Face Recognition using Eigen Values pptx

Face Recognition

1. “FACE RECOGNITION USING EIGENFACES” Dr.Sachin.S.Gurav .

2. Index INTRODUCTION FACE RECOGNITION SYSTEM EIGENFACE APPROACH EIGEN VALUES AND EIGEN VECTORS CALCULATIONS OF EIGEN VALUES AND EIGEN VECTORS ALGORITH TO FIND EIGENFACES EIGENFACES METHOD ADVANTAGE AND DISADVENTAGE APPLICATIONS CONCLUSION REFERENCES

3. Introduction Problem Statement : Given an image, to identify it as a face and/or extract face images from it. To retrieve the similar images (based on a heuristic)from the given database of face images.

4. Introduction Face recognition based on information theory approach of coding and decoding the face image. Proposed methodology is connection of two stages – Eigenface approach uses Principal Component Analysis (PCA) algorithm. dynamic images-- images received from the camera. static images – modified image. Eigenfaces- The scheme is based on an information theory approach that decomposes face images into a small set of characteristic feature images face recognition techniques can be divided into two- 1) Appearance-based 2) Feature-based,

5. Face Recognition Face recognition is the process of putting a name to a face. Once you've detected a face, face recognition means figuring out whose face it is Face is the most common biometric used by humans Applications range from static, mug-shot verification to a dynamic, uncontrolled face identification in a cluttered background Challenges: automatically locate the face recognize the face from a general view point under different illumination conditions, facial expressions, and aging effects

6. FACE RECOGNITION SYSTEM

7. There are six main functional blocks The acquisition module B. The pre-processing module C. The feature extraction module D. The classification module E. Training set F. Face database

8. Stages of Face Recognition (1) face location detection (2) feature extraction (3) facial image classification Approaches of Feature Extraction (1) local feature : eyes, nose, mouth information easily affected by irrelevant information . (2) global feature : extract feature from whole image .

9. Authentication vs Identification Face Authentication/Verification Face Identification/Recognition

10. EIGENFACE APPROACH • Extract the relevant facial information, which may or may not be directly related to human intuition of face features such as the eyes, nose, and lips. • Represent face images efficiently. To reduce the computation and space complexity.

11. EIGEN VALUES AND EIGEN VECTORS In this shear mapping of the Mona Lisa fig A a , the picture was deformed in such away that its central vertical axis (red vector)has not changed direction, but the diagonal vector (blue) has changed direction. Hence the red vector is an eigenvector of the transformation and the blue vector is not. Since the red vector was neither stretched nor compressed, its eigenvalue is 1.

12. CALCULATIONS OF EIGEN VALUES AND EIGEN VECTORS The vector x is an eigenvector of the matrix A with eigenvalue λ (lambda) if the following equation holds: Ax= λ x where

13. Eigen values This equation can be interpreted geometrically as follows: a vector x is an eigenvector if multiplication by A stretches, shrinks, leaves unchanged, flips (points in the opposite direction), flips and stretches, or flips and shrinks x. 1) If the eigenvalue λ > 1 , x is stretched by this factor. 2) If λ = 1 , the vector x is not affected at all by multiplication by A. 3) If 0 < λ < 1 , x is shrunk (or compressed).

14. ALGORITHM TO FIND EIGENFACES 1. Obtain M training images , I 1 I 2 I 3 I 4 I 5 … I M , it is very important that the images are centered.

15. 2. Represent each I i image as a vector Г i as discussed above.

16. 3. Find the average face vector Ψ .

17. 4. Subtract the mean face from each face vector Г i to get a set of vectors Ф i .The purpose of subtracting the mean image from each image vector is to be left with only the distinguishing features from each face and “removing” in a way information that is common. Ф i = Г i - Ψ .

18. 5. Find the Covariance matrix C: Where Here note that C is N 2 ×N 2 matrix & A is N 2 ×M matrix

19. We now need to calculate the Eigenvectors of C , However note that C is a N 2 ×N 2 matrix and it would return N 2 Eigenvectors each being N 2 dimensional. For an image this number is HUGE. The computations required would easily make your system run out of memory.

20. 6) Instead of matrix AA T consider matrix A T A .remember A is a N 2 ×M matrix thus A T A is a M×M matrix M Eigen vectors of dimension M×1 lets call these as Vi

21. 7. Now from some properties of matrices, it follows that A v i . We have found out v i . earlier. This implies that using v i we can calculate the M largest Eigenvectors. Remember that as M is simply the number of training images.

22. 8. Find the best M Eigenvectors of C=AA T by using the relation discussed above. 9. Select the best Eigenvectors, the selection of these Eigenvectors is done heuristically

23. EIGEN FACES The Eigenvectors found at the end of the previous section, when converted to a matrix in a process that is reverse to that in , have a face like appearance. Since these are Eigenvectors and have a face like appearance, they are called Eigen faces. Sometimes, they are also called as Ghost Images because of their weird appearance.

24. EIGEN VECTORS CONVERTED TO MATRIX FORM

25. WEIGHTING Now each face in the training set (minus the mean), These weights can be calculated as :

26. The Euclidean distance between two weight vectors d( Ω i , Ω j) provides a measure of similarity between the corresponding images i and j. If the Euclidean distance between Г NEW and other faces exceeds - on average - some threshold value θ , one can assume that Г NEW is no face at all. e r < θ image recognized e r > θ image not recognized

27. Why is the Threshold im ?

28. Advantages Eigen method distills the large dimension images to Eigen vector which reduces the processing time . Less memory storage .

29. Disadvantages Not able to discriminate between twins * Orientation of face * Time consumption

30. Application Voter id ATM security Airport security purpose Offices Crime investigation Access Control

31. Future Scope Face Detection in motion pictures. Investigate whether eigenfaces is a good solution for this problem by comparing with other feature extraction techniques such as DCT.

32. CONCLUSION In this study, we used the eigenfaces to represent the features vectors for human faces. The features are extracted from the original image to represents unique identity used in classification and recognition. The eigenfaces has proven the capability to provide the significant features and reduces the input size