## 4 Experimental Results
### Comparison of Segmentation Methods  
In order to verify the effectiveness of our proposed star image segmentation method combining correlation coefficient, standard deviation and \(K\) value, the global and local thresholding segmentation methods are used for comparison. We use the statistical method to set the thresholds: T\({}_{1}=\mu+\sigma\) and T\({}_{2}=\mu+2\sigma\). The local thresholding method has different segmentation results due to different sub-blocks, so the principle of the sub-block size is that the minimum false alarms are produced on the basis of identifying more objects. In the comparison, an object streak whose recognition length is more than half of its length is considered to identify successfully, otherwise, the objects are not reflected in the figures. If multiple objects that overlap in original images are identified as an extended object streak whose shape is easy to distinguish, we count according to the original image. The results are shown in Figure 8.  
Figure 8: Results of star image segmentation (green squares are false alarms, orange squares are objects that are not clearly identified, and red ellipses are distinguishable objects). (**a**) S4 is an original image, and the lower right part is seriously affected; S5 has forty simulation streaks, and its background comes from S4; S6 is a simulation image with forty streaks, and the upper left part is affected. (**b**) Global T\({}_{1}=\mu+\sigma\). (**c**) Global T\({}_{2}=\mu+2\sigma\). (**d**) Local T\({}_{1}=\mu+\sigma\). (**e**) Local T\({}_{2}=\mu+2\sigma\). (**f**) Our proposed method. Figure 7: Recognition results of extended objects. (**a**) Original image. (**b**) GS method (th1 = 37.67). (**c**) SDS method (th2 = 24.11). (**d**) Recognized pixel number of the five objects in different \(\sigma\) thresholdings. The star images with a size of 120 \(\times\) 120 pixels have uneven backgrounds. The recognition results are terrible under low and high global thresholdings, and the results of local thresholding segmentation are obviously better. However, the contours of some objects are not clear, and there are many false alarms caused by the selection of windows. We find that gray thresholding segmentation has poor adaptability, and our proposed segmentation method is more effective and identifies more objects. The segmentation results of different star images with different methods are shown in Table 1.  
In addition, we respectively simulated 2000 frames based on the backgrounds of S5 and S6. Forty target streaks in each frame were randomly distributed, and the recognition rate and false alarm rate were calculated. The recognition results are shown in Table 2. Our correlation segmentation method ensures low false alarm rate and achieves high recognition rate. Of course, both metrics are influenced by many factors, such as the noise level, target intensity, background complexity, and threshold selection. For star image recognition, in order to achieve better recognition rate, we can reduce each thresholding at the cost of increasing false alarm rate. Therefore, a balance between the two needs to be struck according to application environments. Moreover, the large fluctuation of image backgrounds and the low target intensity has a great impact on target recognition. For the star images with a size of 120 \(\times\) 120 pixels, we run our algorithm on the platform of Intel Core i5-6500 CPU 3.2 GHz, MATLAB2016a, and the average calculation time of our method is about 0.3s. For ground-based telescope observation, the exposure time is generally at second level. When processing star images with complex backgrounds, we often select some areas of interest with small sizes. Therefore, it meets the real-time requirements. Through the simulation experiments of 2000 frames each, the recognition rate of more than 97% and false alarm rate of less than 0.5% can be stably obtained by our method.