# A Color Consistency Processing Method for HY-1C Images of Antarctica
## 3 Consistency Processing Method
### Color Consistency Framework
#### 3.1.1 Single-view Consistency Process
We combined the Gaussian filter with an auxiliary mask and propose the Gaussian filter with the auxiliary mask:  
\[G(x,y)=\frac{1}{2\pi\sigma^{2}}\exp(-\frac{x^{2}+y^{2}}{2\sigma^{2}}), \tag{6}\]  
\[G^{mask_{auxiliary}}(x,y)=\frac{2\pi\sigma^{2}}{2\pi\sigma^{2}-\int G(x^{ \prime},y^{\prime})}G(x,y), \tag{7}\]  
where \(\sigma\) is the standard deviation of the Gaussian distribution, \(G(x,y)\) is a 2D Gaussian function, and pixels \((x^{\prime},y^{\prime})\) are not of the Antarctic continent part:  
\[mask_{auxiliary}(x^{\prime},y^{\prime})=0. \tag{8}\]  
In the proposed method, the Gaussian kernel size was \(150\times 150\) pixels, and \(\sigma\) can be calculated as follows:  
\[\sigma=0.3\times((ksize-1)\times 0.5-1)+0.8. \tag{9}\]  
The feature map of each image can be calculated by the Gaussian filter with the auxiliary mask as follows:  
\[FM(x,y)=I(x,y)\cdot mask_{auxiliary}(x,y)\bigotimes G^{mask_{auxiliary}}_{ ksize,\sigma}, \tag{10}\]  
where \(\bigotimes\) is the convolution calculation and \(ksize\) is the kernel size. The results of Gaussian filtering with the auxiliary mask for a sample image are shown in Figure 6e. Compared with Figure 6b, it can be seen that the lighting and color consistency in the feature map were improved, without obvious boundary information. The final single-view consistency processing result is shown in Figure 6f. * Uneven light removal The main target of the mosaic task for the HY-1C images of Antarctica was the Antarctic continent. Therefore, to reduce the computational complexity and avoid anomalies, the uneven light was removed only in the Antarctic continent part. Uneven light information was removed from the original image, and a \"no light image\" was produced, which was calculated as follows: \[I_{NL}=I-(FM\cdot mask_{auxiliary}).\] (11) According to Equation (5), \(I_{NL}\) is the difference of the ideal image (\(r(x,y)\)) and the average lighting, \(I\) is the original image (\(f(x,y)\)), and \(FM\cdot mask_{auxiliary}\) is the sum of the average lighting and the uneven lighting information (\(\delta(x,y)\)). The \"no light\" image of the sample image (Figure 6a) is shown in Figure 7.  
Figure 6: A comparison between the proposed method and the standard Gaussian filtering method. (**a**) Original image. (**b**) The feature map extracted by the standard Gaussian filter. (**c**) Single-view color consistency processing results using the standard Gaussian filter. (**d**) The auxiliary mask of the sample image. (**e**) The feature map extracted by the proposed filter. (**f**) Single-view color consistency processing results using the proposed filter. Figure 7: Example of a “no light” image. Calculation of Artificial Lighting Information  
Because \(I_{NL}\) is a uniform light image that does not contain a light source, manually calculated supplementary lighting needed to be added. The cumulative histogram of the original image was calculated, and the pixel values of frequency \(\theta_{max}=(1-0.005)\) are were to a high-frequency width. The artificial lighting information is calculated as follows:  
\[L=254-pix_{ULmax}, \tag{12}\]  
where \(L\) is the artificial lighting information and \(pix_{ULmax}\) is the high-frequency width of each image. * Information overlay  
The original image, the auxiliary mask, and the artificial lighting information were combined to produce an image with color consistency in a single view. Each pixel of the output image is calculated as follows:  
\[I_{consistency}(x,y)= \begin{cases}I(x,y)&(x,y)\in((x,y)\ |\ |FM(x,y)|>L)\\ I_{NL}(x,y)+FM(x,y)+L&(x,y)\in((x,y)\ |\ |FM(x,y)|\leq L)\end{cases} . \tag{13}\]