## 3 Parameter Analysis of Object Determination
### Standard Deviation  
We take Figure 4 as an example to analyze the method of removing false alarms with standard deviation. First, all the pixels in the image are sorted by increasing gray values, and we calculate standard deviations of the minimum 1-100% pixels, which we call grayscale sequence method (GS). Based on experience, we start the calculation of the change rate of standard deviation from the minimum 90% pixels and control the calculation interval to reduce the number of calculations. When GS method is applied to large data sets, star image partitioning becomes more important. We divide the star image into multiple subimages and calculate the data in the regions of interest. The standard deviations that we obtain are increasing, and we analyze their change rate to find the mutation value where the standard deviation is the boundary between the objects and image backgrounds. The change rate of standard deviation is stable when the selected pixels are image backgrounds, and only when a large number of object pixels are selected does it fluctuate significantly. Therefore, the standard deviation thresholding selected with GS method has a certain hysteresis, and a part of the dark objects and stars may be filtered out.  
Figure 3: Image data and fitting models in six positions of Ob 1 and Ob 2 (pixel (**a**–**f**)).  
If the standard deviation corresponds to the object itself rather than the variation trend of image grayscales, the hysteresis can be avoided. We consider our column recognition method where five data are grouped, and the standard deviations of all the groups are calculated and sorted incrementally, which we call standard deviation sequence method (SDS). Since the standard deviation represents the fluctuant characteristics of the object or background, the change rate changes significantly when it is converting from the image backgrounds to the dark objects. The results of thresholding selection in both methods are shown in Figure 4. In Figure 4b,d, a mutation value is greater than all previous values, and there is a relatively large increase in the mean value of a certain interval of the same size before and after this value. However, we cannot expect how significant the mutation of the change rate at this value is, because it is in a short transition interval, after which the change rate increases rapidly. What we can do is to find an optimal value within the transition interval and to obtain the standard deviation at the position of the optimal value as thresholding for the segmentation of backgrounds and dark objects.  
The results show that the selected thresholdings with both methods are respectively 11.4 and 7.29, and we will verify the effectiveness of SDS method in Section 4.2. If the standard deviation of a group of data is less than 7.29, we regard it as a background directly and there is no need to model, which reduces 71% time of model fitting and avoid the risk of misidentifying the background data with Gaussian morphology as the target data. Of course, if the standard deviation of a group of data is greater than 7.29, we cannot rule out the possibility that it is a bad pixel or background noise.