Despite the recent advances in finger-vein biometric recognition, it is still a challenging task in practical application since vein-capturing results are easily affected by many factors, such as illumination, environment temperature, and the behavior of the user. These factors cannot avoid during the capturing process, in this case, the training dataset may contain a large number of low-quality finger-vein images, which may decrease the recognition accuracy. To achieve robust recognition, various approaches are proposed for vein recognition in recent years and are broadly categorized into the following categories (Hou et al., 2022; Shaheed et al., 2022b).

(1) Local descriptor-based approaches: Local descriptor-based approaches mainly consist of local statistical information-based methods and local invariant-based methods. Local statistical information-based methods include local binary pattern (LBP) (Lee et al., 2010, 2011; Yang et al., 2014; Kang et al., 2015), local line binary pattern (LLBP) (Rosdi et al., 2011; Yang et al., 2013), efficient local binary pattern (ELBP) (Liu and Kim, 2016), discriminative binary codes (DBC) (Xi et al., 2016), and fuzzy images (Qin et al., 2022). A typical representation of local invariant-based methods is the scale-invariant feature transform (SIFT) (Qin et al., 2013; Wang et al., 2015).

(2) Superpixel-based feature extraction approach: The representative approaches in this category are the superpixel-based feature (Liu et al., 2014), vein textons map (Dong et al., 2014), hyper information feature (Xi et al., 2014), and personalized feature (Xi et al., 2013). Superpixel-based feature extraction methods have achieved a high recognition rate in some public databases (Kirchgasser et al., 2020).

(3) Subspace-learning-based approaches: Subspace learning as a powerful technique have been widely used in pattern recognition task such as vein identification. A projection matrix computed from training data is employed to map the finger-vein images into subspace, and the resulting features are further used for recognition. The typical methods include principal component analysis (PCA) (Wu and Liu, 2011a), two dimensional principal component analysis (2DPCA) (Qiu et al., 2016), two-directional and two-dimensional principal component analysis ((2D)2PCA) (Yang et al., 2012; Li et al., 2017; Zhang et al., 2021; Ban et al., 2022; She et al., 2022), linear discriminant analysis (LDA) (Wu and Liu, 2011b), high-dimensional state space (Zhang et al., 2022), self-feature-based method (Xie et al., 2022), and latent factor model (Wu et al., 2022).

(4) Deep learning-based approaches: The deep learning-based approaches have been directly used to learn robust features from original images and successfully applied for computation vision tasks. Some researchers brought them into finger-vein recognition. For example, deep learning approaches are employed for vein image segmentation (Liskowski and Krawiec, 2016; Qin et al., 2019; Yang et al., 2019; Shaheed et al., 2022a), quality assessment of vein image (Qin and Yacoubi, 2015; Qin and El-Yacoubi, 2018), fuzzy networks (Liu H. et al., 2022; Lu et al., 2022; Muthusamy and Rakkimuthu, 2022), and finger-vein recognition (Wang et al., 2017; Avci et al., 2019; Gumusbas et al., 2019; Zhang J. et al., 2019).

As discussed in the related works, the handcrafted-based approaches are proposed based on prior human knowledge, some vein features related to recognition may be missed during the feature extraction process. On the contrary, the deep learning-based extraction approaches without any prior assumption can automatically extract high-level features by representation learning that are objectively related to vein recognition. The deep learning-based extraction approach takes the original image pixels as input and iterative uncovers hierarchical features. In this way, the decision errors on recognition are minimized. The need for voids is explicitly extracting some image processing-based features that might discard relevant information about image classification. Therefore, the deep learning-based approaches are capable of extracting more complete vein features for recognition, compared to handcrafted approaches. Currently, deep learning-based methods, such as deep neural networks, show high recognition performance because they harness rich prior knowledge acquired by training them on a huge training dataset. However, in finger-vein recognition, it is impossible to capture a lot of vein samples from the same finger, so the training sample of each class is generally limited. For example, the samples from each finger are < 12 in existing databases (Miura et al., 2004, 2007; Das et al., 2019). Especially, there is only one single sample per finger for single sample per person (SSPP) problem when considering their limited storage and privacy policy. Therefore, it becomes particularly intractable for such an identification system with SSPP when within-class information is not available to predict the unknown variations in query samples. Currently, various approaches have been proposed for biometrics identification with SSPP such as face (Wu and Deng, 2016; Wang et al., 2018), palmprint (Shao and Zhong, 2021), and fingerprint (Chatterjee et al., 2017). Similarly, the corresponding finger-vein recognition systems still suffer from the SSPP problem due to the following facts: 1) There is only one enrollment sample in some recognition systems, such as credit card and large-scale recognition, because of the limitation of storage capability. 2) To achieve online identification, the recognition systems usually store one sample per subject to improve processing speed and time. 3) Some users are not willing to cooperatively capture sufficient samples for their personal privacy. Providing one enrollment sample is convenient, simple, and acceptable for users.

As described in previous works, deep learning techniques show a powerful capacity for feature representation, but they generally require sufficient training samples to train a large number of network parameters. Therefore, their learning capacity may have not been well exploited for finger-vein SSPP due to the limited training data of each class (a person or subject) for SSPP. Besides, the deep learning model is easy to suffer from over-fitting on a small amount of dataset. As a result, deep learning-based vein identification approaches may not achieve high performance for finger-vein SSPP.

Ensemble learning aims at combining multiple learners to obtain a more robust representation of the object and is successfully applied for vision tasks such as SAR image category (Zhao et al., 2016), fault diagnosis (Liu et al., 2021), image cluster (Tsai et al., 2014), and human activity recognition (Jethanandani et al., 2020). In addition, some researchers applied it to biometrics, e.g., classification tasks such as fingerprint classification (Zhang et al., 2011b), palm-vein recognition (Joardar et al., 2017), and face recognition (Bhatt et al., 2014; Ding and Tao, 2018). As the features from different learners can achieve a complementary representation for the input image, their combination performs well for identification. To extract enough features from a single finger-vein training sample, in this article, we further research our work on Liu C. et al. (2022) and proposed a deep ensemble learning approach for finger-vein identification.

The rest of the paper is organized as follows. The methodology and significant contributions are listed in Section 2. In Section 3, the proposed method is described in detail. The contract experiment and the results are reported in Section 4. In Section 5, the full research work is concluded for easy reading.

To achieve robust performance in the SSPP problem, it is necessary to generate multiple feature maps from the single training sample of each class. The feature maps represent different aspects of the object (Felzenszwalb et al., 2010), so their combination can achieve better performance (Li et al., 2018). Here, three baselines (e.g., CNN Das et al., 2019, Gabor filters Zhang et al., 2019a, and LBP Kang et al., 2015) have achieved promising performance for finger-vein recognition, so we employ them to produce feature maps, which are taken as the input of ensemble model for classification.

The ensemble learning model is constructed from the combination of weak classifiers (Sagi and Rokach, 2018). The choice of a weak classifier affects the performance of the ensemble model. In previous work, CNNs were widely used in finger vein recognition and achieved good recognition performance, such as Wang et al. (2017), Gumusbas et al. (2019), Avci et al. (2019), Gumusbas et al. (2019), and Zhang J. et al. (2019). In this article, we choose the CNN model as the independent weak classifier, and each CNN is trained by one feature map, as shown in Figure 1. Each trained CNN model describes one aspect of the finger vein.

Convolutional neural network is a multi-layer perception network with hidden layers. A traditional recognition model for a classifier can be formulated by minimizing the error function. During training a deep network, the gradient descent method is used to update network parameters. The details of the network structure are shown in Tables 2, 3.

In each CNN, the parameters, such as the number of layers and size of the kernel, are different for the different classifiers. In general, the closer relative classifiers have more same parameters. The first feature map and the second feature map are basic features to generate the third feature map, the fourth feature map, the fifth feature map, and the sixth feature map, and a convolutional neural network (CNN) with five layers are employed to extract their feature. As listed in Table 2, the CNN consists of three convolutional layers of 64 kernels with the size of 2 × 2, a convolutional layer of 128 kernels with the size of 2 × 2, and a convolutional layer of 256 kernels with the size of 5 × 5. For the remaining four classifiers, we employ a CNN with six convolutional layers for feature extraction, as shown in Table 3. Specifically, there are 64 kernels with the size of 2 × 2 in the first three convolutional layers and 128 kernels with the size of 2 × 2 in the fourth convolutional layer. The last two convolutional layers include 128 kernels with the size of 5 × 5 and 256 kernels with the size of 5 × 5, respectively. Combing all classifiers, we built an ensemble learning model to identify a subject with a single training sample.

If the feature maps are correlative, we can utilize the knowledge from other weak classifiers to improve the current classifier (Lou et al., 2017). In general, features with higher correlation provides more positive knowledge, which results in the improvement of the weak classifier. So, to achieve the best-shared representations, we compute the similarity among feature maps, which determines the result of shared learning.

During training weak classifiers, the learning speeds of classifiers are different, because the input data are different. When all weak classifiers achieve their best performance, the ensemble model is best. We propose a learning speed adjustment method to control the learning speeds of weak classifiers. The parameter α is used to adjust the learning speed of each classifier. The whole training process is divided into K steps and P epochs in each step. The total number of epochs R is as follows:

The parameter α_{i, u} is used to adjust the number of epochs dynamically for classifier_i of train step u. When the classifier had achieved well performance, the number of epochs will decrease in the next step. The α_{i, u} is computed as follows:

Where the L_{i, u−1} is the loss function value after train step u−1. To ensure the program runs smoothly, a round down is used to ensure the epoch time is an integer and more than 0. So, the number of epochs p_{i, u} for train step u of classifier_i is as follows:

There are two problems during ensemble weak classifiers: (1) How to enhance good weak classifiers while weakening poor weak classifiers; (2) How to make all weak classifiers perform best at the same time. The second problem has been discussed in the previous subsection, in this subsection, we discuss the first problem. To tackle the first problem, an access weight can be set to increase the weight of a good classifier and decrease the weight of the pool classifier. The E⁺ is computed as

where Score_{i, u} is the close test accuracy of each classifier_i after train step u. The E⁻ is computed as

where L_{i, u} is the loss function value after train step u.The ensemble weight W after train step u is updated as follows:

where K is the number of classifiers. The ensemble weight W is updated after each training step. Considering the efficiency of the ensemble model, if the classifier plays poor performance, this classifier could not join the ensemble step. In our model, we use the close test of classifiers to measure their efficiency; if the close test scores more than 0.5, this classifier will join the ensemble step and vice versa.

Three different approaches are proposed in this article.

In this article, we conduct experiments on the HKPU database and FV-USM database.

HKPU database: The HKPU finger-vein image database (Kumar and Zhou, 2012) consists of images from 156 male and female volunteers. It has been acquired between April 2009 and March 2010 using a contactless imaging device at the HKPU campus. It is composed of 3,132 images from 156 subjects, all of them in a BMP format with a resolution of 513 × 256 pixels. In this dataset, about 93% of the subjects are younger than 30 years, and finger-vein images from 105 subjects have been acquired in two separate sessions with a minimum interval of 1 month and a maximum of over 6 months, with an average of 66.8 days. In each session, every subject has provided 6 image samples from the index and middle finger of the left hand. Other 51 subjects have one single session of acquired data. In the experiment, 2,520 images (105 subjects × 2 fingers × 2 sessions × 6 samples) from two separate sessions are employed to test our approach.

FV-USM database: The FV-USM database (Asaari et al., 2014) is from University Sains Malaysia. It consists of left and right-hand index and middle fingers' vein images from 123 subjects. Among them, 83 are male and 40 are female, with an age range of 20 − 52 years. All images have been acquired in two different sessions with six images per finger in every session. There are 2,952 images (123 subjects × 2 fingers × 2 sessions × 6 samples) All images are in gray level BMP format with a resolution of 640 × 480 pixels.

The details of both datasets are described in Table 4.

We aim at solving the finger-vein SSPP problem, so the first image from the first session is selected for training and the three images from the second session are employed for testing. As a result, there are 210 samples in the training set and 630 samples (1,260 fingers × 6 samples) in the test set for the HKPU database. Similarly, there are 246 training samples and 1,476 samples (246 fingers × 6 samples) for the FV-USM database. We train our model on the training set and compute the identification accuracy on the test set to estimate the performance of the proposed method.

In our article, the six feature maps are generated by three baselines (e.g., LBP, Gabor, and CNN), as shown in Table 1, and their parameters are determined based on setting in existing works (Kang et al., 2015; Qin and El-Yacoubi, 2017; Zhang et al., 2019a). For LBP descriptors, the radius is set to 1 which implies that only the one layer around the center pixel and eight pixels around the center pixel are taken into account for the feature's next action. The second baseline e.g., Gabor filter has six scales, namely 7, 9, 11, 13, 15, and 17, the wavelength λ is determined by π/2, and the directions θ are set to 0^o, 45^o, 90^o, and 135^o. For CNN, the network structures and parameters are presented in Tables 2, 3.

In this section, we carry out experiments to verify whether the shared learning scheme improves identification accuracy. As described in Section 3, we proposed a shared learning scheme to learn the knowledge among different feature maps, as shown in Figure 6. Generally, if two feature maps are more relative, the performances of both feature maps are improved by the shared learning scheme. In our article, the similarity/relativity between two feature maps is computed by Equation (9) and further taken as an input of Equation (10) to compute the iteration number of shared learning. As shown in Table 5, the first feature map is highly related to the second feature map, the third feature map, and the fourth feature map on both datasets based on Equation (9). Then, the numbers of interaction steps for there relative shared learning are determined to 4, 1, and 2 by Equation (10), respectively. To achieve shared learning, we employ the second feature map to fine-tune the CNN trained by the first feature map at in four steps, and the resulting CNN model is further trained based on the third feature map, followed by the fourth feature map. In this way, the remaining classifiers are trained for identification. In experiments, we test the six classifiers on both databases mentioned in Section 4.2. For example, there are 210 samples from 210 fingers in the training set and 1,260 samples in the testing set for the HKPU database, and 492 training samples and 2,952 testing samples for the FV-USM database. The identification accuracies of six classifiers with shared learning are listed in Table 6. Also, the performance of each classifier without shared learning is reported in Table 6 for comparison. From the experimental results, we observe that the performance of all classifiers is significantly improved after shared learning. Specifically, the identification accuracy increases by an average of 2% for all weak classifiers, which implies that learning knowledge from other relative feature maps by our shared learning approach can improve the performance of the current classifier. This may be explained by the following facts. Using different features to train weak classifiers can transfer to form a more complementary representation of the original finger-vein image.

The experiment also shows the relation between relativity and performance, as shown in Table 5. The experimental results show that the higher relativity between the two classifiers brings more improvement in identification accuracy. For example, the first feature map achieves the largest improvement in identification performance by transferring the knowledge of the second feature map which has the highest relativity with the first feature map. On the contrary, less improvement is achieved based on the shared learning between the first feature map and the third feature map because the third feature map shows less similarity to the first feature map. The good performance attributes to the fact that the knowledge is easier to be transferred if multiple feature maps have good relativity.

As described in the subsection, our approach is proposed by combining six weak classifiers. In general, the learning speed of each classifier is different. Therefore, the object task can achieve the highest identification accuracy only if each classifier achieves optimal performance at the same time. In this section, the experiments are carried out to evaluate how to impact the performance of object tasks by employing Equation (12) and Equation (13) to adjust the learning speed of each classifier. Figures 11A, B show the identification accuracy of six classifiers and our approach to the HKPU database before and after adjusting the learning speed. In Figure 11A, the performance of all approaches is improved when the number of iteration steps is < 30. However, two classifiers achieve significant degradation in identification accuracy after 35 iterations. The reason is that the two classifiers have higher speed than the remaining classifiers so they cannot achieve optimal performance at the same time. Therefore, it is difficult for object tasks to achieve good performance. In contrast, the learning speed of all weak classifiers is adjusted dynamically, they show the best performance after about 50 iterations (as shown in Figure 11B), which brings the improvement of the objection classifier. Therefore, our approach achieves higher identification accuracy after employing Equation (12) and Equation (13) for learning speed adjustment. The experiments on FV-USM (as shown in Figures 11C, D) show consistent trends that all weak classifiers can achieve optimal performance at the same time (about 40 iterations). In addition, observed training curves (Figures 11A–D), we see that all approaches show good stability after employing the learning speed adjustment scheme.

Table 7 lists the identification accuracy of the basic model, basic approach + shared learning, basic approach + speed adjustment, and basic approach + shared learning + speed adjustment on the HKPU database and FV-USM database. The experimental results have shown that the basic model and basic approach + shared learning achieve a significant improvement in identification accuracy after adjusting learning speed by Equation (13). For example, the basic approach + shared learning and basic approach + shared learning + learning speed adjustment achieve 82.60% and 92.10% identification accuracy on HKPU database and FV-USM database, respectively, and improves identification accuracy by about 7% and 1% compared to basic approach + shared learning. The experimental results in Table 7 imply that our learning speed adjustment scheme is effective to improve the performance of object tasks for an ensemble learning problem.

In this section, we compare our approach with existing approaches to evaluate the performance of our method in terms of improving identification accuracy. In experiments, state-of-art methods, such as Das et al. (2019), Kumar and Zhou (2012), and Song et al. (2011), are employed for finger-vein identification with a single training sample per finger. As described in the section, we select the first image for training and six images collected in the second session for testing. As a result, there are 210 training samples and 1,260 testing samples for the FV-USM database and 496 training samples and 2,952 testing sample for the FV-USM database. The identification accuracies of various approaches have been listed in Table 8 for comparison. From the experimental results, we can observe that the proposed approach (basic approach + shared learning + learning speed adjustment) outperforms the existing approaches and achieves the highest identification accuracy, e.g., 92.11 and 94.17% on the HKPU database and FV-USM database, respectively. Also, we observed that the hand-crafted approaches (Song et al., 2011; Kumar and Zhou, 2012; Qin et al., 2013), considered our work achieve < 91.00% identification accuracy on both databases. Such a poor performance may be attributed following facts: (1) The handcrafted segmentation-based approaches assume that the cross-sectional profile of a vein pattern shows a valley (Miura et al., 2007) or line-like texture (Miura et al., 2004) and proposed various mathematical models to extract vein patterns. However, the vein pixels create more complex distributions instead of the valley or straight lines and the pixels in the non-vein region also show valley or line-like attributes, so their performance is limited. (2) The handcrafted segmentation-based approaches usually match vein networks stored in testing samples and enrolment samples for identification. Therefore, it is difficult for such a matching scheme to achieve good performance when there are larger variations such as rotation, scaling, and translation between two images. Compared to handcrafted segmentation-based approaches, the deep learning-based approach (Qin and El-Yacoubi, 2017) is capable of extracting robust vein networks from a law image because it harnesses rich prior knowledge from huge training samples without any assumption. Therefore, the deep learning-based approach (Qin and El-Yacoubi, 2017) achieves better performance, e.g., 91.75 and 92.29%, identification accuracies on both databases. Similarly, its matching scheme is not robust for image samples with large rotation and translation variations. As a solution, a convolutional neural network (Das et al., 2019) is proposed to extract high-level features instead of a vein network by representation learning that is objectively related to vein identification and achieves promising performance. However, it does not perform well for the SSPP problem. This is explained by the following facts. Deep learning-based approaches generally require a large number of training samples to estimate a usually huge number of deep network parameters. In the SSPP configuration, there is only one training sample for each class, so the learning capacity becomes weak and subject to string overfitting, which leads to low identification performance. Ensemble learning is a solution to the SSPP problem because it can exploit the knowledge from different feature maps to improve identification accuracy. Therefore, our basic approach + shared learning achieves 85.63 and 92.31% accuracies on both datasets, which are further improved to 92.11 and 94.17% by adjusting the learning speed of all weak classifiers. Such a good performance may be attributed to these facts. Each classifier includes different discriminate features. As shown in Table 5, the relative feature maps can make a positive contribution to classification, so the knowledge related to classification is transferred among feature maps by shared learning, which effectively improves the feature representation capacity of object tasks. Meanwhile, the learning speed adjustment ensures each classifier achieves the best performance at the same time so that the object task performs the best representation for vein identification.