# An Aircraft Object Detection Algorithm Based on Small Samples in Optical Remote Sensing Image
## 3 Results  
In many images, aircraft vary in size. Therefore, we use the circle frequency filter first to detect the large and saliency aircraft, then deduct the part of these aircraft on the original image, and finally, the small aircraft. When the weak and small aircraft is included in images, the improved circle frequency filter algorithm is used for detection. The trained SVM model is used to classify the test results, and then the targets classified as non-aircraft are removed. The fusion algorithm flow is shown in Table 1.  
In order to compare the detection results of the proposed method and Faster R CNN [28], we train Faster R CNN on our training set and test it. A pre-trained backbone network VGG16 model on the Imagenet [38] dataset is adopted. In order to ensure that there is no over-fitting, the maximum number of iterations is 2000. Part of the image detection map is shown in Figure 7.  
There are 13,324 aircraft in the test set, which is recorded as P. A total of 18,812 samples were detected using the proposed algorithm. Using the SVM model to eliminate false alarms, 13,687 objects were obtained. Among them, 12,215 samples can be correctly detected, denoted as TP (True Positive). 1109 samples were classified as negative sample. A sample of 1472 non-aircraft objects was incorrectly judged by the improved method and recorded as FP (False Positive). A total of 1109 aircraft targets were not be detected, and they were denoted as FN (False Negative). Therefore, TN (True Negative) is 0.  
Faster R CNN detects a total of 13,687 objects. Among them, 11,335 samples can be correctly detected. 4361 non-aircraft objects was incorrectly judged by Faster R CNN and recorded as FP. A total of 1989 aircraft objects were not be detected, and they were denoted as FN. TN is 0.  
According to the actual test results of the dataset, precision, accuracy, recall, missing alarm and false alarm are shown in Table 2. 12,215 aircraft can be correctly detected by using the proposed algorithm. It can be seen from both the visualization results and some evaluation indicators that the proposed method is better than Faster R CNN on our dataset. In the case of small samples, the detection accuracy of the object detection method based on a convolutional neural network is greatly reduced. On the test set, Faster R CNN takes about 6.383 s to detect an image, while the proposed algorithm only takes 2.951 s. Therefore, the proposed algorithm can be adopted to efficiently detect aircraft objects.  
\begin{table}
\begin{tabular}{l} \hline \hline
**The Proposed Algorithm** \\ \hline
**Input:** Test dataset images \\
**Execute:** \\ (1) According to the statistical radius, the circumference of the corresponding radius is taken for the pixels on each image. \\ (2) Calculate the magnitude of the gray value on the circumference. \\ (3) According to the amplitude value and the special characteristics of the aircraft to determine whether it is an aircraft. \\ (4) According to the weak and small object detection algorithm, process data and calculate the magnitude to determine whether it is an aircraft. \\ (5) Remove some false alarms by clustering algorithm. \\ (6) Use the trained SVM to eliminate a false alarm. \\
**Output:** Images contain the location of the aircraft \\ \hline \hline \end{tabular}
\end{table}
Table 1: The fusion algorithm flow.  
Figure 7: (**a,c,e,g,i**) are the detection results of the proposed method; (**b,d,f,h,j**) are the detection results of Faster R CNN.