face recognition using Principle Componet Analysis
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Face recognition uses principal component analysis (PCA) to reduce the dimensionality of face image data and identify patterns to recognize individuals. PCA involves extracting principal components from the data to summarize it with fewer variables while highlighting similarities and differences. The process involves getting sample face image data, subtracting the mean, calculating the covariance matrix, finding eigenvectors and eigenvalues to form a feature vector for projections of the data in the direction of the principal components. This allows for face recognition by training a database and testing unknown images.
![ In general the covariance matrix is
= [covariance(x,x) covariance(x,y)
covariance(y,x) covariance(y,y)]
= [variance(x) covariance(x,y)
covariance(x,y) variance(y)]
= [6.4228 7.9876
7.9876 9.9528]
To obtain Eigen values by solving function
determinant {A-lamda(I)}=0
Solving equation A, we get the Eigen values are
lamda=16.36809984,0.007462657
Here sum of two eigen values is always equal to
the sum of variances](https://image.slidesharecdn.com/miniproectslides-130116091227-phpapp01/85/face-recognition-using-Principle-Componet-Analysis-9-320.jpg)
![ To obtain Eigen vector by solving for matrix x in
such a way that, {A-lambda(i)}*[X]=[0].
For first Eigen value 16.36809984, we get
[X]=[0.6262
0.7797]
For second Eigen value 0.007462657,we get
[X]=[0.7797
-0.6262]
To obtain coordinates of data point in the direction
of Eigen vectors by multiplying the centered data
matrix to the Eigen vector matrix](https://image.slidesharecdn.com/miniproectslides-130116091227-phpapp01/85/face-recognition-using-Principle-Componet-Analysis-10-320.jpg)
face recognition using Principle Componet Analysis
- 1. Face recognition using principal component analysis by ABHILASH KOTAWAR VENKATA NARAYANA CHETTELA KOMIRISHETTI SRAVAN
- 2. In today's networked world, the need to maintain the security of information is becoming both increasingly important and increasingly difficult. BIOMETRICS represents a good compromise between what’s socially acceptable and what’s reliable, even when operating under controlled conditions. Recently, technology became available to allow verification of "true" individual identity. This technology is based in a field called "biometrics".
- 4. Face Recognition is the process of identification of a person by their facial image. This technique makes it possible to use the facial images of a person to authenticate him into a secure system, for criminal identification, for passport verification,... Face recognition technology is the least intrusive and fastest biometric technology. Face recognition systems unobtrusively take pictures of people's faces as they enter a defined area. This method is found to be fast, relatively simple, and works well in a constrained environment.
- 6. PCA is a dimensionality reduction technique based on extracting the desired number of principal components of the multi-dimensional data. PCA aims to: Summerise data with many independent variables to a smaller set of derived variables. identifying patterns in data, and expressing the data in such a way as to highlight their similarities and differences.
- 7. Get some data: x y 1.4000 1.6500 1.6000 1.9750 -1.4000 -1.7750 Mean=∑ Xi/n -2.0000 -2.5250 -3.0000 -3.9500 2.4000 3.0750 variance=(∑(xi-avg)²)*1/(n-1) 1.5000 2.0250 2.3000 2.7500 sum of variances=16.3756 -3.2000 -4.0500 -4.1000 -4.8500 Average -0.4500 -0.5675 Variance 6.4228 9.9528
- 8. For covariance we will use function (∑(x-xbar)*(y-ybar)/(n-1) X-Xbar Y-Ybar (X-Xbar)*(Y-Ybar) 1.8500 2.2175 4.1024 2.0500 2.5425 5.2121 -0.9500 -1.2075 1.1471 -1.5500 -1.9575 3.0341 -2.5500 -3.3825 8.6254 2.8500 3.6425 10.3811 1.9500 2.5925 5.0554 2.7500 3.3175 9.1231 -2.7500 -3.4825 9.5769 -3.6500 -3.4825 15.6311 7.9876 covariance
- 9. In general the covariance matrix is = [covariance(x,x) covariance(x,y) covariance(y,x) covariance(y,y)] = [variance(x) covariance(x,y) covariance(x,y) variance(y)] = [6.4228 7.9876 7.9876 9.9528] To obtain Eigen values by solving function determinant {A-lamda(I)}=0 Solving equation A, we get the Eigen values are lamda=16.36809984,0.007462657 Here sum of two eigen values is always equal to the sum of variances
- 10. To obtain Eigen vector by solving for matrix x in such a way that, {A-lambda(i)}*[X]=[0]. For first Eigen value 16.36809984, we get [X]=[0.6262 0.7797] For second Eigen value 0.007462657,we get [X]=[0.7797 -0.6262] To obtain coordinates of data point in the direction of Eigen vectors by multiplying the centered data matrix to the Eigen vector matrix
- 11. Projection on Projection on the line of the line of first principal second component principal component X-Xbar Y-Ybar 2.88737 0.505380 1.8500 2.2175 3.26600 0.00622 2.0500 2.5425 -1.53633 0.01545 -0.9500 -1.2075 -2.49680 0.01729 -1.5500 -1.9575 -4.23402 0.12995 -2.5500 -3.3825 4.62439 0.05886 2.8500 3.6325 3.24237 0.10306 1.9500 2.5925 2.7500 3.3175 4.30858 0.06669 -2.7500 -3.4825 -4.43722 0.03664 -3.6500 -4.2825 -5.62453 0.16411 16.36809775 0.007462657
- 12. STEP1.Get some data STEP2.subtract the mean STEP3.Calculate the covariance matrix STEP4.Calculate the Eigen vectors & Eigen values of the covariance matrix STEP5. choosing components and forming a feature vector The variance of projections in the line of principal component is equal to the Eigen values of the principal components. First Eigen vector is able to explain around 99% of total variance
- 13. DATABASE PREPATATION TRAINING TESTING Flow chart indicating the sequence of implementation
- 15. 1.Acess control ATM AIRPORT A door lock control system 2.Entertainment: Video Game Human Computer Interaction Human Robotics
- 16. 3 Smart cards: Driver’s license Passports Voter registrations Pan card 4 Information Security: Desktop Logon Personal Driven Logon Database security 5 law Enforcement And Surveillance: Advanced video surveillance Drug trafficking And some other Commercial Applications:
- 17. HARD TO FOOL Face recognition is also very difficult to fool. It works by comparing facial and marks - specific proportions and angles of defined facial features - which cannot easily be concealed by beards, makeup. Byusing the facial recognition software, there's no need for a picture ID, bankcard or personal identification number (PIN) to verify a customer's identity. This way business can prevent fraud from occurring.
- 18. A face needs to be well lighted by controlled light sources in automated face authentication systems. This is only a first challenge in a long list of technical challenges that are associated with robust face authentication. The risk involved with identity theft.
- 19. Face recognition is a both challenging and important recognition technique. Among all the biometric techniques, face recognition approach possesses one great advantage, which is its user-friendliness. Face recognition promises latest security invents in the upcoming trends based on bio- metrics and pattern matching techniques and algorithms.
- 20. CONCLUSION:
- 22. The image may not always be identified in facial recognition alone. A picture is taken of a patch of skin, & is then broken up into smaller blocks, Using algorithms. It can identify differences between identical twins, which is not yet possible using facial recognition software. Accurate identification can increase by 20 to 25 percent.