1. Performance Analysis of 1D and 2D Statistical Measures on Standard Facial Image Databases
International Conference on Emerging Trends in Engineering & Technology
(ICETET-2K16)
Venue: Arunachala College of Engineering for Women
R.Senthilkumar
Assistant Professor, Department of Electronics and Communication Engineering
Institute of Road and Transport Technology
Erode, Tamilnadu, India
Dr.R.K.Gnanamurthy
Professor and Director
P.P.G. Institute of Technology
Coimbatore,
Tamilnadu, India

2. Aim
Compare the performance of different statistical measures on different face databases
Such as:
1D Measure
Mean
Mode
Median
Sample Standard Deviation

3. Variance Skewness Kurtosis 2D Measure Mean Square Error(MSE) Peak Signal-to-Noise Ratio(PSNR)

4. Statistical Measures From
1D statistical parameters are extracted from the recognition rate of test set of face image databases
2D statistical parameters are evaluated from the reconstructed test face images

5. Face Databases 11 Standard face databases are tested ORL Yale YaleB
YaleExtendedB
FERET
Cohn-Kanade CK+

6. 7) Indian Face 8) Surveillance Infrared 9) Georgia Tech 10) Morphological database 11) Makeup database

7. Figure.1. A sample face image from each 11 different standard face databases

8. Feature Extraction Method
Feature vectors are extracted from the face databases using 2dPCA method
Step 1
Covariance Matrix Calculated

9. Step 2 Distance between train set and test set projected vectors using following any on distance metrics:
Three distance metrics used in this analysis are:
L1 norm
L2 norm
Mahalanobis

10. The ‘Covxy-1’ is the cross covariance inverse matrix
The ‘Covxy-1’ is the cross covariance inverse matrix. The mean of train and test projected vectors are denoted by and respectively

11. Step 3 Recognition Accuracy calculated using the formula Where ‘X’ denotes the train set faces denotes the mean of train set ‘M’ number of faces in train set ‘N’ number of faces in test set ‘n’ number of faces in test set correctly recognized

12. Mean, Median and Mode

13. Sample Standard deviation and Variance

14. Skewness and Kurtosis

15. The distribution of ‘R’ is said to be positively skewed, negatively skewed or unskewed depending on skew(R) is positive, negative, or 0. If the distribution is positively skewed then the probability density function has a long tail to the right and if the distribution is negatively skewed then the probability density function has long tail to the left. A symmetric distribution is unskewed. Kurtosis is always nonnegative. The probability density function of a distribution with large kurtosis has flatter tails, compared with the probability density function of a distribution with smaller kurtosis. The kurtosis of the standard normal distribution is ‘3’. The excess kurtosis of ‘R’ is defined to be kurt(R)-3.

16. Mean Squared Error

17. Peak Signal-to-Noise Ratio

18. 1D Statistical Measures
Table I. 1d and 2d Statistical Measures on Facial Image Databases and Performance Comparison of Different Metrics
Face
Databases
Comparison
of Metrics
1D Statistical Measures
2D Statistical
Measures
Mean
Mode
Median
Std
Var
Skewness
Kurtosis
Range
MSE
PSNR
ORL
L1 Metric
93.8 96
1.47
2.17
2.7905
08.50
31.89
16.23
L2 Metric 93
95.5
1.85
3.42
2.9104
11.00
Mahalanobis
40.5
13.5 42
7.35
54.0
1.9545
46.50
Yale
81.33
70.67 84
2.58
6.68
2.5185
15.99
36.72
11.40
82.40 72
2.46
6.03
2.8069
16.00
58.53
34.66
65.33
5.91
34.9
2.3393
36.01

19. YaleB
L1 Metric
85.2 85
2.48
6.13
1.3346
14.00
33.40
14.72
L2 Metric
28.4 86
1.21
1.47
2.9310
08.00
Mahalanobis
47.83 17 28
4.44
19.7
0.3389
1.7452
27.00
Yale
ExtendedB
30.83 45
5.42
29.4
0.1351
1.8080
35.00
33.84
14.28
54.67
40.42
51.25
4.65
21.6
0.1740
1.7295
29.58
5.91
2.08 5
1.44
0.7588
2.4193
09.58
FERET
39.49
38.38
1.49
2.21
0.7511
2.5497
10.10
37.25
10.87
1.42
2.02
1.2563
2.9603
09.09
17.98
19.19
1.38
1.91
1.9556

20. Cohn- Kanade CK+ L1 Metric 100 NaN 36.19 11.93 L2 Metric Mahalanobis
NaN
36.19
11.93
L2 Metric
Mahalanobis
96.66
2.98
8.89
3.2500
16.67
Indian Face
84.66
81.66 85
1.19
1.42
0.0343
1.4191
06.67
30.75
17.37
81.33
1.67
2.76
2.0787
10.00
Surveillance
Infrared 68
0.57
0.32
2.5000
04.00
34.36
13.70
62.8 62
0.44
0.19
0.4082
1.1667
02.00
Georgia Tech
76.54
75.4
76.3
0.47
0.22
1.0210
2.7411
03.10
30.90
17.20

21. Georgia Tech
L1 Metric
76.54
75.4
76.3
0.47
0.22
1.0210
2.7411
03.10
30.90
17.20
L2 Metric
74.40
72.3
74.3
0.72
0.52
0.2155
1.7439
04.55
Mahalanobis
27.99
11.4 26
4.70
22.0
1.8839
30.02
Morphological
database
49.33
36.67 50
3.45
11.9
2.1982
23.33
33.87
14.25
47.33 40
46.67
1.98
3.91
2.2166
13.3.3
16.66
16.67
2.50
6.23
0.7686
2.4971
Makeup
54.49
42.15
56.8
3.31
10.9
2.0672
21.57
30.05
18.07
54.68
43.13
55.88
3.16
9.98
1.8876
19.59
17.63
2.94
15.68
5.34
28.5
0.0946
1.3066
29.41

23. Figure.2. (a) Top shows the comparison of sample standard deviation for different face databases, (b) Bottom shows the comparison of sample variance for different face databases

24. Figure.3. Range of recognition rate for 11 different face databases for three different distance metrics

25. Figure.4. Comparison of Mean Squared Error in dB for 11 different face databases

26. Figure.5. Comparison of Peak Signal-to-Noise Ratio in dB for 11 different face databases

27. Important Points Gathered From the Results
The Cohn-Kanade face database gives highest mean, median and mode values of 100.
The FERET face database shows lowest around 40, mean, median and mode values. This is due to the test set of this database consist of 90 degree left rotated and right rotated faces.
The ORL face database, gives highest sample standard deviation of 7.35 and corresponding variance of 54. This is due to the fact that ORL database consists of frontal faces.

28. The minimum standard deviation and variance(0. 57,0
The minimum standard deviation and variance(0.57,0.32) are obtained for Surveillance face database. This is due to only Infrared faces are present in this database.
The range difference is low for L1 metric and L2 metric and is high for Mahalanobis metric for all 7 face databases and it is minimum for YaleExtendedB, FERET, Surveillance and Morpological face database.
The highest MSE obtained for FERET face database is 37.25dB and if MSE is high, then only low PSNR value 10.87dB obtained for FERET.
The highest PSNR 18.07dB is evaluated for Makeup dataset and its MSE is dB.

29. Both MSE and PSNR are independent of L1 metric, L2 metric and Mahalanobis metric.
Since PSNR depends on MSE value and MSE in turn depends on difference between reconstructed test face images using 2dPCA feature vectors and original test face images.
The databases with low correlated faces, extreme different poses with respect to the center of eyes and background images gives poor recognition rate and thereby low mean, median and PSNR values.
Faces with more sharp features involved like Georgia Tech, Indian face databases give low MSE and high PSNR.

30. The skewness left tailed for databases with frontal face images alone and for databases with varying poses the skewness is positive value.
The kurtosis value is high for databases with frontal face images like ORL, Yale and it is crossed the peak value 3 for Cohn-kanade face database for Mahalanobis distance metric.

31. Future Work Our work can be extended by incorporating
the correlation analysis
regression analysis
receiver transfer characteristic and
evaluation of confusion matrix.

32. Acknowledgement
We wish to thank universities, research laboratories and individuals who have given permission to download their databases discussed in this paper at free of cost for education and research purpose.

33. Our other works Related to this area of Research
Face Databases Developed by us : Our Face Recognition Toolbox using Open Source Scilab Conference Papers: A detailed survey on 2D and 3D still face and face video databases part I A detailed survey on 2D and 3D still face and face video databases part II

34. A New Approach in Face Recognition: Duplicating Facial Images Based on Correlation Study ACM Digital Library Journal Paper A Comparative Study of 2D PCA Face Recognition Method with Other Statistically Based Face Recognition Methods Journal of the Institution of Engineers-Springer

35. Technical Volume (Institution of Engineers-Electronics and Telecommunication Engineering Division) Construction of Own Face and Video Face Databases for Face Recognition and Testing with Standard Face Recognition Methods