和非負矩陣分解演算法做比較。A fundamental problem of Non-negative Matrix Factorization (NMF) is that it does not always extract basis components manifesting localized features which are essential in face recognition. The aim of our work is to strengthen localized features in basis images and to impose orthonormal characteristic of Principle Component Analysis (PCA) on NMF. Such improved technique is called Basis-emphasized Non-negative Matrix Factorization (BNMF). In order to reduce noise disturbance in the original image such as facial expression, illumination variation and partial occlusion, Wavelet Transform (WT) is applied before the BNMF decomposition. In this paper, a novel subspace projection technique, called Basis-emphasized Non-negative Matrix Factorization with Wavelet Transform (wBNMF), is proposed to represent human facial image in low frequency sub-band and yields better recognition accuracy. These results are compared with those produced by PCA and NMF.1 Introduction . . . . . . . . . . . . . . . . . . . . . 1 1.1 Related Work . . . . . . . . . . . . . . . . . . . . 1 1.2 Face Database . . . . . . . . . . . . . . . . . . . . 4 1.2.1 CBCL face database . . . . . . . . . . . . . . . . 4 1.2.2 ORL face database . . . . . . . . . . . . . . . . . 4 1.2.3 Normalized ORL face database . . . . . . . . . . . 5 1.2.4 AR face database . . . . . . . . . . . . . . . . . 6 1.3 Principle Component Analysis . . . . . . . . . . . . 7 1.4 Non-negative Matrix Factorization . . . . . . . . . . 9 2 Basis-emphasized Non-negative Matrix Factorization. . 11 2.1 Drawbacks of NMF. . . . . . . . . . . . . . . . . . 11 2.2 Extensions of NMF . . . . . . . . . . . . . . . . . 12 2.3 Algorithm of BNMF . . . . . . . . . . . . . . . . . 14 2.4 Comparison of NMF-related Algorithms . . . . . . . 17 2.5 Image Training and Testing . . . . . . . . . . . . 18 2.6 Metric Determination . . . . . . . . . . . . . . . . . . . . . 20 3 Wavelet Transform . . . . . . . . . . . . . . . . . . 29 3.1 Introduction . . . . . . . . . . . . . . . . . . . 29 3.2 Two-Dimensional Discrete Wavelet Transform . . . . 30 3.3 Multi-Resolution Analysis using Filter Banks . . . 31 3.4 Wavelet Filter . . . . . . . . . . . . . . . . . . 34 3.5 Wavelet Sub-Bands . . . . . . . . . . . . . . . . . 35 3.6 Basis-emphasized Non-negative Matrix Factorization with Wavelet Transform . . . . . . . . . . . . . . 41 3.7 Biometric Recognition System . . . . . . . . . . . 46 3.8 Wavelet Determination of wBNMF . . . . . . . . . . 47 4 Face Recognition . . . . . . . . . . . . . . . . . . 55 4.1 Introduction . . . . . . . . . . . . . .. . . . . . 55 4.2 Facial Expression . . . . . . . . . . . . . . . . . 58 4.3 Illumination Variation . . . . . . . . . . . . . . 63 4.4 Occlusion Disturbance . . . . . . . . . . . . . . . 67 4.5 Cross Validation . . . . . . . . . . . . . . . . . 70 5 Conclusion . . . . . . . . . . . . . . . . . . . . . 731493971 bytesapplication/pdfen-US非負矩陣分解演算法小波轉換non-negative matrix factorizationwavelet transformthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/54014/1/ntu-95-R93922132-1.pdf