# Real-Time Moving Ship Detection from Low-Resolution Large-Scale Remote Sensing Image Sequence
## 2 Low-Resolution Sequence Target Detection Algorithm
### Feature Identification  
The feature identification process calculates the gray features of all the targets in the first-level suspected target set and classifies whether they are ship targets according to the elements. Among them, the simplified HOG feature (S-HOG) is used for gray feature calculation, and nonlinear binary classification SVM is used for binary classification.  
I.S-Hog Feature Calculation  
After preprocessing, simplified HOG enhanced the edge and gray distribution of the target, while gamma enhancement will increase the noise interference on the target. Therefore, the calculation process of S-HOG is mainly divided into the following steps (as shown in Figure 5):  
Step 1: For any region \(A^{\prime}_{i}\), take its centroid \(C_{i}=[mean(\overrightarrow{x}^{\prime}_{i}),mean(\overrightarrow{y}^{ \prime}_{i})]\) as the center, extract slice \(D_{i}\) with a length of 52 pixels from the original image \(I\), and perform S-HOG feature calculation;  
Step 2: Slice \(D_{i}\) was segmented. The size of each cell was 13 \(\times\) 13 pixels. The gradient features calculated for each cell were divided into 8 directions, and each cell had 8 feature values;  
Step 3: The features of every four adjacent cells form a block, then there are 9 blocks in total, each block has 32 eigenvalues \(Block(i,j)=[Cell(i,j),Cell(i+1,j),Cell(i,j+1),Cell(i+1,j+1)]\), and the eigenvector \(\overrightarrow{Block}\) has 288 eigenvalues in total.  
II. Nonlinear Binary SVM Calculation  
The eigenvalue \(\overrightarrow{Block}_{i}\) of single slice image \(D_{i}\) is calculated by SVM binary classification. Considering the high feature dimension, nonlinear SVM is adopted. The training and decision calculation are divided into the following steps:  
Step 1: First, input the training feature value and category set A, B is the category to be distinguished, '0' represents the interference target, '1' represents the ship target;  
Figure 4: Relationship between the number of reconstruction iterations \(R\) and the mean SNR increment after processing.  
Step 2: Construct and solve the optimization formula  
\[\min\ 0.5\sum_{i=0}^{j-1}\sum_{j=0}^{p^{\prime}-1}y_{i}y_{j}a_{i}a_{j}K(x_{i},x_{ j})-\sum_{j=0}^{p^{\prime}-1}a_{j} \tag{5}\]  
The constraint condition is  
\[\sum_{i=0}^{p^{\prime}-1}ya_{i}=0,0\leq a_{i}\leq C \tag{6}\]  
where C is the loss parameter, \(a_{i}\) is the Lagrange multiplier, and \(K(x_{i},x_{j})\) is the radial basis kernel function:  
\[K(x_{i},x_{j})=e^{-\gamma||x_{i}-x_{j}||^{2}},\gamma>0 \tag{7}\]  
According to Equations (5)-(7), the optimal Lagrange multiplier solution \(a^{*}\) is obtained, and the threshold \(b\) is calculated as follows:  
\[b=y_{i}-\sum_{i=0}^{p^{\prime}-1}y_{i}a_{i}^{*}K(x_{i},x_{j}) \tag{8}\]  
Step 3: The final decision function formula is  
\[f(x)=\text{sgn}(\sum_{i=0}^{p^{\prime}-1}a_{i}^{*}y_{i}K(x,x_{i})+b) \tag{9}\]  
Therefore, after feature identification of the first-level suspected target set \(A_{i}^{\prime}\), the result of the second-level suspected target set \(A_{i}^{\prime\prime}\) (the number of effective targets is \(P^{\prime\prime}\)) is as follows:  
\[A_{i}^{\prime\prime}=f(\overset{\rightarrow}{Block}_{i}(A_{i}^{\prime})) \tag{10}\]  
Figure 5: S-HOG eigenvalues calculated by slices and their set.  
For \(S\) sequence set \(\overset{\rightarrow\rightarrow\prime\prime}{A_{q,i}}=[A_{q,i}^{\prime\prime},A_{q+1,i }^{\prime\prime\prime},\cdots,A_{q+S-1,i}^{\prime\prime}]\) of target \(i\) in the sequence image, after S-YOLO identification, if the judgment result of the effective target in the sequence exceeds the threshold D, the sequence is considered as effective sequence and target, that is, the fourth level suspected target set \(A_{q,i}^{\prime\prime\prime}\) is calculated as follows:  
\[A_{q,i}^{\prime\prime\prime}=\left\{\begin{aligned} A_{q,i}^{ \prime\prime\prime},\text{ }&\text{ }\text{when }[\sum\limits_{t=q}^{q+S-1}Y(A_{t,i}^{ \prime\prime\prime})]/S\geq Thr_{Y}.\\ \phi,\text{ }&\text{ }\text{else.}\end{aligned}\right. \tag{12}\]