在本篇論文中，我們提出了一個以限制條件的非線性判別分析加上位階概念的方法來實現年齡估計。不同於以往的方法，我們的演算法是根據一對人臉影像中具有順序的資訊加以處理：我們使用了兩張不同年紀的人臉圖案的差值來當做我們使用的特徵，而非原始的整張影像。我們所提出的限制條件的非線性判別分析能經由對一對對人臉影像差值的分類工作，求得原始單張影像的位階(順序)值. 我們接著就用求得的位階值來做年齡估計。此外，為了達到正確的年齡估計，我們所加上的限制是針對同年紀的單張影像，讓它們在投影之後位階值能夠靠近。在本篇論文中，我們會說明一對人臉影像的差值可被當作具有鑑別力的特徵，及我們加上的限制可有效地降低誤差。從實驗結果來看，我們的方法也與現有的方法不分軒輊。

In this thesis, we propose a constrained kernel discriminant analysis (CKDA) to realize age estimation via the ranking concept. Unlike the previous work, the design of our algorithm is based on the relative order information among the pairwise facial images. In other words, we propose to utilize the difference of the data pairs as the feature rather than the original image samples. We first extract the ranking relation via binary classification on pairwise data and then conduct CKDA to compute the ranking (ordered) value of each sample via binary classifier. We next use this ranking value to do the age estimation. In addition, we further include a constraint on original samples according to their age labels to improve the estimation accuracy. In this paper, we show that the differences of image pairs can be a discriminant feature for age estimation, and our constraint also effectively decreases the error. Experimental result shows that the performance of our method is comparable to other existing works.

[1] S. Mika, G. Rätsch, J. Weston, B. Schölkopf and K.R Müller, “Fisher discriminant analysis with kernels,” Neural Networks for Signal Processing IX, 1999.
[2] The FG-NET Aging database, http://www.fgnet.rsunit.com/
[3] T. F. Cootes, G. J. Edwards, and C. J. Taylor, “Active Appearance Models,” in Proc. ECCV, vol. 2, pp. 484-498, 1998.
[4] C.-C. Chang and C.-J. Lin, “LIBSVM : a library for support vector machines,” ACM Transactions on Intelligent Systems and Technology, Vol. 2 Issue 3, April 2011. http://www.csie.ntu.edu.tw/~cjlin/libsvm
[5] K.Y. Chang, C.S. Chen and Y.P. Hung, “Ordinal Hyperplanes Ranker with Cost Sensitivities for Age Estimation,” IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2011
[6] P. Yang, L. Zhong and D. Metaxas,“Ranking Model for Facial Age Estimation,
” International Conference on Pattern Recognition , ICPR 2010
[7] G. Guo, G. Mu, Y. Fu and T.S. Huang, “Human age estimation using bio-inspired features,” IEEE International Conf. on CVPR, 2009.
[8] G. Guo, Y. Fu, T.S. Huang and C. Dyer, “Locally adjusted robust regression for human age estimation,” IEEE Workshop on WACV, 2008.
[9] X. Geng, Z.H. Zhou, Y. Zhang, G. Li, and H. Dai, “Learning from Facial Aging Patterns for Automatic Age Estimation,” Proc.ACM Conf. on Multimedi , 2006.
[10] T. Xiong and V. Cherkassky,“A Combined SVM and LDA Approach for Classification”, International Joint Conference onNeural Networks, 2005
[11] Statistical Pattern recognition toolbox , http://cmp.felk.cvut.cz/cmp/software/ stprtool/
[12] X. Geng and K. Smith, “Facial Age Estimation by Multilinear Subspace Analysis,” IEEE ICASSP, 2009.
[13] The PAL Face Database https://pal.utdallas.edu/facedb/
[14 ] “Fisher linear discriminant,” in Wikipedia.
[15] K.Y. Chang, C.S. Chen and Y.P. Hung, “A Ranking Approach for Human Age Estimation Based on Face images,” ICPR, 2010
[16] K.H. Chen, “Constrained Nonnegative Matrix Factorization for Facial Age Estimation and Beyond,” Master thesis, 2011
[17] S. Yan, H. Wang, X. Tang and T.S. Huang, “Learning Auto-Structured Regressor from Uncertain Nonnegative Labels,” IEEE International Conf. on Computer Vision, 2007.