Intelligent Control and Automation, 2008. WCICA 2008.
-
Upload
julia-alexander -
Category
Documents
-
view
216 -
download
0
Transcript of Intelligent Control and Automation, 2008. WCICA 2008.
Facial Expression Recognition Based on PCA and NMFIntelligent Control and Automation, 2008. WCICA 2008.
Outline• Introduction• Principal Component Analysis (PCA) Method• Non-negative Matrix Factorization (NMF) Method• PCA-NMF Method• Experiments Result and Analysis• Conclusion
Introduction• In this paper, we have detailed PCA and NMF, and
applied them to feature extraction of facial expression images.
• We also try to process basic image matrix and weight matrix of PCA and make them as the initialization of NMF.
• The experiments demonstrate that the method has got a better recognition rate than PCA and NMF.
Principal Component Analysis MethodLet’s suppose that m expression images are selected to take part in training, the training set X is defined by
Covariance matrix corresponding to all training samples is obtained as
u, average face, is defined by
Principal Component Analysis Method
# of training data
𝑥1 𝑥2 𝑥3 𝑥4
average face
𝑟𝑜𝑤+ + +
𝟒
𝑢
𝑐𝑜𝑙𝑛=𝑟𝑜𝑤×𝑐𝑜𝑙
Training Data Set
Principal Component Analysis Method
LetThen (2) becomes𝐴∈𝑅𝑛×𝑚
𝐶∈𝑅𝑛×𝑛❑⇒Matrix has eigenvectors
and eigenvalues.
Principal Component Analysis Method
Image50x50
⇒𝑛=50×50=2500
It is difficult to get 2500 eigenvectors and eigenvalues.
Therefore, we get eigenvectors and eigenvalues of by solving eigenvectors and eigenvalues of .
𝐴𝑇 𝐴∈𝑅𝑚×𝑚
Principal Component Analysis Method
The vectors and scalars are the eigenvectors and eigenvalues of covariance matrix . Then, eigenvectors of are defined by
Sorting by size: Generally, the scale is capacity that eigenvalues occupied:
Principal Component Analysis Method
Set is a projection matrix,
And then, every facial expression image feature can be denoted by following equation
PCA basic images
Non-negative Matrix Factorization MethodGiven a non-negative matrix , the NMF algorithms seek to find non-negative factors and of ,such that :
where is the number of feature vector satisfies
Non-negative Matrix Factorization MethodIterative update formulae are given as follow:
set hen define objective function
Non-negative Matrix Factorization Method
And then, every facial expression image feature can be denoted by following equation
NMF basic images
PCA-NMF Method
First, get projective matrix and weight matrix by PCA method.
Initialization is performed for matrices and by following
Experiments Result And Analysis
anger disgust fear happy neutral sad surprise
anger disgust fear happy neutral sad surprise
Experiments Result And Analysis
The comparison of recognition rate for every expression( The training set comprises 70 images and the test set of 70 images)
Experiments Result And Analysis
The comparison of recognition rate for every expression( The training set comprises 70 images and the test set of 143 images)
Experiments Result And Analysis
The comparison of recognition rate for every expression( The training set comprises 140 images and the test set of 73 images)