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face recognition using fisher face analysis linear discriminant analysis(LDA)

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- 1. BY:- Suraj Kumar(BT11CS008) Saroj Paswan(BT11CS005) FACE RECOGNITION USING FISHER FACE ANALYSIS(LDA)
- 2. TOPICS OF DISCUSSION Face Recognition. Linear Discriminant Analysis(LDA). Class Separation using LDA. Algorithm used in LDA approach. Application of LDA. Database used. References.
- 3. FACE RECOGNITION Face recognition system is a computer application for automatically identify or verifying a person from a digital image or video frame. In this system automatically searching of faces from the face databases, typically resulting in a group of facial images ranked by computer evaluated similarity.
- 4. USE OF FACE RECOGNITION SYSTEM Face recognition system is typically used in security system and personal information access. SECURITY Airport, seaport, railway station etc. Find Fugitive. PERSONAL INFORMATION ACCESS ATM. Computer system.
- 5. FACE RECOGNITION ALGORITHM Linear Discriminant Analysis(LDA). Principle Component Analysis(PCA).
- 6. Linear Discriminant Analysis(LDA) Linear discriminant methods group images of the same classes and separates images of the different classes. To identify an input test image, the projected test image is compared to each projected training image, and the test image is identified as the closest training image.
- 7. To explain discriminant analysis, here we consider a classification involving two target categories and two predictor variables. The following figure shows a plot of the two categories with the two predictor’s orthogonal axes: Figure 1. Plot of two categories
- 8. The target variable may have two or more categories. Images are projected from two dimensional spaces to c dimensional space, where c is the number of classes of the images. To identify an input test image, the projected test image is compared to each projected Training image.
- 9. Class Separation Using LDA Linear discriminant analysis finds a linear transformation (discriminant function) of the two predictors, X and Y that yields a new set of transformed values that provides a more accurate discrimination than either predictor alone: Transformed Target = C1*X + C2*Y
- 10. The following figure shows the partitioning done using the transformation function: Figure 2. Partitioning done using the transformation function
- 11. Maximizing the between class scatter matrix, while minimizing the within-class scatter matrix, a transformation function is found that maximizes the ratio of between-class variance to within-class variance and find a good class separation as illustrated as follows: Figure 3. Class Separations in LDA
- 12. ALGORITHM USED IN LDA In Linear discriminant analysis we provide the following steps to discriminant the input images: STEP-1: We need a training set and at last one image in the test set. These examples should represent different frontal views of subjects with minor variations in view angle. They should also include different facial expressions, different lighting, background condition and only the face regions. It is assumed that all images are already normalized to m × n arrays.
- 13. b b 2 1 2 N 2 2 a a a 1 2 b N 1 2 N c c c e e 2 1 2 2 N 2 d d d 1 2 e N 1 2 N f f f representing faces
- 14. STEP-2: For each image and sub image, starting with the two dimensional m × n array of intensity values I(x, y), we construct the vector expansion Φ R m× n. This vector corresponds to the initial representation of the face. Thus the set of all faces in the feature space is treated as a high-dimensional vector space.
- 15. STEP-3: By defining all instances of the same person’s face as being in one class and the faces of different subjects as being in different classes for all subjects in the training set, we establish a framework for performing a cluster separation analysis in the feature space. we compute the within-class and between-class scatter matrices.
- 16. Now with-in class scatter matrix ‘Sw’ and the between class scatter matrix ‘Sb’ are defined as follows: 푵풋 (휞풊 Sw = Σ풄 Σ풋=ퟏ 풊=ퟏ 풋 − 흁풋) (휞풊 풋 − 흁풋)푻 ------ (1) 푗, the 푖푡ℎ. samples of class j, 휇푗 is the mean of class j, c is the number Where , Γ푖 of classes, 푁푗 is the number of samples in class j. 풄 (흁풋 − 흁) (흁풋 − 흁)푻 ---------------- (2) Sb = Σ풋=ퟏ Where, μ represents the mean of all classes.
- 17. mean of class a b h a b h 1 1 1 1 2 2 2 m where M 2 2 2 , 8 N N N M a b h Then subtract it from the training faces a m b m c m d m a m b m c m d m 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 a b c d , , , , m m m m a m N 2 N 2 b m c m N 2 N 2 N 2 N 2 d m N 2 N 2 e m f m e m f g m h m 1 1 1 1 2 2 m g m h m e , f g h m m e m N 2 N 2 2 2 2 2 2 2 1 1 1 1 2 2 2 2 2 2 , , m m f m g m h m N N N N N N
- 18. The subspace for LDA is spanned by a set of vectors w=[푎 푚, 푏푚, …, ℎ푚], Satisfying w = arg max = mod 푤푇 푆푏 푤 푤푇 푆푤 푤 -----(3) The with-in class scatter matrix represents how face images are distributed closely with-in classes and between class scatter matrix describes how classes are separated from each other. When face images are projected into the discriminant vector w. Face images should be distributed closely with-in classes and should be separated between classes, as much as possible. In other words, these discriminant vectors minimize the denominator and maximize the numerator in equation (3).
- 19. The testing phase of LDA is as shown as in figure. Face Database Training Set Testing Set Projection of Test Image LDA(Feature Extraction) Feature Vector Feature Vector Classifier (Euclidean distance) Decision making
- 20. APPLICATION OF LDA Linear discriminant analysis techniques used in statistics, pattern recognition and machine learning to find a linear combination of features which characterized or separates two or more classes of objects. DATABASE USED ORL Database, All the files are in PGM format. The size of each image is 92×112 pixels. with 256 grey levels per pixel. Fig. 4. One of ORL face database with ten different expressions.
- 21. REFERENCES [1] [Online]. Available: http://www.animetrics.com/technology/frapplications.html http://en.wikipedia.org/wiki/Facial_recognition_system http://vis-www.cs.umass.edu/~vidit/IndianFaceDatabase http://www.originlab.com [2] B. J. Oh, Face Recognition using Radial Basis Function Network based on LDA. World Academy of Science, Engineering and Technology 7 2005 [3] R. Duda and P. Hart, Pattern Classification and Scene Analysis. [4] R. Chellappa, C. Wilson, and S. Sirohey, Human and Machine Recognition of Faces: A Survey, Proc. IEEE, vol. 83, no. 5, pp. 705- 740, 1995. [5] ORL face database: AT &T Laboratories, Cambridge,U.K..[Online]. Available: http://www. cam-orl.co.uk / facedatabse.html.
- 22. THANKS…

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