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This paper proposes a novel image region descriptor for face recognition, named kernel Gabor-based weighted region covariance matrix (KGWRCM). As different parts are different effectual in characterizing and recognizing faces, we construct a weighting matrix by computing the similarity of each pixel within a face sample to emphasize features. We then incorporate the weighting matrices into a region covariance matrix, named weighted region covariance matrix (WRCM), to obtain the discriminative features of faces for recognition. Finally, to further preserve discriminative features in higher dimensional space, we develop the kernel Gabor-based weighted region covariance matrix (KGWRCM). Experimental results show that the KGWRCM outperforms other algorithms including the kernel Gabor-based region covariance matrix (KGCRM).

Feature extraction from images or image regions is a key step for image recognition and video analysis problems. Recently, matrix-based feature representations [

However, the previous methods based on RCM consider each pixel in the training image to be contributing equally when reconstructing the RCM, ^{2}, where

Motivated by the above-mentioned reasons, we hence propose in this paper a weighted region covariance matrix (WRCM) to explicitly exploit the different importance of each pixel of a sample. WRCM can only extract linear face features. However, by using nonlinear features it can achieve higher performance for face recognition tasks [

The RCM [_{i}

As a result there are _{i}_{i}_{= 1,…},_{N}

The image region can then be represented by a _{i}_{i}

The computation process is given in

Based on the feature vectors _{i}_{ii}

Comparing _{ij}^{2}, which implies that RCM is a special case of the WRCM method. However, as all the weights in RCM are 1/^{2}, RCM cannot exploit the different importance of each pixel of a sample. On the other hand, the WRCM can assign different weights for each pixel of a sample, so it can preserve more discrimination information than RCM.

As _{W}_{1},…,_{c}

To preserve the local and global patterns, similar to [_{1}, _{2}, _{3}, _{4}, and _{5}) (_{W}_{1}, _{W}_{2}, _{W}_{3}, _{W}_{4}, and _{W}_{5}) are constructed from five different regions. As _{W}_{1} is the weighted region covariance matrix of the entire image region _{1}, it is a global representation of the face. The _{W}_{2}, _{W}_{3}, _{W}_{4}, and _{W}_{5} are extracted from four local image regions (_{2}, _{3}, _{4}, and _{5}), so they are part-based representations of the face.

After obtaining WRCMs of each region, it is necessary to measure the distance between the gallery and probe sets. Let

To generalize WRCM to the nonlinear case, we use a nonlinear kernel mapping ^{d} → ϕ^{d}_{1} and _{2} are two rectangular regions in the gallery and probe set images, respectively. Let _{1} and _{2}, respectively. _{1} and _{2}, where, _{1}), _{2}),…, _{m}_{1}), _{2}),…, _{n}_{1} and _{2}, respectively.
^{#} = D^{#} − S^{#}.

Hence

As any eigenvector can be expressed by a linear combination of the elements, there exist coefficients _{i}_{j}_{1},_{2},…_{m}^{T} and _{1},_{2},…_{n}^{T}.

Combining

The detailed derivation of

We defined matrices

When

However, in many cases,

Based on eigenvalues obtained by _{1} and _{2} using

In _{u,v}_{v}_{max}^{v}_{u}_{max}

Therefore, a feature mapping function based on Gabor features is obtain by:

As the Gabor wavelet representation can capture salient visual properties such as spatial localization, orientation selectivity, and spatial frequency characteristic, Gabor-based features can carry more important information. The proposed KGWRCM method can be briefly summarized as follows:

partition a face image into five regions (_{2}, _{3}, _{4}, and _{5}), and extract basic features of five regions using

compute two weight matrices ^{#} using

with

based on the distance defined in

We tested the GKWRCM algorithm on the ORL Face database [

The Yale face database contains 165 grayscale images with 11 images for each of 15 individuals. These images are subject to expression and lighting variations. In this recognition experiment, all face images with size of 80 × 80 were resized to 40 × 40. Five images of each subject were randomly chosen for training and the remaining six images were used for testing. There are hence 462 different selection ways. We select 20 random subsets with five images for training and six for testing.

The AR database consists of over 4,000 images corresponding to 126 people's faces (70 men and 56 women). These images include more facial variations, including illumination change, and facial occlusions (sun glasses and scarf). For each individual, 26 pictures were taken in two separate sessions and each section contains 13 images. In the experiment, we chose a subset of the data set consisting of 50 male subjects and 50 female subjects with seven images for each subject. The size of images are 165 × 120. We select two images for training and five for testing from the seven images. There are 21 different selection ways.

In our experiment, all images are normalized to zero mean and unit variance. We compare the developed WRCM and KGWRCM with the RCM, the RCM with Gabor features GRCM [

The average recognition accuracies on the ORL, Yale and AR databases are shown in

These results clearly show that the proposed KGWRCM method can capture more discriminative information than other methods for face recognition. Particularly KGWRCM and WRCM outperform KGRCM and RCM, which implies that the weighted approaches can better emphasize more important parts in faces and deemphasize the less important parts, and also preserve discriminated information for face recognition.

In this paper, an efficient image representation method for face recognition called KGWRCM is proposed. Considering that some pixels in face image are more effectual in representing and recognizing faces, we have constructed KGWRCM based on weighted score of each pixel within a sample to duly emphasize the face features. As the weighted matrix can carry more important information, the proposed method has shown good performance. Experimental results also show that the proposed KGWRCM method outperforms other approaches in terms of recognition accuracy. However, similar to KGRCM, the computational cost of KGWRCM is high due to the computation of the high dimensional matrix. In future work, an effective KGWRCM method with low computational complexity will be developed for face recognition.

This work is supported by the Research Fund for the Doctoral Program of Higher Education of China (NO. 20100191110011), and the Fundamental Research Funds for the Central Universities (NO. CDJXS11122220, CDJXS11121145).

By some simple algebraic,

Based on

Let _{i}_{j}_{i}_{j}

Substituting

Based on

To express ^{T}

Similarly, we multiply ^{T}

Combining

Five regions of a face image. Five WRCMs are constructed from the corresponding regions.

Five examples of the first subject in (

The performance of different approaches on the ORL face database.

KGRCM | 98.41 | 1.24 |

GRCM | 97.06 | 1.28 |

RCM | 91.88 | 2.57 |

GPCA | 89.78 | 2.43 |

GLDA | 97.5 | 1.37 |

KPCA | 94.43 | 1.55 |

The performance of different approaches on the Yale face database.

KGRCM | 76.23 | 9.04 |

GRCM | 72.00 | 10.58 |

RCM | 51.94 | 7.22 |

GPCA | 67.94 | 9.36 |

GLDA | 73.47 | 7.06 |

KPCA | 73.28 | 8.11 |

The performance of different approaches on the AR face database.

KGRCM | 91.80 | 2.58 |

GRCM | 81.46 | 11.73 |

RCM | 41.31 | 12.54 |

GPCA | 78.64 | 5.35 |

GLDA | 88.99 | 4.18 |

KPCA | 66.89 | 7.68 |