Keywords

1 Introduction

Face recognition has been widely used in the real world and become a mature research field while the amount of approaches published every year is high. One may state that the recognition problem is already well solved but it is not true. It holds only for the cases when the faces are sufficiently well aligned and have limited amount of lighting variations. The performance of a face recognition system is considerably affected by the pose, expression, and illumination variations in face images. As discussed in [1], illumination treatment for image variation has been considered as one of the most critical preprocessing steps in face recognition. Variation in illumination conditions can make the appearance of a face in an image change greatly. Lighting causes larger differences in facial images compared with pose variations [2]. There has been much researches about how to overcome the illumination problem. As a rule, these methods can be separated into two main categories of methods for processing grayscale face images and processing color face images, respectively.

The methods used for color images can be divided into three subcategories. Illumination normalization-based methods [3] that are used to perform illumination normalization in face images captured under different lighting conditions. Reflectance model-based methods [4] extract illumination invariant components and then use these components as features for face recognition. Methods of modeling faces [5] under varying illumination as a low-dimensional linear subspace in the face space require a large amount of both training data and constraints in real applications. Accordingly one can argue that compensation of illumination on faces can not only improve the face recognition performance but also prove to be very useful for the improvement of face color quality. While most of the methods attempt to resolve the problem of illumination variation for grayscale face images, a few methods have processed color face images recently [6,7,8].

In this paper, a novel illumination compensation method called wavelet-based method combined with singular value decomposition (WSVD) is proposed for reducing the effect of light on a color face image when there is insufficient light, and improving the capability of recognition systems. The method first transforms a color face image to the two-dimensional (2D) discrete wavelet domain and then adjusts the magnitudes of the three color channels automatically by multiplying singular value matrices of the three magnitude matrices of the RGB color channels with corresponding compensation weight coefficients. The experimental results obtained by using the known color face database show that our method can render color face images more clear, natural, and smoother, even if the face image is under lateral lighting. Therefore, it is very useful for the color face recognition task.

The rest of this paper is organized as follows. Section 2 presents the proposed method for a color face image. Experimental results are reported in Sect. 3 and concluded in Sect. 4.

2 Wavelet-Based Method Combined with Singular Value Decomposition (WSVD)

In order to reduce the effect of illumination on color, we propose the method of lighting variation compensation based on wavelet subbands, where the compensation value varies dynamically with the ratio of the average individual RGB values. The singular value decomposition of the color image Ξ A can be expressed as

$$ f_{A} = U_{A} \sum\nolimits_{A} {V_{A}^{T} } , $$
(1)

where A = {R, G, B}, representing the employed RGB color space; Σ A is a matrix containing the sorted singular values on its main diagonal; and U A and V A are orthogonal square matrices. Daubechies wavelet characterized by a maximal number of vanishing moments for some given supports is applied to decompose the face image. The first-level coarse resolution is adopted to reduce the computation complexity and computing time. The size of the color image \( f_{A} \) is assumed to be M × N and the 2D discrete wavelet trasnsform is applied to decompose the three RGB color channels into their four subbands at scale level 1. The matrices are denoted as the LL, HL, LH, and HH wavelet subbands, and their mean values are \( \mathop \mu \nolimits_{\text{LL}} \), \( \mathop \mu \nolimits_{\text{HL}} \), \( \mathop \mu \nolimits_{\text{LH}} \), \( \mathop \mu \nolimits_{\text{HH}} \), respectively; the matrices G_LL, G_HL, G_LH, and G_HH are also denoted as the associated Gaussian templates, respectively.

$$ {\text{Max(}}\mathop \mu \nolimits_{\text{LL}} ,\mathop \mu \nolimits_{\text{LH}} ,\mathop \mu \nolimits_{\text{HL}} ,\mathop \mu \nolimits_{\text{HH}} ) = \varpi , $$
(2)
$$ \xi_{\text{LL}} = \left( {\frac{\varpi }{{\mu_{\text{LL}} }}} \right)*\frac{{{\text{Max}}\left( {\sum\nolimits_{{\text{G}\_\text{LL}}} {} } \right)}}{{{\text{Max}}\left( {\sum\nolimits_{\text{LL}} {} } \right)}}, $$
(3)
$$ \xi_{\text{HL}} = \left( {\frac{\varpi }{{\mu_{\text{HL}} }}} \right)*\frac{{{\text{Max}}\left( {\sum\nolimits_{{\text{G}\_\text{HL}}} {} } \right)}}{{{\text{Max}}\left( {\sum\nolimits_{\text{HL}} {} } \right)}}, $$
(4)
$$ \xi_{\text{LH}} = \left( {\frac{\varpi }{{\mu_{\text{LH}} }}} \right)*\frac{{{\text{Max}}\left( {\sum\nolimits_{{\text{G}\_\text{LH}}} {} } \right)}}{{{\text{Max}}\left( {\sum\nolimits_{\text{LH}} {} } \right)}}, $$
(5)
$$ \xi_{\text{HH}} = \left({\frac{\varpi }{{\mu_{\text{HH}} }}} \right)*\frac{{{\text{Max}}\left({\sum\nolimits_{{\text{G}\_\text{HH}}} {} } \right)}}{{{\text{Max}}\left({\sum\nolimits_{\text{HH}} {}} \right)}}, $$
(6)

where the mean and standard deviation of the synthetic Gaussian intensity matrix ΣG are 0.5 and 1, respectively. Based on the maximum mean vale \( \varpi \), LL, HL, LH, and HH wavelet subband coefficients of the RGB color channels are updated by multiplying the singular value matrices of each color channel wavelet subband with their corresponding compensation weight coefficients \( \xi_{\text{LL}} \), \( \xi_{\text{HL}} \), \( \xi_{\text{LL}} \), and \( \xi_{\text{LL}} \) to adjust the image contrast caused by illumination variation. After compensation, the equalized image f EA can be derived as follows:

$$ f_{EA} = U_{A} (\xi \sum\nolimits_{A} {)V_{A}^{T} } . $$
(7)

The face contrast was adaptively adjusted by multiplying the singular value matrix of each subband coefficient matrix by the corresponding compensation coefficients.

3 Results and Discussions

In this research, we used the color FERET database [9]. The database provides the standard testing subsets that constitute one gallery set fa and one probe set fb. The set fb has face images with different facial expressions, taken seconds after the corresponding fa. The images show variation in terms of pose, expression, illumination, and resolution. We made use of 100 fa images as gallery set, while 100 fb images were used as probe set. To remove the effect of background and hair style variations, the face region is cropped by excluding background and hair regions. The images are taken at resolution 512 × 768 pixels and were rescaled to 100 × 100 in pixels. The recognition rate is defined by the ratio of the number of correct recognition to the size of the probe set. In the experiments on recognition, we used projection color space (PCS) [10] to transform and process images after WSVD illumination compensation by using the following equation

$$ H_{C,R} \cdot \mathop H\nolimits_{C,G}^{T} \cdot H_{C,B} = \mathop I\nolimits_{H} , $$
(8)

where \( \mathop I\nolimits_{H} \in \mathop R\nolimits^{m \times n} \) is the PCS transformed image, where “\( \cdot \)” stands for the dot production. \( H_{C,R} \), \( H_{C,G} \), and \( H_{C,B} \) are respectively the R, G, and B color channels with WSVD illumination compensation. PCS transformation involves enabling a linear analysis in analyzing the nonlinear characteristics of image processing and using the linking information between color and image. Moreover, the elevated dimensions can obtain the correlation among image information. The automatic detection technique proposed in [11] is adopted to obtain T-shape face regions comprising eyes, nose, and mouth. Then, the T-shape regions were restored to matrix form. The compensated T-shape results are shown in Fig. 1, where column (a) shows the original images, column (b) shows the recombined T-shape faces with lighting compensation, and column (c) shows the PCS images of (b).

Fig. 1.
figure 1

Example images taken from the color FERET database. (a) Original images. (b) Recombined T-shape region images of (a) with WSVD compensation. (c) PCS images of (b).

Full size image

In order to analyze the clustering performance of raw faces and compensated faces, we used the leading ten eigenvectors derived from principal component analysis (PCA) [12] to examine the capability of collecting similar objects into groups. The trained and tested face images are classified using 1-NN. We conducted 10 experiments to evaluate the performance of the proposed method. In the experiment, we used 5 images from each subject as the training images and the other 5 images as the probe images. The comparisons of original images, SVD compensation (without wavelet decomposition), and WSVD compensation are shown in Table 1 to confirm that the proposed method can be applied in the real applications.

Table 1. Recognition rates for original (Ori), SVD, and WSVD images, obtained by applying eigenfaces, fisherfaces, and proposed methods to the color FERET database images (rate in %)
Full size table

4 Conclusions

In this work, we present the WSVD method for efficient face recognition. The proposed face recognizer is robust to large lighting variation. Experiments show that the proposed method can efficiently recognize a face in a short time less than 1 s. The presented framework was implemented with Microsoft Visual C++ 2010. The experiments were run on a PC with Intel Core i7-6700 (3.4 GHz) (4 GB RAM, Windows 7 operating system).