# Learning Motion Constraint-Based Spatio-Temporal Networks for Infrared Dim Target Detections
## 3 Results and Discussion
### Performance Comparison and Discussion
#### 3.3.1 Comparison to State-of-the-Art Methods  
A sufficient number of experiments were conducted to investigate the performance of the proposed method and the current best models in this subsection. To comprehensively reflect their effectiveness, we compare the proposed model to six state-of-the-art (SOTA) methods, including recurrent YOLO (ROLO) [39], infrared small target detection with GAN (IRSTD-GAN, GAN: Generative Adversarial Network) [40], dynamic programming algorithm (DP) [11], time variance filter algorithm (TVF) [10], weighted strengthened local contrast measure (WSLCM) [41], and the multi-scale Laplacian of Gaussian (MCLoG) [42]. ROLO and IRSTD-GAN are representatives of CNN-based methods. DP and TVF are representatives of multiple-frame methods. WSLCM and MCLoG are classical single-frame detection methods. \begin{table}
\begin{tabular}{c c} \hline \hline
**Layer** & **Parameter** \\ \hline conv-lstm-2D\_0 (ConvLSTM) & 9856 \\ batch\_normalization\_0 (BatchNorm Normalization) & 64 \\ conv-lstm-2D\_1 (ConvLSTM) & 55,424 \\ batch\_normalization\_1 (BatchNorm Normalization) & 128 \\ conv-lstm-2D\_2(ConvLSTM) & 27,712 \\ batch\_normalization\_2 (BatchNorm Normalization) & 64 \\ conv3d\_0 (Conv3D) & 6928 \\ batch\_normalization\_3 (BatchNorm Normalization) & 64 \\ conv3d\_1 (Conv3D) & 3464 \\ batch\_normalization\_4 (BatchNorm Normalization) & 32 \\ conv3d\_2 (Conv3D) & 3472 \\ batch\_normalization\_5 (BatchNorm Normalization) & 64 \\ up\_sampling3d\_0 (UpSampling3D) & 0 \\ up\_sampling3d\_1 (UpSampling3D) & 0 \\ concatenate (Concatenate) & 0 \\ concatenate (Concatenate) & 0 \\ Total params & 107,272 \\ Trainable params & 107,064 \\ Non-trainable params & 208 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters of the entire model. For the sake of fairness, CNN-based methods are retrained on our datasets. Moreover, for traditional methods, we follow the parameters of the original paper for our experiments. The partially set parameters are shown in Table 3. For the TVF, the time domain window size T and the iteration step_size are, respectively, T = 16 and S_Z = 8. For the DP, the number of frames in batch processing is T = 8. For the WSLCM, the coefficient of the Gaussian filter is set to K = 9, and the factor of the threshold operation is set to \(\lambda\) = 0.8. For the MCLoG, the number of scales is set to K = 4. Considering that the moving speed of the target in our dataset is no more than five pixels, the input frame length of the proposed method in the experiment is supposed to be T = 5. Figure 12 shows the convergence of our model. Figure 12a plots the training error curve and the validation variation tendency. It can be seen that the loss value decreases considerably at the beginning of the training phase, indicating that the learning rate is appropriate and the gradient descent process is performed. The loss curve tends to smooth out after a certain stage of learning, and the network achieves convergence. Figure 12b visualizes the evolution of the learning rate. As shown in the subplot, the learning rate decreases normally during the training phase and stabilizes after 25 epochs. The quantity of the discussed methods is subsequently assessed by using DR and FA. Table 4 shows the quantitative results. Traditional single-frame methods (WSLCM and MCLoG) have a positive detection rate as well as a high false alarm rate. This is particularly evident in self-made datasets with more isolated noise. They fail to distinguish isolated points caused by sensor inhomogeneities because these two methods are based on gradient differences between the target and the background, whereas the pseudo-target shares this property. The multiple-frame methods (DP and TVF) exploit the temporal association of the target, which partly alleviates the false alarm rate. However, when the background becomes complex and variable, the algorithm commences to become less effective. The temporal model with fixed parameters is not adaptable to prolonged detection. ROLO and the IRSTD-GAN acquire acceptable results.