本篇論文探討如何利用單張彩色影像來重建出三維人臉模型。我們的方法是利用彩色影像來取代灰階值去建立張量模型(tensor model)，在人臉資料庫中，是用典型相關分析(Canonical correlation analysis) 是來建立彩色影像與深度資訊的對應關係，一旦建立好屬於各自的對應關係後，在重建人臉的過程中，就只需要單張彩色影像即可利用典型相關分析的對應關係來推算出正確的深度資訊。實驗中，我們的方法可以在不同的光線環境跟人臉角度得到不錯的效果。

This paper develops a tensor-based 3D face reconstruction approach from a single color image. Instead of the grayscale image, we also consider additional color factors in constructing the tensor model. Canonical correlation analysis is applied to establish the relationship between the color image and the depth information in the face database. During the face reconstruction, given a single color face image, the depth estimation is computed from the CCA-based mapping between the tensor models. Experimental results show our approach is better suited under different lighting conditions and poses.

[1] S. Seitz, B. Curless, J. Diebel, D. Scharstein, and R. Szeliski, “A comparison and evaluation of multi-view stereo reconstruction algorithms,” in Computer Vision and Pattern Recognition, 2006 IEEE Computer Society Conference on, vol. 1. Ieee, 2006, pp. 519–528.
[2] C. Tomasi and T. Kanade, “Shape and motion from image streams under orthography:a factorization method,” International Journal of Computer Vision,
vol. 9, no. 2, pp. 137–154, 1992.
[3] S. Romdhani and T. Vetter, “Efficient, robust and accurate fitting of a 3d
morphable model,” in Computer Vision, 2003. Proceedings. Ninth IEEE International Conference on. IEEE, 2003, pp. 59–66.
[4] R. Zhang, P. Tsai, J. Cryer, and M. Shah, “Shape-from-shading: a survey,”
Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 21,
no. 8, pp. 690–706, 1999.
[5] M. Vasilescu and D. Terzopoulos, “Multilinear analysis of image ensembles:
Tensorfaces,” Computer Vision?ECCV 2002, pp. 447–460, 2002.
[6] T. Kolda and B. Bader, “Tensor decompositions and applications,” SIAM review, vol. 51, no. 3, 2009.
[7] M. Okutomi and T. Kanade, “A multiple-baseline stereo,” Pattern Analysis
and Machine Intelligence, IEEE Transactions on, vol. 15, no. 4, pp. 353–363,
1993.
[8] M. Hansen, G. Atkinson, L. Smith, and M. Smith, “3d face reconstructions from photometric stereo using near infrared and visible light,” Computer Vision and Image Understanding, vol. 114, no. 8, pp. 942–951, 2010.
[9] L. Torresani, A. Hertzmann, and C. Bregler, “Nonrigid structure-from-motion:
Estimating shape and motion with hierarchical priors,” Pattern Analysis and
Machine Intelligence, IEEE Transactions on, vol. 30, no. 5, pp. 878–892, 2008.
[10] Y. Hu, D. Jiang, S. Yan, L. Zhang et al., “Automatic 3d reconstruction for face recognition,” in Automatic Face and Gesture Recognition, 2004. Proceedings.
Sixth IEEE International Conference on. IEEE, 2004, pp. 843–848.
[11] V. Le, H. Tang, L. Cao, and T. Huang, “Accurate and efficient reconstruction of 3d faces from stereo images,” in Image Processing (ICIP), 2010 17th IEEE International Conference on. IEEE, 2010, pp. 4265–4268.
[12] I. Kemelmacher-Shlizerman and R. Basri, “3d face reconstruction from a single image using a single reference face shape,” Pattern Analysis and Machine
Intelligence, IEEE Transactions on, vol. 33, no. 2, pp. 394–405, 2011.
[13] Z. Lei, Q. Bai, R. He, and S. Li, “Face shape recovery from a single image
using cca mapping between tensor spaces,” in Computer Vision and Pattern
Recognition, 2008. CVPR 2008. IEEE Conference on. IEEE, 2008, pp. 1–7.
[14] I. Jolliffe and MyiLibrary, Principal component analysis. Wiley Online Library, 2002, vol. 2.
[15] A. Hyv‥arinen, J. Karhunen, and E. Oja, Independent component analysis.
Wiley-interscience, 2001, vol. 26.
[16] S. Baker and I. Matthews, “Equivalence and efficiency of image alignment algorithms,”in Computer Vision and Pattern Recognition, 2001. CVPR 2001.
Proceedings of the 2001 IEEE Computer Society Conference on, vol. 1. IEEE,
2001, pp. I–1090.
[17] S. Milborrow and F. Nicolls, “Locating facial features with an extended active shape model,” Computer Vision–ECCV 2008, pp. 504–513, 2008.
[18] T. Cootes, C. Taylor, D. Cooper, J. Graham et al., “Active shape models-their training and application,” Computer vision and image understanding, vol. 61, no. 1, pp. 38–59, 1995.
[19] S. Li, R. Chu, S. Liao, and L. Zhang, “Illumination invariant face recognition using near-infrared images,” Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 29, no. 4, pp. 627–639, 2007.
[20] M. Reiter, R. Dormer, G. Langs, and H. Bischof, “3d and infrared face reconstruction from rgb data using canonical correlation analysis,” in Pattern Recognition, 2006. ICPR 2006. 18th International Conference on, vol. 1. IEEE,
2006, pp. 425–428.
[21] M. Castelan and E. Hancock, “A simple coupled statistical model for 3d face
shape recovery,” in Pattern Recognition, 2006. ICPR 2006. 18th International
Conference on, vol. 1. IEEE, 2006, pp. 231–234.
[22] T. Melzer, M. Reiter, and H. Bischof, “Appearance models based on kernel
canonical correlation analysis,” Pattern recognition, vol. 36, no. 9, pp. 1961–
1971, 2003.
[23] P. Viola and M. Jones, “Robust real-time face detection,” International journal of computer vision, vol. 57, no. 2, pp. 137–154, 2004.
[24] P. Besl and N. McKay, “A method for registration of 3-d shapes,” IEEE Transactions on pattern analysis and machine intelligence, vol. 14, no. 2, pp. 239–256, 1992.
[25] Casia-3d facev1. [Online]. Available: http://biometrics.idealtest.org/
[26] S. Gupta, M. Markey, and A. Bovik, “Anthropometric 3d face recognition,”
International journal of computer vision, vol. 90, no. 3, pp. 331–349, 2010.
[27] S. Gupta, K. Castleman, M. Markey, and A. Bovik, “Texas 3d face recognition
database,” in Image Analysis & Interpretation (SSIAI), 2010 IEEE Southwest Symposium on. IEEE, 2010, pp. 97–100.
[28] Texas 3d face recognition database. [Online]. Available: http://live.ece.utexas.edu/research/texas3dfr/index.htm