Almost all the face recognition algorithms are unsatisfied due to illumination variation. Feature with high frequency represents the face intrinsic structure according to the common assumption that illumination varies slowly and the face intrinsic feature varies rapidly. In this paper, we will propose an adaptive scheme based on FBEEMD and detail feature fusion. FBEEMD is a fast version of BEEMD without time-consuming surface interpolation and iteration computation. It can decompose an image into sub-images with high frequency matching detail feature and sub-images with low frequency corresponding to contour feature. However, it is difficult to determine by quantitative analysis that which sub-images with high frequency can be used for reconstructing an illumination-invariant face. Thus, two measurements are proposed to calculate weights for quantifying the detail feature. With this fusion technique, one can reconstruct a more illumination-neutral facial image to improve face recognition rate. Verification experiments using classical recognition algorithms are tested with Yale B, PIE and FERET databases. The encouraging results show that the proposed scheme is very effective when dealing with face images under variable lighting condition.
© 2013 OSA
Face recognition is the biometric identification of a human face, which matches the image against a library of known faces. It has attracted significant attention because of its wide range of applications in public security, law enforcement and commerce, access control, information security and intelligent surveillance [1–3]. Over the last few years, numerous algorithms have been proposed for face recognition, including principal component analysis (PCA) [4, 5], linear discriminant analysis (LDA) , independent component analysis (ICA) [7, 8], local feature analysis (LFA) , elastic bunch graph matching (EBGM) , neutral networks , active appearance model , 3D morphable model , hidden Markov model , support vector machine , Hausdorff distances [16, 17], kernel methods , image-based recognition , volume holographic correlator , a correlation method along with ICA model , parallel correlated recognition  etc.
Despite of a certain level of maturity and several practical successes, automatic face recognition remains a challenging task with uncooperative users as well as uncontrolled environment such as facial expression, pose changes and variable lighting conditions. The existing recognition algorithms may face a dramatic drop due to these variations. Changes in lighting conditions during training and testing stages contribute more significantly. It is believed that lighting variations are even larger than differences among distinct individuals. In recent years, research on face recognition has been focused on diminishing the impact of illumination changes. Much progress and research work has been made to implement illumination normalization before recognizing.
Generally speaking, these schemes can be categorized into three groups: modeling, preprocessing and feature extraction.
Modeling schemes tend to model 3D human faces containing almost all the environment variations [23–26]. However, there are two major drawbacks in these schemes, which limit their applications in practical recognition systems. One is that these methods need numerous experimental samples to simulate face images under disparate lighting conditions. The other is that these methods consider human face as convex object and thus ignore casting shadows.
Feature extraction scheme: This approach attempts to extract facial features that are invariant to illumination variations. Such examples discussed by researchers are edge maps, image intensity derivatives, adaptive feature-specific imaging  and masked fake face detection . However, none of the methods is sufficient to avoid interference from illumination variations. The Self-quotient image (SQI) is introduced to implement illumination-invariant recognition when lighting conditions change . But this method requires Bootstrap database and its performance may degrade if dominant features between training and test samples are misaligned.
Preprocessing schemes are to eliminate the influence of illumination variations using some image processing techniques before recognition, including: logarithm transform , adaptive histogram equalization , block-based histogram equalization , symmetric shape-from-shading and a generic 3-D model , logarithm total variation, discrete cosine transform in logarithm domain (LOG-DCT) , advanced correlation filter , Bi-dimensional empirical mode decomposition (BEMD) normalization , etc. For Ref , it is difficult to deal with non-uniform illumination using global methods. Ref . can cope with non-uniform illumination variation but the performances are still not satisfactory. Ref . enhances the recognition rates greatly only for frontal face images. The kernel algorithm in Ref , DCT, is not adaptive with external basic function needed. The kernel algorithm in Ref , BEMD, has some drawbacks unsolved in itself such as mode mixing, boundary effects and time consuming.
The major drawback in BEMD is the frequent appearance of leaky wave, caused by 2D mode mixing. Leaky wave can be explained that some elements originally belonging to one BIMF (Bi-dimensional Intrinsic Mode Function) may leak into other BIMFs. This phenomenon makes the decomposition incomplete. To overcome the problem, a new noise-assisted data analysis method , named bi-dimensional ensemble empirical mode decomposition (BEEMD), was introduced. This ensemble method takes too much time because of a huge number of BEMD trials, though it is quite efficient. Therefore, a fast BEEMD (FBEEMD) approach based on envelope estimation and self-similar boundary extension will be proposed in this paper.
The contribution of this paper is as follows: Firstly, fast decomposition method, FBEEMD, will be used to decompose a facial image into a set of multi-scale BIMFs. And then effective BIMFs will be extracted and then fused together as illumination-invariant feature of face. In this process, two measurements are proposed to calculate weights for quantifying the detail feature contained in each BIMF. With these two methods, the contribution ratio of each BIMF to global feature can be computed adaptively. By reconstructing facial image, we can reduce the overall effect of illumination variation effectively. Recognition results in six experiments are reported using Yale B, FERET and Carnegie Mellon University’s Pose Illumination and Expression (PIE) databases.
2. Bi-dimensional ensemble empirical mode decomposition
The successful application of empirical mode decomposition has stimulated the development of BEMD [38–42]. However, there generally exists a major drawback called 2D mode mixing in BEMD. It can be defined  as any BIMF consisting of oscillations of dramatically disparate scales. When mode mixing occurs, a BIMF may cease to have physical meaning by itself, suggesting that the clean separation of scales has been damaged.
To alleviate the problem, a new noise-added method of signal analysis, named BEEMD, was proposed by N. E. Huang et al . The method defines BIMF components as the mean of an ensemble of trials, each consisting of original signal and white noise with finite amplitude. This new approach takes full advantage of statistical characteristic of white noise. Since the noise in each trial is different, it is canceled out in the ensemble mean of sufficient trails and the ensemble mean is treated as the true answer. Moreover, this ensemble decomposition method has been applied in 2D signal processing and information demodulation [44, 45].
However, it is noteworthy that such an ensemble BEMD approach requires large computational resource, proportional to the number of BEMD trials. A typical implementation of BEEMD is usually 100 independent trials in the ensemble. If processing a 256 × 256 image, it will take about 200 seconds in each trial. The large demand of computational resource has imposed a barrier of developing BEEMD by far. Therefore, in section 3, some new details will be introduced to original BEMD in order to implement BEEMD much faster and better.
3. The new BEEMD details
3.1 Local extrema detection
Detecting the local extrema from a 2D source signal is the first problem to be tackled in BEMD. Some BEMD methods used mathematical morphology method to locate the local extrema, but this will make the extreme points reduce quite fast. It means that the residual signal will become too smooth to find sufficient extreme points for fitting a surface after extracting two or three BIMFs.
Neighboring window method  is used to find the local maxima and minima points in this study. A data point is considered as a local maximum (minimum), if its value is strictly higher (lower) than all of its neighbors within a window. Generally, 3 × 3 window could result in an optimum extrema map. Although the larger windows are also used to reduce the computation cost in some cases, the extreme points will reduce very fast as the mathematical morphology method.
3.2 A fractal-based processing method for boundary effect
Another difficulty in BEMD comes from the processing of boundary effect . As the number of iterations increases, this effect will not only appear at the boundary, but also propagate into the interior of the transformed data, which may finally make the decomposition useless.
A self-similar extension method will be proposed to reduce boundary effect in this study. From the original image, we can find a self-similar part corresponding to the extended part. The concrete algorithm is shown in Fig. 1 as follows:
Assume the size of original image I is N × N. The size of the extended block is k × k. After extending, the size of the new image is (N + 2k) × (N + 2k), where the middle N × N block is the original image. The original image I is divided to N/k blocks with each one k × k size. Each extended block ie has three neighbor blocks, denoted as in, in the original image. And then in the original image I, find the blocks which are the most similar to in. The criteria for judging similarity is based on the MAD (Mean Absolute Difference) for representing the distances different between boundary blocks and the matched blocks. At last, the block with most similar neighbor blocks is used as the extended block.
Before the above extension processing, an important parameter has to be determined, which is the boundary width. It is found that 8 or 16 are enough for most textures and natural images. After boundary processing based on the self-similar extension, the boundary interference in BEMD will be reduced, and the BIMF components is more significant.
3.3 A fast BEMD method
The ensemble method demands a huge number of trials to eliminate the added white noise. Moreover, the extraction of each BIMF in a single BEMD trial requires the repetitive iterations until finding an optimized fitting surface. This makes the decomposition process complex and excessively time-consuming.
A fast BEMD (FBEMD) method based on envelope estimation is proposed by S. M. A. Bhuiyan et al [48, 49]. The process of surface estimation runs faster than that of the interpolation in traditional BEMD. Moreover, this method can help reduce the number of iterations per BIMF greatly. All of these make FBEMD a rapid and efficient algorithm.
In traditional BEMD, SD is employed as the fundamental stopping criterion and at the same time, the maximum number of allowable iterations (MNAI) is applied as an additional stopping criterion to prevent the over-sifting [50, 51]. Moreover, similar or even better results could be produced by fast BEMD with the one iteration per BIMF than those achieved by traditional BEMD with a few iterations. Therefore, we will just use the MNAI criterion to stop the process of sifting iterations, which could limit the number of iterations per BIMF to one or a few times considered being sufficient.
To increase adaptivity of the FBEMD method, K. Patorski et al. proposed a simple modification in . The adjustment step for the extrema detector window width is added at the beginning of calculating each BIMF. Proposed modification extends the computation time but it is specially tailored to yield adaptivity of FBEMD.
3.4 Comparison between some traditional BEMDs and FBEEMD
Figure 2 shows the development process of BEMD clearly: When the traditional BEMDs suffered from two major drawbacks (mode-mixing and time consuming), two study branches appeared. The ensemble concept was introduced to BEMD by N. E. Huang et al to overcome the mode-mixing, called E-BEMD or BEEMD usually. The fast thought was proposed for BEMD by S. M. A. Bhuiyan et al to overcome the time consuming, called F-BEMD. Then in the study, we will propose a decomposition method combining the above ensemble and fast BEMD methods together, named as FBEEMD by our research team.
A typical example will be used to illustrate the problem of 2D mode mixing and then present the performance in resolving the problem. FBEEMD is utilized to decompose Lena image with 5 iterations, 100 trails and the standard deviation of white noise signal set to one fifth of the one of the original signal.
Through examination of each BIMF component in Fig. 3, one can clearly see several zones with deep color, for example, at the edge of face, nose, arm and hat, considered as 2D mode mixing, which is so serious as to make the fundamental components unclear, especially in Fig. 3(c) and Fig. 3(d).
In Fig. 4, one can scarcely see the zones with deep color, and the fundamental components are uncontaminated by the intermittence and much more visible than the corresponding one in Fig. 3. Improvement of the BIMF quality for Lena image is obvious with FBEEMD. The decomposition method more clearly reveals the edges and other characteristic features at different scales compared to the BIMFs obtained by original BEMD.
The orthogonality index (OI) has been proposed in Ref , the extended formula for two dimension is defined as follows:51]. Generally, OI value less than 0.1 are acceptable. The OI values of the Lena image by FBEEMD and other classical methods are shown in the Table 1.
As the Table 1 shown, FBEEMD can reduce the OI effectively, which improve the traditonal BEMD method. Although the gross consuming time is a little longer than others, the average time of each BEMD trial is only about 3.6 seconds. Therefore, from the experimental results, it proves that our FBEEMD algorithm cannot only yield a better image representation, but also can resolve the major drawback, which is too much consuming time.
FBEEMD is adopted to decompose face images under different illumination conditions into a set of BIMFs. Only 3 BIMFs are shown in Fig. 5, including BIMF2, BIMF3 and BIMF4.
4. Illumination-reflectance model
The theoretical foundation of the majority of existing photometric normalization techniques can be linked to the Retinex theory developed and presented by Land and McCann in . The theory tries to explain the basic principles governing the process of image formation and states that an image I(x,y) can be modeled as the product of the reflectance R(x,y) and luminance functions L(x,y):
The nature of L(x,y) is determined by the lighting source, while R(x,y) is determined by the characteristic of the surface of object. Therefore, which R(x,y) can be regarded as illumination insensitive measure. In general, a common assumption indicates that L(x,y) varies slowly corresponding to skin, background and some other large-scale features while R(x,y) can change abruptly matching edges, corners or some other small-scale features on face images.
Taking logarithm transform for Eq. (3), we can get
This is to transform the product of illumination-reflectance model into a sum of two components that are low-pass and high-pass respectively. Then, FBEEMD is performed to separate these components into a set of multi-scale BIMFs. And then effective BIMF components will be fused together as illumination invariant feature of face. In next section, we will propose two measurements to calculate weights for quantifying the detail feature contained in these BIMFs.
5. Fusion of multi-scale detail features
5.1 A computing framework
It is a difficult task to avoid the interference from illumination since detail information with high frequency and illumination variation in different conditions are embedded in a face image closely. FBEEMD can separate face image into several BIMFs according to local features. However, it is hard to master clearly that which detail information in those BIMFs can depict a face better.
Therefore, it is considered to propose a computing framework to fuse essential detail features extracted from BIMFs. At first, a set of BIMFs are obtained by FBEEMD. Then, weights of each BIMF will be calculated with certain measurements. At last, those BIMFs with effective features will be fused together to reconstruct an illumination-invariant face. The computing framework can be expressed as follows:
It is assumed that there exist two images I and I’ needed to measure feature distance. Through FBEEMD, one can obtain two sets of BIMFs respectively: I1, I2,…,In and I’1, I’2,…,I’n. di is feature distance between Ii and I’i.
With a certain measurement, the value for quantifying detail information in each BIMF can be obtained: MI1, MI2,…,MIn and MI’1, MI’2,…,MI’n, where M stands for an operator of information extraction. Therefore, the value λi can be computed as follows:
5.2 The measurement for quantifying information of detail feature
Two measurements for quantifying detail information will be proposed in this section.
5.2.1 The number of extreme points in each BIMF
The BIMFs contain a large number of edge curves depicting contour feature. The more these curves are, the more detailedly essential features are described. The edge curves are a series of extreme points distributed continuously in local area of gray-scale image.
The fine-scale BIMFs contain much more extreme points than the large-scale ones. The total number of extreme points EPk in a BIMF can be considered as a criterion for quantifying detail information. The formula can be expressed as follows:Figure 6 is plotted based on 100 images and shows that the value EPk of BIMFs from 1 to 6 orders changes as the value k.
5.2.2 The sum of contrast ratio in each BIMF
Contrast ratio can be defined as difference between disparate pixels. It is apparent that the larger the difference is, the easier it is for human eyes to distinguish and then the more information the image contains. One can obtain a set of multi-scale BIMFs through FBEEMD. Fine-scale BIMFs have larger contrast ratio for they contains more detail information while large-scale BIMFs have smaller contrast ratio with less detail information. Therefore, the sum of local contrast ratio (CVk) can be a measure criterion to quantify detail information contained in a BIMF:Figure 7 is plotted based on 100 images and shows that the value CVk of BIMFs from 1 to 6 orders changes as the value k.
5.2.3 The measurements based on the weights of computing framework
It can be observed in Fig. 6 and Fig. 7 that these two values decrease monotonously as the decomposition order increases. Without any external parameters, these values are calculated by BIMF’s own features adaptively. It cannot be proved whether the above two methods can precisely quantify detail information. But a huge number of experiments show that these values can reflect a relative value of detailed information quantity between different images. Therefore EPk and CVk are adopted in fusion computing framework.
One can obtain the values EPi and EP’i, CV’i and CV’i respectively by using EPk and CVk to quantify detail information in the i-th BIMF I and I’. One can also obtain two types of schemes to compute weights of framework after putting these four values into Eq. (5).
6. Experiments and analysis
There are many methods proposed to eliminate interference from illumination variation. We choose only three of them compared with ours: SQI , LOG-DCT , BEMD . The images are recognized by PCA, after normalizing the illuminated image by using each of four schemes. At last, we will arrange an experiment to test the performance of our de-illumination method under four different face-recognition algorithms.
All these experiments are evaluated based on Yale B , PIE , and FERET  databases respectively. All the faces images are cropped to remove the background and the hair. We use only the frontally illuminated images as the training and testing samples.
6.1 Reconstructing illumination-invariant face images
A typical example will be used to present the performance of our scheme in eliminating illumination variations of five face images under disparate illumination conditions.
In our scheme, we firstly take logarithm transform to transform a face image into a sum of two components that are low-pass and high-pass respectively. Then, FBEEMD is performed to separate these components into a set of multi-scale BIMFs. Thirdly three effective BIMFs will be fused together as illumination-invariant feature of face, where any image under good illumination is used as reference image for measuring feature distance. At last, an illumination-invariant face will be reconstructed as the input of recognition algorithms.
Figure 8 shows example images under different illumination conditions. The original images are in upper row and the corresponding processed images are in lower row. It can be observed from the upper row that there are large changes in illumination, which may have a greater effect on recognition rates than individuals. After de-illumination, the corresponding illumination-neutral faces are obtained in the lower row. The recognition rates will be enhanced greatly with this kind of processed face images.
6.2 Experiments based on Yale B face database
9 different poses of 10 individuals are presented in the Yale B database. 64 different illumination conditions exist for each pose. We use 64 frontal facial images to evaluate 4 illumination compensation methods. The database with 640 images can be divided into five subsets according to illumination angle: subset-1(0°-12°), subset-2(13°-25°), subset-3(26°-50°), subset-4(51°-77°), subset-5(≥78°). The image number of five subsets is: 70, 120, 120, 140 and 190.
The first experiment: use the subset-1 (70 images) with the best illumination condition as training sample and use the other 570 facial images as test samples. The recognition rates using four methods are compared in Fig. 9.
The second experiment: use the subset-4 (140 images) with the worst illumination condition as training sample and use the other 500 facial images as test samples. The recognition rates using four methods are compared in Fig. 10.
The third experiment: use a facial image of each person in the subset-1 (10 images) as training sample and use the other 630 facial images as test samples. The recognition rates using four methods are compared in Fig. 11.
6.3 Experiments based on PIE face database
PIE is another database that is often used for studies of illumination variations. The database consists of 68 individuals (28 wearing glasses) at 3 poses (frontal, side and profile) under illumination from 21 different directions and ambient light only. We only use illumination subset (C27) as experiment data. This subset has 21 facial images of each individual under different illumination conditions. The experiment uses a face image of each person (68 images) as training sample and uses the other 1380 facial images as test samples. The recognition rates using four methods are compared in Fig. 12.
6.4 Experiments based on training sample of variable size
We will implement a comparative experiment: Training sample sets vary in size from 2 to 10. Each experiment involved training using the specified training set, recognition, and recording rates. For PCA nine experiments are run with the same four de-illumination methods: SQI , LOG-DCT , BEMD  and ours. Performance is quantified by recognition rate over all experiments. The recognition rates for different recognition methods are presented in Fig.13.
6.5 Experiments using different recognition algorithms based on FERET face database
The FERET database is one of the most famous databases for the evaluation of face recognition algorithms all frontal face images are divided into five categories: fa, fb, fc, dup1 and dup2. Fa images and fc images were taken under different illumination conditions. As we are only concerned with the illumination problem, 1196 fa images are used as gallery and 194 fc images are used as test set.
We will make a comparison experiment based on FERET database in order to present the performance of our compensation method on four different classical recognition algorithms (such as PCA [4, 5], LDA , LFA  and EBGM ). Through the proposed method, 1390 illumination-neutral faces images will be obtained as the input of four algorithms. The results of recognition rates are shown in Fig. 14.
It can be concluded through the above experiments that the performance of the de-illumination method proposed in this paper is prior to other three classical approaches. With our method, the recognition rate is improved obviously in small training sample experiments such as experiement#3 based on Yale B, experiment based on PIE and experiment based on training sample of variable size. Moreover, the last experiment shows that our pre-processing scheme can be applied to other classic recognition algorithms to avoid mistaken recognition efficiently.
Components with high frequency corresponding to face detail information can be considered as illumination-invariant feature for they are not affected by illumination changes so much. FBEEMD can efficiently decompose a facial image into multi-scale BIMFs, each of which contains detail features with disparate quantity and frequency. A fusion computation framework has been proposed to extract effective BIMFs. At the same time, two adaptive measurements without any external parameters are proposed to quantify detail information and then calculate fusion weights. A number of experiments are conducted to demonstrate that the proposed method is efficient. Moreover, the scheme can also be applied in many optical fields to eliminate the illumination components or DC background.
The authors are grateful for the research support received from the National High Technology Research and Development Program of China (863 Program No. 2012AA040106) and the National Natural Science Foundation of China (NSFC No. 10972137).
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