# Finger-Vein Verification Based on LSTM Recurrent Neural Networks
## 4 Discussion  
The experiments depicted in Tables 1 and 2, Figures 10 and 11 show that the proposed SCNN-LSTM-based models achieve best performance among the all approaches considered in our work, including seven baselines and the CNN-based model. For example, the EER achieved by the best one (CNN) among existing approaches is reduced to 2.53% using the proposed SCNN-LSTM model with unsupervised encoding scheme on the data set acquired from two sessions. The verification accuracy may be further improved by combing the features of sequences along more directions or enlarging the training set. The good performance can be explained by the following fact. The existing handcrafted approaches (seven baselines) explicitly extract some features by image processing method, which might discard relevant information about finger-vein pattern. Also, they do not get any prior knowledge from the different images as they segment each image independently from the others. In addition, all approaches, including CNN, independently process each pixel based on a predefined neighborhood region or cross-sectional profile during the segmentation procedure, and ignore the spatial dependencies among different vein pixels. By contrast, the proposed approach uncovers hierarchical features for vein texture representation by training its CNN module and harnesses rich dependency information by training its LSTM module on a huge sequence set from different images. Therefore, it is capable of predicting the probability of a pixel belonging to a vein pattern. We can also observe from the experimental results (Tables 1 and 2, Figures 10 and 11), the performance is improved after adopting a supervised encoding scheme. For instance, the EER is reduced to 0.95% (about 6% relative error reduction) on the data from two mixed sessions. When we employ the images in the first session as templates and the remaining images captured at the second session as testing samples, a EER, namely 2.38% (about 8.1% relative error reduction) is achieved by the SCNN-LSTM + Supervised encoding. The experimental results are explained by this fact. The existing finger-vein encoding approaches do not infer any prior knowledge from the different images because they compute the threshold from each image independently from others or employ some empirical threshold \begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **EER (\%)** & **Sensitive Index (d’)** \\ \hline Repeated line tracking [24] & 12.85 & 2.26 \\ Maximum curvature point [15] & 8.30 & 2.76 \\ Region growth [27] & 5.71 & 3.15 \\ Wide line detector [13] & 7.62 & 2.86 \\ Gabor filters [3] & 5.08 & 2.97 \\ Mean curvature [14] & 4.20 & 3.45 \\ Difference curvature [43] & 7.90 & 2.92 \\ CNN [33] & 3.02 & 3.72 \\ SCNN-LSTM+Unsupervised encoding & 2.59 & 3.89 \\ SCNN-LSTM+Supervised encoding & 2.38 & 3.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: EER of various approaches on image dataset from two different sessions. Figure 11: Receiver operating characteristics on image data from two separate sessions. values such as 0.5 and 0. By contrast, the proposed encoding approach harnesses a rich prior knowledge acquired by maximizing the distance between the genuine score set and impostor score set (as shown in Equation (14)) and the resulting threshold is directly related to verification error reduction. Therefore, our approach can extract the discriminative vein texture for verification. Also, the experimental results show that the supervised encoding shows more significant improvement on the data acquired in two sessions. The reason is that there is not large room for improvement because it is easier to distinguish the images from one session compared to those from two sessions. Actually, the 2-seessions scenario is more realistic so the supervised encoding scheme is effective to reduce the verification error.