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# Face recognition vaishali

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### Face recognition vaishali

1. 1. FACE RECOGNITION By Vaishali S. Bansal M.Tech Computer C.G.P.I.T. Bardoli
2. 2. LEARNING OBJECTIVES THE VERY BASICS :  What is face recognition?  Difference between detection & recognition !!!  The origin and use of this technology ?  What are the various approaches to recognize a face? OUR SELECTED FACE RECOGNITION METHOD :  Introduction to PCA Based Eigen Face Recognition Method.
3. 3. WHAT IS FACE RECOGNITION?  “Face Recognition is the task of identifying an already detected face as a KNOWN or UNKNOWN face, and in more advanced cases, TELLING EXACTLY WHO’S IT IS ! “ FEATUREFACE DETECTION FACE RECOGNITION EXTRACTION
4. 4. METHODS FOR FEATUREEXTRACTION/FACE RECOGNITION
5. 5. FACE DETECTION V/S FRECOGNITION Face database Output: Mr.Chan Face detection Face recognition Prof..Cheng5 face interface v.2a
6. 6. THE "PCA" ALGORITHM
7. 7.  STEP 0: Convert image of training set to image vectors A training set consisting of total M images Each image is of size NxN 
8. 8.  STEP 1: Convert image of training set to image vectors A training set consisting of total M image foreach (image in training set) { 1 Image converted to vector NxN Image N …… Ti } Vector • Free vector space
9. 9.  STEP 2: Normalize the face vectors 1. Calculate the average face vectors A training set consisting of total M image Image converted to vector Calculate average face vector „U‟ U …… Ti • Free vector space
10. 10.  STEP 2: Normalize the face vectors 1. Calculate the average face vectors 2. Subtract avg face vector from each face vector A training set consisting of total M image Image converted to vector Calculate average face vector „U‟ U …… Then subtract mean(average) face Ti vector from EACH face vector to get to get normalized face vector Øi=Ti-U • Free vector space
11. 11.  STEP 2: Normalize the face vectors 1. Calculate the average face vectors 2. Subtract avg face vector from each face vector A training set consisting of total M image Image converted to vector Øi=Ti-U U …… Eg. a1 – m1 Ti a2 – m2 Ø1= . . . . • Free vector space a3 – m3
12. 12.  STEP 3: Calculate the Eigenvectors (Eigenvectors represent the variations in the faces ) A training set consisting of total M image Image converted to vector To calculate the eigenvectors , we U need to calculate the covariance …… vector C Ti C=A.AT where A=[Ø1, Ø2, Ø3,… ØM] • Free vector space N2 X M
13. 13.  STEP 3: Calculate the Eigenvectors A training set consisting of total M image Image converted to vector U C=A.AT …… Ti N2 X M M X N2 = N2 X N2 Very huge • Free vector space matrix
14. 14.  STEP 3: Calculate the Eigenvectors A training set consisting of total M image N2 eigenvectors …… Image converted to vector U C=A.AT …… Ti N2 X M M X N2 = N2 X N2 Very huge • Free vector space matrix
15. 15.  STEP 3: Calculate the Eigenvectors A training set consisting of total M image N2 eigenvectors …… Image converted to vector • But we need to find only K • U eigenvectors from the above …… N2 eigenvectors, where K<M Ti Eg. If N=50 and K=100 , we need to find 100 eigenvectors from 2500 • Free vector space (i.e.N2 ) VERY TIME CONSUMING
16. 16.  STEP 3: Calculate the Eigenvectors A training set consisting of total M image N2 eigenvectors …… Image converted to vector • SOLUTION • U …… “DIMENSIONALITY REDUCTION” Ti i.e. Calculate eigenvectors from a covariance of reduced • Free vector space dimensionality
17. 17.  STEP 4: Calculating eigenvectors from reduced covariance matrix A training set consisting of total M image M2 eigenvectors …… Image converted to vector • New C=AT .A • U …… M XN2 N2 X M = M XM Ti matrix • Free vector space
18. 18.  STEP 5: Select K best eigenfaces such that K<=M and can represent the whole training set  Selected K eigenfaces MUST be in the ORIGINAL dimensionality of the face Vector Space
19. 19.  STEP 6: Convert lower dimension K eigenvectors to original face dimensionality A training set consisting of total M image ui = A vi ui = ith eigenvector in the higher dimensional space vi = ith eigenvector in the lower dimensional space Image converted to vector 100 eigenvectors • • U …… Ti …… • Free vector space
20. 20. 2500 eigenvectors ui ……Each 2500 X 1 dimension ui = A v i =A 100 eigenvectors vi …… Each 100 X 1 dimension
21. 21. 2500 eigenvectors ui …… Each 2500 X 1 dimensionyellow colour shows K selected eigenfaces = ui
22. 22.  STEP 6: Represent each face image a linear combination of all K eigenvectors w1 Ω= w2 : w of mean face wk ∑ w1 w2 w3 w4 …. wkWe can say, the above image contains a little bit proportion of all these eigenfaces.
23. 23. Calculating weight of each eigenface The formula for calculating the weight is: wi= Øi. Ui For Eg.  w1= Ø1. U1  w2= Ø2. U2
24. 24. Recognizing an unknown faceInput image ofUNKNOWN FACE a1 – m1 Convert the r1 Normaloze the a2 – m2 input image to r2 a face vector face vector . . : . . rk a3 – m3RECOGNIZED AS Is Project Normalized YES Distance face onto the NO eigenspace €> threshold ∂? UNKNOWN FACE w1 Calculate Distance between Ω= w2 input weight vector and all the : weight vector of training set wk €=|Ω–Ωi|2 i=1…M Weight vector of input image
25. 25. Applications..
26. 26. Thank you…