Face recognition based on DCT and 2DLDA

1. Face recognition based on DCT and 2DLDA Hongtao Yin, Ping Fu, and Jiaqing Qiao Innovative Computing ,Information and Control, International Conference on 2007 Reporter : 許進順 ID:Q38971116 電通所 IT-LAB 2009/12/22

2. Outline • Introduction • Discrete Cosine Transform • 2DLDA • Experimental result • Conclusion

3. Outline • Introduction • Discrete Cosine Transform • 2DLDA • Experimental result

4. Introduction • Propose to A face recognition method based on the discrete cosine transform (DCT) and two dimensional linear discriminant analysis (2DLDA) • Fisher linear discriminant analysis (FLDA) has been successfully applied to face recognition area in the past few years. Nevertheless, FLDA usually encounters the small sample size problem in which the within-class scatter matrix becomes singular and thus the traditional FLDA algorithm fails to use • 2DLDA becomes an interesting technique in face recognition, since it can extract discriminative feature faster than the one dimensional discrimination analysis

5. Outline • Introduction • Discrete Cosine Transform • 2DLDA • Experimental result

6. Discrete Cosine Transform • An input (M x N) image f(x,y) , it’s DCT ,C(u,v) is obtained by the equation u=0,1,…M-1 v=0,1,…N-1

7. Discrete Cosine Transform Truncated DCT Coefficient

8. Outline • Introduction • Discrete Cosine Transform • 2DLDA • Experimental result

9. 2DLDA • The initial idea of 2DLDA is to perform the uncorrelated image matrix-based linear discriminant analysis (IMLDA) twice : the first one is in horizontal direction and the • second is in vertical direction

10. 2DLDA • c known pattern classes • S is the total number of training samples, • Si is the number of training samples in class i • In class i, the jth training image is denoted by an m × n matrix • The mean image of training samples in class i is denoted • The mean image of all training sample is

11. IMLDA in horizontal direction c • Gb is the between-class scatter matrix • Gw is the within-class scatter matrix • The generalized Fisher criterion A r c r A A r c d Φ c

12. IMLDA in horizontal direction • To find a set of optimal discriminating vectors by maximizing the Fisher criterion • is the set of generalized eigenvectors of Gb and Gw corresponding to the d largest generalized eigenvalues , ie.. • The image feature extraction of horizontal direction d c d B A r r Φ c

13. The IMLDA in vertical direction • Using the feature matrix B that extracted in first IMLDA transform in horizontal direction. • Hbbetween-class scatter matrices • Hwwithin-class scatter matrices • Find a set of optimal discriminating vectors • by the maximizing Fisher criterion. • The feature matrix of B denotes • The result matrix C is e x d matrix e d r Ω d B d r B

14. Illustration of 2DLDA transformation B A

15. Block diagram

16. Outline • Introduction • Discrete Cosine Transform • 2DLDA • Experimental result

17. Experimental result • ORL(Olivertti Research Laboratory) face images • 400 images of 40 individuals in this database • Randomly 3,4,5 images from each subject to construct the training data set • Each experiment is repeated 20 times. • A nearest neighbor classifier is used to decide the class of an unknown face image

18. Experimental result • In different size of truncated DCT coefficient

19. Experimental result

20. Experimental result

21. 實驗心得 • 訓練的樣本越多其辨識的結果會越好，這應該算是合理的現象。 • DCT係數的尺寸大小並不一定越大就越好，也就是25x25的辨識的結果不一定就會比10x10或者15x15的結果好。 • 投影後的尺寸大小並不一定越大就越好，由實驗結果得知，投影的尺寸太小，其辨識結果會越低，但越大時所增加的辨識率也有限。

22. Q&A • Q1:為什麼DCT 係數尺寸比較大的辨識結果不會比DCT係數尺寸小的為佳? • ANS : 因為DCT係數呈現的方式會依照左上至右下，由大至小的方式分佈，越往左上代表的資訊越完整，而越往右下，則雜訊的成份越重，故當訓練的尺寸越大時，越有可能將高頻的資訊拿來訓練，而訓練樣本及測試樣本的高頻資訊本身其關連性並不高，故當拿高頻的資訊訓練時，於測試時誤判的機率亦相對提高，而造成辨識率下降。 • Q2:要如何找到最佳的投影空間大小? • ANS : 目前實驗的結果發現此投影空間假如太小，則辨識結果會變得很差，但空間太大辨識率也會呈現收斂的情形，但越大的空間其運算的時間將越長。目前的投影空間大小是由測試時指定的，並沒有考量其投影時eigenvector本身的差異情形，以及訓練樣本DCT係數的分佈情形，或許可以藉由反覆的測試結果，依據經驗法則的方法，來推敲求得最佳化的方法，然而需要實驗後才能得知其結果。

23. Conclusion • A face recognition algorithm based on DCT and 2DLDA. It implements2DLDA in DCT domain instead of space domain。 • Experimental results on the ORL face database show that the proposed method is not only faster but also better in recognition performance than DCT and DCT+LDA algorithms。

24. 謝謝指教