## 1 Introduction  
Biometric recognition aims to distinguish individuals based on human physiological and behavioral characteristics and is widely applied in Internet-of-Things security [1], financial payment [2], and security systems [3], etc. A biometric system usually includes image acquisition [4], preprocessing [5], feature extraction [6], and matching [7], as shown in Figure 1. Due to the convenience of acquisition, finger-based biometric recognition methods have developed rapidly. With the increasing demand for accurate identity recognition in recent years, multimodal recognition methods have attracted wide attention [8; 9; 10]. Finger vein (FV) and inner knuckle print (IKP) are two modalities of the finger. FV is the tiny blood vessels inside the finger close to the cortex [11], and IKP is the pattern of the inner surface of the knuckle [12]. We use these two modalities to achieve identity recognition in this study.  
Figure 1: The architecture of the biometric recognition system.  
There are two main problems to be solved in designing an method based on multimodal biometric recognition: how to extract each modality's features and how to fuse multiple modalities' information.  
The traditional feature extraction of IKP and FV mainly relies on hand-designed schemes [13; 14; 15; 16; 17]. Although traditional feature-extraction methods can achieve good results from specific designs, they are complicated. To solve this problem, we use deep learning models for feature extraction. CNN is suitable for image feature extraction, as the model has a strong generalization ability after pretraining large-scale data. More importantly, the input images of the model do not require complicated preprocessing. We use the Inception-ResNet-v1 [18] model for feature extraction in this study. The experimental results show that the model can extract IKP and FV image features well. In addition, we introduce the triplet loss function [19] as the loss function to optimize the model. The function forces the feature representation distance of different sample images of the same person to be close and that of sample images of different people to be far away. It improves the expression ability of the fusion feature.  
Feature-level fusion is the mainstream method for multimodal fusion when using deep neural networks to extract image features [20; 21; 22; 23]. The feature dimension is large, and the operability space of fusion is strong. Some previous works only performed a simple concatenation operation on multimodal features [24; 25]. Such fusion method does not consider the features of different stages in the feature-extraction process, which will affect the final recognition performance. Multilevel feature fusion can better represent features. Therefore, we propose to fuse IKP and FV features at different scales and perform multilevel feature fusion. Given the difference between the two modalities, the method takes FV as the main task modality and IKP as the auxiliary task modality. In summary, our contributions are as follows:  
* We propose a Dual-Branch-Net network to extract the features of FV and IKP. The features of the FV branch at multiple levels of the network are fused with the corresponding features of the IKP branch, achieving deep fusion between the features of the FV and the IKP.
* We use transfer learning and triplet loss function to optimize the multimodal feature representation and perform identity recognition by measuring the similarity of feature vectors.
* We perform a series of experiments to verify that the recognition performance of our method is superior to both unimodal and other multimodal recognition methods.