*6.3. Comparison of Di*ff*erent Methods*

In order to further evaluate the proposed local coding method, here we compare it with some common feature extraction methods (LBP [16], GLBP [20], LLBP [17], SLGS [23], and MOW-LGS [24]). The ROCs are plotted in Figure 15, and the simulation results are listed in Table 4.

**Figure 15.** Comparisons of different methods.

**Table 4.** Comparisons on EER (%) and time cost (single individual).


From Figure 15, we observe that the EER of the proposed approach is lowest among these feature extraction methods. Hence, feature expression based on the proposed coding approach can effectively address the problem of illumination and finger posture variation in finger trimodal fusion recognition.

From Table 4, we can clearly see that the proposed local coding algorithm not only produces the best recognition accuracy, and also that the computation cost of feature extraction is also lowest as compared with other methods. This shows that our method is more robust to finger feature representation.

#### **7. Conclusions**

In this paper, a posture correction approach was first designed for reducing the finger pose variation. To solve the problem that the feature expression method was sensitive to illumination variation and posture rotation, a novel local coding algorithm was proposed for finger trimodal fusion recognition. On the one hand, the Gabor filter, to some extent, can effectively reduce the influence of illumination and noise in an image. On the other hand, the posture correction method and the local coding method were used to address the problem of finger posture variation. The proposed Gabor-GSLGS algorithm made full use of the texture features in multiple orientations between surrounding pixels. Furthermore, the proposed method assigned the same weights in symmetrical pixels, which improved the equilibrium

of the feature representation of the finger images. The experimental results showed that our method could improve the accuracy and computational efficiency of finger trimodal fusion recognition.

As part of our future work, we will apply the proposed local coding algorithm to other public biometric databases. Moreover, we will focus on reducing the dimensions of the feature vector and improving the efficiency of finger multimodal fusion recognition. At the same time, we will aim to exploit a more robust and effective fusion method which can integrate multiple modal features for personal identification.

**Author Contributions:** S.L. and H.Z. conceived and designed the experiments; S.L. performed the experiments and analyzed the data; S.L., H.Z., Y.S. and J.Y. wrote the paper.

**Funding:** This work is supported by the National Natural Science Foundation of China (No. 61806208, No. 61502498) and the Fundamental Research Funds for the Central Universities (NO. 3122017001).

**Conflicts of Interest:** The authors declare no conflict of interest.
