對於現今的量測技術，由於條紋投影輪廓儀 (Projected Fringe Profilometry，PFP) 具有非接觸式的特色，目前被廣泛使用於量測物體三維形貌，本論文即利用條紋投影輪廓儀中的傅立葉輪廓術(Fourier transform profilometry，FTP) 重建物體的三維形貌，其優點具有快速、精準度高且只需單一影像即可還原物體三維形貌。本實驗運用FTP於人臉輪廓上的還原，並在重建的人臉三維形貌上擷取特徵值，利用每個人特徵值具有差異性的特性，提出雙重辨識方法達到辨識的效果。
但在實際拍攝時，人臉會因為傾斜與操作距離不同而產生計算之誤差，透過兩種傾斜修正方法將人臉正規化，並利用三角測距法推算出實際距離，使本系統具有小角度傾斜容忍度以及35~55公分的拍攝容許距離。
我們將人臉資料庫中的85人相互比對，總共比對3570次，藉由雙重辨識方法辨識，辨識率高達99.91%。

Because of fringe projection profilometry (PFP) has the advantages of non-contact measuring method, and it is widely use for measuring the three-dimensional shape of objects now. In this study, using Fourier transform profilometry (FTP) to reconstruct the three-dimensional shape of an object, which has the advantages of fast, high accuracy and only a single image that can restore the three-dimensional shape of an object. So we use FTP to restore three-dimensional shape of human face and get the feature value from it. Because of each person has unique feature, we proposed the method for double-identification to identification.
In the measuring process, there are some artificial errors which are occurred by human face tilting and shifting. To solve this problem, we proposed two kinds of tilt-correction methods to normalize each human face, and calculating actual distance by using optical triangulation. So that, it allows a small tilt angle tolerance for system and extend shooting distance to 35~55 centimeters. Finally, we compare 85 persons with each other from face database, a total of comparison is 3570 times. By using double-identification method to identify 85 persons for each other, the recognition rate reaches 99.91%.

[1] H. A. Rowley, S. Baluja, and T. Kanade, “Neural Network-Based Face Detection,” IEEE Patt. Anal. Mach. Intell. 20, 23-38 (1998).
[2] K. K. Sung and T. Poggio, “Example-Based Learning for View-Based Human Face Detection,” IEEE Patt. Anal. Mach. Intell. 20, 39-51 (1998).

[3] M. Turk and A. Pentland, “Eigenfaces for Recognition,” J. Cognitive Neuroscience. 3, 71-86 (1991).

[4] P. Belhumeur, J. Hespanda and D. Kriegman, “Eigenfaces Versus Fisherfaces: Recognition Using Class Specific Linear Projection,” IEEE Patt. Anal. Mach. Intell. 19, 711-720 (1997).

[5] L. Wiskott, J. M. Fellous, N. Krü and C. V. D. Malsburg, “Face Recognition by Elastic Bunch Graph Matching,” IEEE Patt. Anal. Mach. Intell. 19, 775-779 (1997).

[6] J. A. K. Suykens and J. Vandewalle, “Least Squares Support Vector Machine Classifiers,” Neural Processing Lett. 9, 293-300 (1999).

[7] P. N Belhumeur, J. P. Hespanha, and D. J. Kriegman, “Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection,” IEEE Patt. Anal. Mach. Intell. 19, 711-720 (1997).

[8] M. Kirby and L. Sirovich, “Application of The Karhunen-Loeve Procedure for The Characterization of Human Faces,” IEEE Patt. Anal. Mach. Intell. 12, 103-108 (1990).

[9] J. Zakzeski, P. C. A. Bruijnincx, A. L. Jongerius, and B. M. Weckhuysen, “The Catalytic Valorization of Lignin for The Production of Renewable Chemicals,” Chem. Rev. 110, 3552-3599 (2010).

[10] R. Brunelli and T. Poggio, “Face Recognition: Features Versus Templates,” IEEE Patt. Anal. Mach. Intell. 15, 1042-1052 (1993).

[11] Z. Pan, R. Adams, and H. Bolouri, “Image Redundancy Reduction for Neural Network Classification Using Discrete Cosine Transforms,” Proc. Int. Joint Conf. Neural Netw. 3, 149-154 (2000).

[12] P. Belhumeur and D. Kriegman, “What Is The Set of Images of An Object under All Possible Lighting Conditions,” J. Computer Vision. 28, 245-260 (1998).

[13] T. R. Raviv and A. Shashua, “The Quotient Image: Class Based Re-rendering and Recognition with Varying Illuminations,” CVPR. 23, 566–571 (1999).
[14] C. P. Chen and C. S. Chen, “Lighting Normalization with Generic Intrinsic Illumination Subspace for Face Recognition,” ICCV. 2, 1089-1096 (2005).

[15] S. H. Rowe and W. T. Welford, “Surface Topography of Non-Optical Surfaces by Projected Interference Fringes,” Nature 216, 786-788 (1967).
[16] S. H. Rowe, “Projected Interference Fringes in Holographic Interferometry,” JOSA 61, 1599-1603 (1971).
[17] R. Crane, “Interference Phase Measurement,” Appl. Opt. 8, 538 (1969).

[18] J. H. Bruning, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, and D. R. Herriott, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693 (1974).

[19] H. Takasaki, “Moiré topography,” Appl. Opt. 9, 1467–1472 (1970).

[20] V. Srinivasan, H. C. Liu, and M. Halioua, “Automated Phase-measuring Profilometry of 3-D Diffusive Objects,” Appl. Opt. 23, 3105-3108 (1984).

[21] V. Srinivasan, H. C. Liu, and M. Halioua, “Automated Phase-measuring Profilometry: A Phase Mapping Approach,” Appl. Opt. 24, 185–188 (1985).

[22] M. Takeda, H. Ina, and S. Koboyashi, “Fourier-transform Method of Fringe-pattern Analysis for Computer-based Topography and Interferometry,” JOSA 72, l56–l60 (1982).

[23] M. Takeda and K. Motoh, “Fourier Transform Profilometry for The Automatic Measurement of 3-D Object Shapes,” Appl. Opt. 22, 3977–3982 (1983).

[24] J. L. Li, H. J. Su, and X. Y. Su, “Two-frequency Grating Used in Phase-measuring Profilometry,” Appl. Opt. 36, 277–280 (1997).

[25] X. Y. Su, J. Li, and L. R. Gou, “An Improved Fourier Transform Profilometry,” Proc. SPIE 954, 32–35 (1988).

[26] J. F. Lin and X. Y. Su, “Two-dimensional Fourier Transform Profilometry for The Automatic Measurement of Three-dimensional Object Shapes,” Opt. Eng. 34, 3297–3302 (1995).

[27] M. Takeda, Q. Gu, M. Kinoshita, H. Takai and Y. Takahashi, “Frequency-multiplex Fourier-transform Profilometry: A Single-shot Three-dimensional Shape Measurement of Objects with Large Height Discontinuities and/or Surface Isolations,” Appl. Opt. 36, 5347–5354 (1997).

[28] Y. D. Hao, Y. Zhao, and D. C. Li, “Multifrequency Grating Projection Profilometry Based on The Nonlinear Excess Fraction Method,” Appl. Opt. 38, 4106–4110 (1999).

[29] K. G. Larkin and B. F. Oreb, “Design and Assessment of Symmetrical Phase-shifting Algorithms,” JOSA A 9, 1740-1748 (1992).
[30] S. Zhang, “High-resolution 3-D Profilometry with Binary Phase-shifting Methods,” Appl. Opt. 50, 1753–1757 (2011).

[31] X. Su and W. Chen, “Fourier Transform Profilometry: A Review,” Opt. Laser Eng. 35, 263–284 (2001).

[32] 柯韋廷，利用條紋投影技術進行物體表面之三維形變量量測，國立中山大學材料與光電科學學系研究所碩士論文，中華民國一百零一年。

[33] W. H. Su, “Color-encoded Fringe Projection for 3D Shape Measurements,” Opt. Express 15, 13167–13181 (2007).

[34] 徐維懋，鏡像輔助斷層掃描相位顯微鏡，國立中央大學光電所碩士論文，中華民國一百零三年。

[35] R. Cusack, J. Huntley, and H. Goldrein, “Improved Noise-immune Phase- unwrapping Algorithm,” Appl. Opt. 34, 781-789 (1995).

[36] B. Gutmann and H. Weber, “Phase Unwrapping with The Branch-cut Method: Role of Phase-field Direction,” Appl. Opt. 39, 4802-4816 (2000).

[37] L. An, Q. S. Xiang, and S. Chavez, “A Fast Implementation of The Minimum Spanning Tree Method for Phase Unwrapping,” IEEE Trans Med Imaging. 19, 805-808 (2000).

[38] D. C. Ghiglia, G. A. Mastin, and L. A. Romero, “Cellular-automata Method for Phase Unwrapping,” JOSA A 4, 267-280 (1987).

[39] D. C. Ghiglia and L. A. Romero, “Robust Two-dimensional Weighted and Unweighted Phase Unwrapping that Uses Fast Transforms and Iterative Methods,” JOSA A 11, 107-117 (1994).

[40] R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite Radar Interferometry: Two‐dimensional Phase Unwrapping,” Radio Science 23, 713-720 (1988).

[41] A. Buckingham, R. Disch, and D. Dunmur, “Matrix Formulation of the Reconstruction of Phase Values from Phase Differences,” Physica 23, 825-837 (1957).

[42] M. F. Costa, “Surface Inspection by An Optical Triangulation Method,” Opt. Eng. 35, 2743 (1996).

[43] Mitsuo and Kazuhiro Mutoh, “Fourier Transform Profilometry for The Automatic Measurement of 3-D Object Shapes,” Appl. Opt. 22, 3977-3982 (1983).

[44] 林信宏，以光學疊紋法作人臉辨別之研究，元智大學電機工程研究所碩士論文，中華民國八十九年。