Face Detection based on Eigenfaces and Legendre Moments




                  Face Detection based on Eigenfaces and
     ...
Face Detection based on Eigenfaces and Legendre Moments
  Abstract




Abstract




              Presents a hybrid system...
Face Detection based on Eigenfaces and Legendre Moments
  Introduction




Introduction


      Face Detection is
        ...
Face Detection based on Eigenfaces and Legendre Moments
  Introduction




Introduction cont...



                 Eigenw...
Face Detection based on Eigenfaces and Legendre Moments
  Proposed Methodology




Proposed Methodology



      The propo...
Face Detection based on Eigenfaces and Legendre Moments
  Proposed Methodology
     Calculating Principal Component Analys...
Face Detection based on Eigenfaces and Legendre Moments
  Proposed Methodology
     Calculating Principal Component Analys...
Face Detection based on Eigenfaces and Legendre Moments
  Proposed Methodology
     Calculating Legendre Moments



Legend...
Face Detection based on Eigenfaces and Legendre Moments
  Proposed Methodology
     Calculating Legendre Moments



Calcul...
Face Detection based on Eigenfaces and Legendre Moments
  Proposed Methodology
     Training Support Vector Machine



Sup...
Face Detection based on Eigenfaces and Legendre Moments
  Proposed Methodology
     Training Support Vector Machine



SVM...
Face Detection based on Eigenfaces and Legendre Moments
  Proposed Methodology
     Training Support Vector Machine



Tra...
Face Detection based on Eigenfaces and Legendre Moments
  Proposed Methodology
     Face Detection



Face detection




 ...
Face Detection based on Eigenfaces and Legendre Moments
  Proposed Methodology
     Results & Discussions



Results & Dis...
Face Detection based on Eigenfaces and Legendre Moments
  Proposed Methodology
     Conclusion



Conclusion




         ...
Face Detection based on Eigenfaces and Legendre Moments




                                               THANK YOU
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  1. 1. Face Detection based on Eigenfaces and Legendre Moments Face Detection based on Eigenfaces and Legendre Moments S.M. Jaisakthi September 9, 2009
  2. 2. Face Detection based on Eigenfaces and Legendre Moments Abstract Abstract Presents a hybrid system which combines two different approaches eigenfaces/PCA and legendre moment Produces 96% accuracy.
  3. 3. Face Detection based on Eigenfaces and Legendre Moments Introduction Introduction Face Detection is A pattern analysis problem Applicable in Bankcard Identification System,Security Monitoring,Computer Vision etc. Difficult Problem Broadly classified as Appearence Based Approach Feature Based Approach Moment Based Approach
  4. 4. Face Detection based on Eigenfaces and Legendre Moments Introduction Introduction cont... Eigenweights and moments are calculated for each image in the training set Calculated weights and moments are combined and trained with SVM For any new image weights and moments are calculated and are given to the SVM for classification
  5. 5. Face Detection based on Eigenfaces and Legendre Moments Proposed Methodology Proposed Methodology The proposed algorithm comprises of 4 main modules calculating eigenfaces (PCA) calculating legendre moments (LM) training SVM face detection
  6. 6. Face Detection based on Eigenfaces and Legendre Moments Proposed Methodology Calculating Principal Component Analysis Principal Component Analysis(PCA) finds patterns in high dimensional data expresses the data to highlight their similarities and differences Compresses a set of high dimensional vectors into a set of lower dimensional vectors
  7. 7. Face Detection based on Eigenfaces and Legendre Moments Proposed Methodology Calculating Principal Component Analysis Computing PCA 1 Organize the input data. 2 Calculate the mean value µ. N 1 µ= xi N i=1 3 Mean correct all the points by subtracting the mean value from each data A = xi − µ 4 Calculate the covariance matrix C C = AAT 5 Compute the eigenvectors and eigenvalues of the covariance matrix C. 6 Calculate the eigenweights. T
  8. 8. Face Detection based on Eigenfaces and Legendre Moments Proposed Methodology Calculating Legendre Moments Legendre Moments Statistical expectation of certain power functions of a random variable. ∞ µ = E (X ) = xf (x)dx −∞ The p-th moment is estimated as 1 N p mp = Σ x N i=1 i it can be extended 2-D
  9. 9. Face Detection based on Eigenfaces and Legendre Moments Proposed Methodology Calculating Legendre Moments Calculation of LM legendre moments can be calculated using the expression N−1 N−1 Lpq = λpq Pp (xi )Pq (yi )f (i, j) i=0 j=0 where the normalizing constant is, (2p + 1)(2q + 1) λpq = N2 xi and yj denote the normalized pixel coordinates in the range of (-1,1), which are given by 2i 2j xi = − 1 and yi = −1 N −1 N −1
  10. 10. Face Detection based on Eigenfaces and Legendre Moments Proposed Methodology Training Support Vector Machine Support Vector Machine Statistical learning method Finds the hyperplane that best separates two class using f (x) = wx + b Identify optimal hyperplane
  11. 11. Face Detection based on Eigenfaces and Legendre Moments Proposed Methodology Training Support Vector Machine SVM Cont... Find support vectors which is given by wxi + b = ±1 Optimal hyperplane can be found by solving 1 W2 min 2 subject to yi (wxi + b) − 1 ≥ 0, i = 0, 1, ..., N. Using lagrangian formulation, the optimal hyperplane function can be written as f (x) = λi yi (xi x) + b i S Non-linear case, SVM creates non-linear hyperplane by mapping the input space into higher dimensional space using kernal functions
  12. 12. Face Detection based on Eigenfaces and Legendre Moments Proposed Methodology Training Support Vector Machine Training SVM Eigenweights and Moments for training images are calculated and combined together and stored in a single vector This vectors are trained with SVM classifier.
  13. 13. Face Detection based on Eigenfaces and Legendre Moments Proposed Methodology Face Detection Face detection For a new image calculate eigenweights and legendre moments combine both weights and moments and pass to SVM classifier
  14. 14. Face Detection based on Eigenfaces and Legendre Moments Proposed Methodology Results & Discussions Results & Discussions Produces 96% accuracy for 10-fold cross validation Miss-classification rate Table: Comparison of error rates Method False False Detection negative positive rate errors errors PCA 1.6% 8.0% 91% Legendre Moments 9.2% 7.2% 83% Proposed Method 1.2% 3.2% 96%
  15. 15. Face Detection based on Eigenfaces and Legendre Moments Proposed Methodology Conclusion Conclusion Results in high performance when compared to the previous work Can be extened by including feature based methods
  16. 16. Face Detection based on Eigenfaces and Legendre Moments THANK YOU

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