_{1}

^{*}

Over the last fifteen years, face recognition has become a popular area of research in image analysis and one of the most successful applications of machine learning and understanding. To enhance the classification rate of the image recognition, several techniques are introduced, modified and combined. The suggested model extracts the features using Fourier-Gabor filter, selects the best features using signal to noise ratio, deletes or modifies anomalous images using fuzzy c-mean clustering, uses kernel least square and optimizes it by using wild dog pack optimization. To compare the suggested method with the previous methods, four datasets are used. The results indicate that the suggested methods without fuzzy clustering and with fuzzy clustering outperform state- of-art methods for all datasets.

Facial recognition has been an active research topic since the early nineties. There have been several advances in the past few years in terms of face detection and tracking, feature extraction mechanisms and the related machine learning techniques. Face recognition has drawn the attention of researchers in fields from image analysis and processing, computer vision, to psychology and security [

Principal component analysis (PCA) converts a set of faces images of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. PCA can be used to capture as much as possible of the variability of the face image where the eigenfaces matrix can be used to recognize the new faces by minimizing [

where U is the eigenfaces matrix or features matrix, _{b} and the mean. Linear discriminant analysis (LDA) selects eigenvectors U in such a way that the ratio of the between-class scatter and the within class scatter is maximized which characterizes or separates two or more classes of faces images

where S_{B} and S_{W} are the between class scatter matrix and the within class scatter matrix respectively and U_{opt} can be found by solving the generalized eigenvalue problem [

Fourier (m, n, imgA) =

Gabor filters have been used to solve the configuration, orientations and emotions problems. A filter bank consisting of Gabor filters with various scales and rotations can be created and combined with different methods to enhance the recognition rate. The most commonly used filter in face recognition have the form [

where

The output locations for each Gabor sub-matrix are specified by x and y.

The suggested method modifies and combines several techniques to enhance the face recognition. The main steps can be summarized as following:

1) Extract features from each image using Fourier-Gabor filte

2) Select the best features using signal to noise ratio (SNR)

3) Delete or modify anomalous images using fuzzy c-mean cluster

4) Model the training images using the least square method

5) Use a new non linear kernel

6) Optimize the weight vector using wild dog pack optimization (WDPO)

There are several methods have been used to extract the features from the face images, one among the best methods is Fourier-Gabor filter which is introduced in [

1) Resize the images to 40 × 40

2) Transform the images to frequency domain by applying Fourier transform in Equation (3)

3) Use Equation (4) to prepare 8 Gabor filters for orientation and 10 filters for scaling. Thus 80 different filters will be constructed

4) Multiply the result matrix in step 2 by each matrix in step 3.

5) Resize each matrix in step 4 as one row

6) Construct the feature vector for each face by concatenation all the rows in step 5.

The number of the extracted features is 40 × 40 × 80 = 104,000. To delete insignificant features, Signal-to- Noise Ratio (SNR) method is applied [

where

If face x in a class is closer to the faces in another class, this will lead to misclassification of the new faces that are close to the face x. Therefore, fuzzy clustering is used to modify the faces that have low membership degree in the correct class and delete the faces that have high membership degree in the wrong classes. Thus the fuzzy c-mean clustering will be modified as following:

1) Initialize the membership randomly

2) Calculate the centers

3) Update the memberships

4) Go to step 2 until no significant improvement.

5) For all

Consider

If _{ }

Delete

If _{ }

Modify

6) Go to step 2 until the above conditions become invalid.

_{i} is the i^{th} face in the dataset, c_{j} is the center of the cluster, s and r are parameters to be tuned in the experimental section, n is number of images and m is number of classes or clusters (the fuzzy c-mean clustering before modification can be found in [

Once the features and the observations have prepared, several classifiers can be used such as neural networks, support vector machine (SVM) and regularized least squares classification (RLSC) [

w is the weight vector, y is the target class,

To train RLSC the parameters

Algorithm 1: Wild dog pack optimization (WDPO) Generate n dogs randomly

while (t < iter)

Evaluate Locations using the updated parameters

Choose the best location as alpha

Every few iterations update the parameters using self competition

Update the dogs locations with regard to alpha using Equation (12):

c: is used to control the diversity from alpha

Evaluate dogs

Choose the best dog as alpha

If no improvement for v iterations

Use Hoo procedure to escape from the local minimum

In this study four datasets are used: AT & T database of faces (ATT), Indian Face Database (IFD), Faces95 from Essex university database and Yale face database (Yale) [

All the results in this section are found by using 10-fold cross validations. The code is written by using Matlab 10. The experiments are divided into three stages. The first stage is used to find the best number of features using signal to noise method. The implementation in this stage is repeated several times, each time the number of the features is reduced by 10,000.

Datasets | Images | Subjects | Total | Variations |
---|---|---|---|---|

ATT | 10 | 40 | 400 | lighting and expressions |

IFD | 11 | 40 | 440 | Face direction |

Faces95 | 20 | 72 | 1440 | Distance and scale |

Yale | 165 | 15 | 2475 | Expressions |

#Features | Datasets | |||
---|---|---|---|---|

Yale | Face95 | IFD | ATT | |

104,000 | 96.3 | 92.2 | 94.0 | 94.7 |

80,000 | 97.2 | 94.8 | 95.8 | 96.9 |

50,000 | 97.3 | 93.0 | 92.8 | 95.4 |

10,000 | 93.0 | 91.6 | 89.7 | 92.1 |

5000 | 88.9 | 84.2 | 78.1 | 83.0 |

Clustering parameters | Datasets | |||
---|---|---|---|---|

Yale | Face95 | IFD | ATT | |

s = 20 and r = 5 | 94.7 | 91.5 | 90.3 | 91.6 |

s = 30 and r = 10 | 96.1 | 93.0 | 91.0 | 93.1 |

s = 40 and r = 20 | 96.3 | 95.9 | 94.5 | 92.8 |

s = 50 and r = 30 | 97.4 | 95.7 | 96.7 | 98.0 |

s = 60 and r = 40 | 93.1 | 92.1 | 93.1 | 95.2 |

Method | Datasets | |||
---|---|---|---|---|

Yale | Face95 | IFD | ATT | |

PCA | 91.2 | 81.1 | 80.2 | 94.2 |

LDA | 95.1 | 89.2 | 85.6 | 95.7 |

Gabor SVM | 95.6 | 86.2 | 86.4 | 95.6 |

Proposed without clustering | 95.7 | 90.1 | 88.6 | 95.1 |

Proposed with clustering | 97.1 | 92.5 | 91.8 | 96.0 |

Method | Datasets | |||
---|---|---|---|---|

Yale | Face95 | IFD | ATT | |

PCA | 92.4 | 82.7 | 89.9 | 95.7 |

LDA | 96.2 | 92.6 | 93.4 | 96.2 |

Gabor SVM | 96.2 | 90.2 | 92.3 | 96.6 |

Proposed without clustering | 96.5 | 92.1 | 93.9 | 95.9 |

Proposed with clustering | 98.2 | 94.5 | 96.1 | 97.6 |

Face recognition presents a challenging problem in the field of image analysis and computer vision, and as such has received a great deal of attention over the last few years because of its many applications in various domains. The performance of the proposed method was demonstrated on various datasets that contain several images per individual, different facial expressions, configuration, orientations and emotions. The results are quite promising; the suggested method outperforms the previous methods for all datasets. The future work will be dedicated to apply and combine the other features that are extracted by various techniques.

Essam Al Daoud, (2015) Face Recognition Using Fuzzy Clustering and Kernel Least Square. Journal of Computer and Communications,03,1-7. doi: 10.4236/jcc.2015.33001