**1. Introduction**

With the arrival of the informational age and the rapid development of computer technology, people have higher requirements for the accuracy of biometric identification technology [1]. Compared with other common biometric traits, finger-based traits (e.g., fingerprint [2], finger-vein [3] and finger-knuckle-print [4],) have some advantages in uniqueness, anti-counterfeit, user acceptance, and high security [5–8]. However, affected by the external environment and the inherent differences of individuals, only relying on finger unimodal biometrics for identity authentication still has many security risks, which can no longer achieve the high-performance requirements of a user. Hence, fusing three traits from a finger together should be beneficial to address the person recognition problem [9,10].

However, the quality of three modal finger images is usually degraded seriously due to illumination variation in skin surfaces, which is unhelpful for reliable feature representation [11–13]. In addition, the finger trimodal images vary with the finger in pose rotation during imaging, which reduces the discriminability of images and further decreases the recognition accuracy rate. Therefore, exploring a robust feature representation method is very favorable for finger-based recognition improvement.

Recently, some researchers have developed some coding-based feature expression methods, which were often considered to be able to solve the above two problems [14–21]. Ojala et al. first proposed the classical local binary pattern (LBP) algorithm for facial recognition, which has great rotation invariant and was insensitive to illumination variation [16]. In 2011, Rosdi et al. proposed a local line binary pattern (LLBP) algorithm to effectively make use of the position relationships among surrounding pixels in horizontal and vertical orientations [17]. Meng et al. [19] proposed a local direction coding

(LDC) algorithm, which utilized the gradient relationships to express a venous feature for finger-vein recognition. In 2013, Peng et al. [20] combined the Gabor wavelet and LBP (GLBP) for feature extraction, which could effectively improve the ability of local and global features representation.

Noteworthy, some methods related to local graph have been presented in succession, and their variants have been successfully applied to many biometric fields [22–29]. Abusham et al. first proposed a local graph structure (LGS) algorithm to extract face features, which was insensitive to illumination [22]. However, the structure was non-symmetric, which led to a feature representation with no-equilibrium in the left and right neighborhoods. In order to balance feature representation of neighbor pixels on both sides, Mohd et al. [23] improved the original LGS operator to the SLGS operator by building a symmetrical structure. In 2015, Dong et al. [24] presented a MOW-SLGS operator for the representation of vein networks, and used the ELM to accomplish finger-vein image classification. On the basis of this information, in 2018, Yang et al. [25] put forward the Weber SLGS, which integrated differential direction features by Weber Law and the local graph structure algorithm. However, these algorithms still have some limitations in the application of representing finger multimodal features. On the one hand, the methods above only describe the relationships between the target pixel and its adjacent ones in a fixed neighborhood, while neglecting the hidden relationships among surrounding pixels. On the other hand, the assignment of different weights for symmetric pixels on left and right sides usually results in an imbalance of the feature expression in images.

To effectively overcome these limitations, we propose a Gabor generalized symmetric local graph structure (Gabor-GSLGS) for finger multimodal fusion recognition, as shown in Figure 1. In the image capture part, first, a finger imaging device is designed, and a pose correction algorithm is proposed to reduce pose variations. A robust finger region of interest (ROI) localization approach is then employed. Secondly, a bank of 6-orientation and single-scale Gabor filters are utilized for finger ROI image enhancement. Thirdly, based on the proposed GSLGS operator, a local coding algorithm is developed for finger features representation. The coded trimodal feature images of a finger are then divided evenly into non-overlapping blocks. Thus, for a finger, we can obtain a feature vector by concatenating the histograms of all blocks. Finally, by computing the similarities between the obtained vectors, the matching results can be reported statistically. Experimental results on our established database demonstrated that the proposed feature description approach exhibits better effects than other traditional approaches in finger multimodal fusion recognition.

**Figure 1.** Finger multimodal recognition process based on the Gabor generalized symmetric local graph structure (Gabor-GSLGS).

The reminder of this paper is organized as follows: The finger trimodal imaging device and the proposed posture correction are introduced in Section 2. The enhancement methods used for finger ROI images are described in Section 3. Section 4 details the structure of the proposed local coding algorithm. A feature matching scheme is employed to implement finger multimodal fusion recognition and described in Section 5. Section 6 outlines the extensive experiments conducted and presents the analysis of experimental results in details. Finally, Section 7 presents the summarization.
