The document presents a hybrid face detection system that combines eigenfaces/PCA and Legendre moments. It calculates eigenweights and moments for training images and combines them to train an SVM classifier. For new images, it extracts eigenweights and moments, combines them, and classifies the image with SVM. The proposed method achieves 96% accuracy for face detection, outperforming systems using only PCA or Legendre moments.

1. Face Detection based on Eigenfaces and Legendre Moments
Face Detection based on Eigenfaces and
Legendre Moments
S.M. Jaisakthi
September 9, 2009

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