Performance Analysis of 1D and 2D Statistical Measures on Standard Facial Image Databases International Conference on Emerging Trends in Engineering & Technology (ICETET-2K16) 10.12.2016 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 E-mail: rsenthil_1976@yahoo.com Dr.R.K.Gnanamurthy Professor and Director P.P.G. Institute of Technology Coimbatore, Tamilnadu, India E-mail: rkgnanam@yahoo.co.in

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

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

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

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

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

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

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

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

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

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

Mean, Median and Mode

Sample Standard deviation and Variance

Skewness and Kurtosis

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.

Mean Squared Error

Peak Signal-to-Noise Ratio

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 -1.2190 2.7905 08.50 31.89 16.23 L2 Metric 93 95.5 1.85 3.42 -1.2834 2.9104 11.00 Mahalanobis 40.5 13.5 42 7.35 54.0 -0.4610 1.9545 46.50 Yale 81.33 70.67 84 2.58 6.68 -1.0162 2.5185 15.99 36.72 11.40 82.40 72 2.46 6.03 -1.1105 2.8069 16.00 58.53 34.66 65.33 5.91 34.9 -0.9306 2.3393 36.01

YaleB L1 Metric 85.2 85 2.48 6.13 -0.3229 1.3346 14.00 33.40 14.72 L2 Metric 28.4 86 1.21 1.47 -1.1731 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 -0.2715 1.9556

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 -1.5000 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 -0.6160 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

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 -0.2611 1.8839 30.02 Morphological database 49.33 36.67 50 3.45 11.9 -0.3356 2.1982 23.33 33.87 14.25 47.33 40 46.67 1.98 3.91 -0.3702 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 -0.5154 2.0672 21.57 30.05 18.07 54.68 43.13 55.88 3.16 9.98 -0.4844 1.8876 19.59 17.63 2.94 15.68 5.34 28.5 0.0946 1.3066 29.41

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

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

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

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

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.

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 30.05dB.

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.

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.

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

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.

Our other works Related to this area of Research Face Databases Developed by us : http://www.face-rec.org/databases/ Our Face Recognition Toolbox using Open Source Scilab http://www.face-rec.org/source-codes/ Conference Papers: A detailed survey on 2D and 3D still face and face video databases part I http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6 950080 A detailed survey on 2D and 3D still face and face video databases part II http://ieeexplore.ieee.org/document/6799620/

A New Approach in Face Recognition: Duplicating Facial Images Based on Correlation Study ACM Digital Library http://dl.acm.org/citation.cfm?id=2926032 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 http://link.springer.com/article/10.1007/s40031-015-0212-6

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 https://www.ieindia.org/PDF_IMAGES/CouncilData/ATV_ETDB.pdf