監視系統的攝影機常常都只能拍下低解析度的影像，所以我們也很難去看清楚影像裡的人物。為了解決這個問題，便開始有很多的專家學者提出一些不同的方法，來針對這些影像做超解析化。
    在這裡我們也針對人臉影像的超解析化，提出了一個使用正交區域保留投影OLPP（Orthogonal Locality Preserving Projections）的技術。目的是發現區域鄰接的幾何流形結構，產生正交的基底函數。我們利用區塊來完成臉部超解析化的演算法。首先將訓練資料庫裡的低解析度人臉影像根據五官位置分割成4個區塊，分別利用PCA（Principal Component Analysis）降低維度，再建構出OLPP轉換矩陣。另一方面，利用已知資料的低解析影像的OLPP係數與相對應的高解析影像訓練廣義迴歸網路 GRNN（General Regression Neural Network）。對於一張待重建的低解析影像，一樣分成4個區塊，分別已建構好的OLPP求出它們的係數。這些係數再分別輸入已經訓練好的GRNN，將區塊重建成原來的解析度。根據實驗結果，本文所提的方法都有滿意的結果。

Due to cost consideration, the quality of images captured from surveillance systems usually is poor. It makes the face recognition difficult in these low-resolution images. Here we propose a block-based algorithm called Orthogonal Locality Preserving Projections (OLPP) for super-resolution of face images. The purpose is to discover the local structure of the manifold and produce orthogonal basis functions for face images. 
    To train the system, we divide the high-resolution images and the corresponding low-resolution images into 4 blocks (forehead, eyes, nose, and mouth). For each block, we use the low-resolution ones to find an OLPP transformation matrix. Then, use the obtained coefficients from the OLPP (input) and the corresponding high-resolution one (target) to train a GRNN (General Regression Neural Network). For an unseen low-resolution face image, it is divided into 4 blocks similarly and the corresponding coefficients for each block are obtained by the trained OLPP transformation matrix. Finally, an improved super-resolution block is obtained by feeding the coefficients of OLPP into GRNN. And a super-resolution face image is achieved by combining all blocks. Comparing to existing methods, the proposed method has shown an improved and promising results.

目錄	III
圖目錄	V
第一章 緒論	1
1.1 研究背景、動機與目的	1
1.2	 研究內容	4
1.3	 論文架構	6
第二章 相關研究及理論基礎	7
2.1 人臉超解析化相關研究	7
2.2 理論基礎	14
2.2.1. LPP（Locality Preserving Projections）	14
2.2.2. OLPP（Orthogonal Locality Preserving Projections）	17
2.2.3. GRNN（Generalized Regression Neural Network）	18
第三章 人臉超解析化	19
3.1 樣本訓練過程	19
3.2 人臉超解析化過程	22
第四章 實驗結果與探討	24
4.1 實驗結果	24
4.2 實驗結果探討	28
4.3 實驗結果比較	31
第五章 結論與未來研究方向	33
5.1 結論	33
5.2 未來研究目標與方向	34
參考文獻	35
附錄—英文論文	38
圖1. 1  高、低解析度臉部影像 (A)為原始高解析臉部影像，(B)為低解析度影像，(C)為(B)直接放大的影像。	1
圖1. 2  樣本訓練流程圖	5
圖1. 3  人臉超解析化流程圖	5
圖2. 1  ERROR BACK-PROJECTION流程圖[2]	8
圖2. 2  LAPLACIANFACES線性嵌入2D平面圖[5]	10
圖2. 3  DIRECT LOCALITY PRESERVING PROJECTIONS演算流程圖[7]	12
圖2. 4  廣義回歸神經網路結構圖	18
圖3. 1  樣本訓練流程圖	19
圖3. 2  高解析臉部影像分割區塊圖 (A)為完整高解析臉部影像，(B)為額頭區塊(32 X 144 PIXELS)，(C) 為眼睛區塊(32 X 144)，(D) 為鼻子區塊(56 X 144)，(E) 為嘴巴區塊(72 X 144)。	20
圖3. 3  低解析臉部影像分割區塊圖 (A)為完整低解析臉部影像，(B)為額頭區塊(4 X 18 PIXELS)，(C) 為眼睛區塊(4 X 18)，(D) 為鼻子區塊(7 X 18)，(E) 為嘴巴區塊(9 X 18)。	20
圖3. 4  人臉超解析化流程圖	22
圖3. 5  人臉拼合及融合示意圖 (A)為拼合完成的人臉，(B)為MASK(權重比率大小為藍0.8、黃0.6、綠0.4。)，(C)為BI-CUBIC放大的低解析影像，(D)為融合的結果。	23
圖4. 1  實驗結果 (A)為輸入的低解析臉部影像，(B)為本文的結果，(C)為原始高解析影像。	27
圖4. 2  K值測試比較圖 (A)為K = 15所得的結果，(B)為K = 30所得的結果，(C)為K = 45的結果，(D)為原始眼睛區塊。可以看出K=30的結果與原始眼睛區塊較為相近。	28
圖4. 3  L值測試比較圖 (A)為L = 20所得的結果，(B)為L = 40所得的結果，(C)為L = 100的結果，(D)為原始眼睛區塊。可以看出L=40的結果與原始眼睛區塊較為相近。	29
圖4. 4  SPREAD值測試比較圖 (A)為SPREAD = 20所得的結果，(B)為SPREAD = 100所得的結果，(C)為SPREAD = 500的結果，(D)為原始眼睛區塊。	29
圖4. 5  MASK權重比較圖 (A)為拼合完成的人臉，(B)為MASK(藍0.9、黃0.5、綠0.3)， (C) MASK(藍0.8、黃0.6、綠0.4)， (D) MASK(藍0.7、黃0.5、綠0.3)，(E)為原始高解析臉部影像。	30
圖4. 6  實驗結果與其他方法比較圖 (A)為輸入的低解析臉部影像(24 X 18 PIXELS)，(B)為BI-CUBIC，(C) 為PARK ET AL. [6]，(D)為VIJAY KUMAR ET AL. [9]，(E)為本文的方法，(F)為原始的高解析影像。	32

[1] S. Baker and T. Kanade, “Hallucinating Faces,” Proceedings of the Fourth IEEE International Conference on Automatic Face and Gesture Recognition. Grenoble, France, pp. 83-88, 2000.

[2] J. S. Park and S. W. Lee, “Resolution Enhancement of Facial Image Using An Error Back-projection of Example-based Learning,” in Proc. 6th IEEE Conf. Automatic Face and Gesture Recognition, Seoul, Korea, pp. 831-836, 2004.

[3] M. Turk and A. Pentland, “Eigenfaces for recognition,” Cogn Neurosci vol. 3, no. 1, pp. 71-86, 1991.

[4] P. Belhumeur, J. Hespanha, and D. Kriegman, “Eigenfaces VS. Fisherfaces: Recognition Using Class Specific Linear Projection,” IEEE Trans Pattern Anal Mach Intell vol. 19, no. 7, pp. 711-720, 2001.

[5] X. He, S. Yan, Y. Hu, P. Niyogi, and H. J. Zhang, “Face Recognition Using Laplacianfaces,” IEEE Trans Pattern Anal Mach Intell vol. 27, no. 3, pp. 328-340, 2005.

[6] S. W. Park and M. Savvides, “Breaking Limitation of Manifold Analysis for Super-resolution of Facial Images,” ICASSP, pp. 573-576, 2007.

[7] S. Ahmed, N. I. Rao, A. Ghafoor, and A. M. Sheri, “Direct Hallucination: Direct Locality Preserving Projections (DLPP) for Face Super-Resolution,” International Conference on Advanced Computer Theory and Engineering, pp. 105-110, 2008.

[8] X. He, S. Yan, Y. Hu, P. Niyogi, and H. J. Zhang, “Orthogonal Laplacianfaces for Face Recognition,” IEEE Transations on Image Processing, vol. 15, no. 11, pp. 3608-3614, 2006.

[9] B. G. Vijay Kumar and R. Aravind, “Face Hallucination Using OLPP and Kernel Ridge Regression,” ICIP, pp. 353-356, 2008.

[10] M. Belkin and P. Niyogi, “Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering,” Advances in Neural Information Processing Systems 14, pp. 585-591, MIT Press, Cambridge, MA, USA, 2002.

[11] J. B. Tenenbaum, V. Silva, and J. C. Langford, "A Global Geometric Framework for Nonlinear Dimensionality Reduction," Science, vol. 290, pp. 2319-2323, 2003.

[12] S. Roweis and L. K. Saul, "Nonlinear Dimensionality Reduction by Locally Linear Embedding," Science, vol. 290, pp. 2323-2326, 2000.

[13] D. Hu, G. Feng, and Z. Zhou, “Two-dimensional Locality Preserving Projections (2DLPP) with It’s Application to Palmprint Recognition,” Pattern Recognition 40, pp. 339-342, 2007.

[14] K. C. Lee, J. Ho, and D. Kriegman in “Acquiring Linear Subspaces for Face Recognition under Variable Lighting,” IEEE Trans Pattern Anal Mach Intell vol. 27, no. 5, pp. 684-698, May, 2005.

[15] http://www.nist.gov/humanid/colorferet