**6. Experimental Results**

In order to verify the proposed coding-based method, a finger trimodal database from a homemade image acquisition system is used in our experiments. The database contains a total of 17,550 images from 585 individual fingers (index finger, middle finger, and ring finger) of both hands, and each finger contains 30 images (10 images per modality). Here, we randomly select 3000 images samples from 100 different individuals, each of which, respectively, contains 10 images on the FP, FV, and FKP traits, as the experimental database.

Here, the proposed Gabor-GSLGS algorithm is implemented using MATLAB R2014a on a standard desktop PC which is equipped with Inter Core i5-7400 CPU 3 GHz and 8 GB RAM.

The detailed experiments are as follows: In Section 6.1, we mainly describe the analysis of the influence of different parameter selection on the recognition rate. Section 6.2 presents the detailed comparison of the performance of unimodal and multimodal recognition. The experimental results of different feature extraction methods are compared in Section 6.3.

#### *6.1. Parameter Selection*

#### 6.1.1. Selection of *k*

On the basis of the above introduction in Sections 3 and 4, we can see that the number of orientations in the local coding algorithm corresponds to the number of channels in the Gabor filter. Hence, different *k* values produce different effects on the performance of the finger multimodal recognition. In order to find the optimal parameters of *k*, we evaluate it using two recognition indicators, equal error rate (EER) and the time cost of feature extraction. EER listed in Table 1 is the error rate where FRR and FAR are equal. Here, FAR indicates the identification result of incorrect acceptation for an individual, while FRR demonstrates the result of incorrect rejection. The ROC (receiver operating characteristic) curves for intersection coefficient measures are plotted in Figure 11, where FAR and FRR are shown in the same plot at different thresholds.

**Table 1.** Comparisons on equal error rate (EER) (%) and time cost (single individual).

**Figure 11.** Receiver operating characteristic (ROC) of different *k*.

From Figure 11, we can see that the EER is lowest when *k* is 6. However, as the value of *k* increases, the time cost of finger feature extraction also increases. Considering recognition efficiency and accuracy, the parameter *k* corresponding to 6 is selected in following experiments.

#### 6.1.2. Selection of Neighborhood and Image Division

Apart from parameters *k*, the size of the neighborhood *n* × *n* that constitutes the structure of the GSLGS operator and the number of image division blocks *M* are also critical factors for finger trimodal recognition. Considering that *n* and *M* have a great influence on the recognition performance of the proposed algorithm, therefore, it is important to select suitable parameters. Here, we select different neighborhoods and image block sizes to perform the experiments. Some EERs of different parameters are listed in Table 2, with some ROCs shown in Figures 12 and 13.

**Table 2.** Comparisons on EER(%) for different parameters.

**Figure 12.** ROC of different neighborhoods in *M* = 6, 7, 8, 9.

**Figure 13.** ROC of different division blocks *M* in a 5 × 5 neighborhood.

From Figure 12, it can be clearly seen that the ROC curves vary by changing *n* (*n* = 3, 5 or 7, respectively). This shows that different neighborhoods have different effects on the performance of finger trimodal recognition. By observing these obtained curves in the condition of the same image division block, such as *M* = 6, we find that the EER is lowest when the size of the neighborhood is selected as 5 × 5 (*n* = 5). Similarly, when *M* = 7, 8 or 9, respectively, the pixels selected in a 5 × 5 neighborhood for constructing the GSLGS operator also have optimal accuracy. The reason is that a 3 × 3 neighborhood is more sensitive to noise, while the 7 × 7 neighborhood is relatively weak in the capability of feature expression. However, the 5 × 5 neighborhood is preferred for feature expression among surrounding pixels and is insensitive to noise. Hence, *n* = 5 is the optimal parameter for constructing the proposed GSLGS operator.

The experimental results of different division blocks by using GSLGS with a 5 × 5 neighborhood are shown in Figure 13. From Figure 13, we can find that the proposed local coding algorithm obtains the best accuracy when the number of division blocks is 8 × 8 (*M* = 8). This shows that an appropriate image division scheme is beneficial for improving recognition accuracy rate. Hence, the image division blocks *M* = 8 is an optimal choice for the proposed Gabor-GSLGS approach in finger trimodal recognition.

#### *6.2. Comparison of Unimodal and Multimodal*

The proposed local coding algorithm of finger trimodal can also be applied for finger single modal recognition. Here, the experiments of finger unimodal and multimodal recognition are performed when *n* = 5 and *M* = 8. The experimental results of different modal combinations are listed in Table 3.


**Table 3.** Comparisons on EER (%) and time cost (single individual).

From Figure 14, we can see that the EER rate of different modal combinations are different. It is noted that the bimodal combination (FV + FKP and FV + FP) can achieve a better accuracy than single modal, especially for the FP trait and FKP trait.

**Figure 14.** Comparison results of different modal combinations. (**a**) ROC of unimodal recognition; (**b**) ROC of multimodal recognition.

From Table 3, we can find that three modal combination have the best recognition accuracy, while the time cost increases with the increase of the modality number. It is noteworthy that in single modal recognition, FV trait performs better than FP trait and FKP trait. This shows that the FV trait is the most dominant trait in the three modalities.

In total, these results show that multimodal fusion recognition performs better than single modal. The reason is that the multimodal combination can make full use of the discrimination of different modalities and different modalities can complement each other in multimodal fusion recognition. However, the computational efficiency of multimodal recognition can still be improved.
