# A Color Matching Method for Mosaic HY-1 Satellite Images in Antarctica
## 4 Analysis and Discussion  
### Image Quality Analysis  
The mean value and standard deviation of an image can be used as objective indexes for image quality evaluation [43]. To conduct a quantitative analysis of the color-matching effect, four overlapping regions of images (A, B, C, D in Figure 8) are selected for evaluation according to the features of the image coverage area. The gray mean difference and the standard deviation difference of each image's overlap areas were introduced to evaluate the quality [20], and the formula is as follows:  
\[\Delta\mathrm{m}=\left|\frac{\sum_{i=1}^{\mathrm{N}}\sum_{j=1}^{\mathrm{M}}f^ {\prime}(i,j)}{\mathrm{N}\times\mathrm{M}}-\frac{\sum_{i=1}^{\mathrm{N}}\sum_{ j=1}^{\mathrm{M}}\mathrm{f}(i,j)}{\mathrm{N}\times\mathrm{M}}\right| \tag{8}\]  
\[\Delta\mathrm{s}=\left|\sqrt{\frac{\sum_{i=1}^{\mathrm{N}}\sum_{j=1}^{\mathrm{ M}}\left(f^{\prime}(i,j)-u^{\prime}\right)^{2}}{\mathrm{N}\times\mathrm{M}}}-\sqrt{ \frac{\sum_{i=1}^{\mathrm{N}}\sum_{j=1}^{\mathrm{M}}\left(f(i,j)-\mu\right)^{2 }}{\mathrm{N}\times\mathrm{M}}}\right| \tag{9}\]  
where \(\mathrm{f}(i,j)\) and \(f^{\prime}(i,j)\) are the gray values of the two overlapping images, \(\mathrm{\mu}\mathrm{and}\mathrm{\mu}^{\prime}\) are the mean values of the images in two overlapping areas, and M and N are the number of rows and columns of the image, respectively. \(\Delta\mathrm{m}\) indicates the color difference between images. The smaller \(\Delta\mathrm{m}\) is, the smaller the color difference between images is, and the better the visual effect is. \(\Delta\mathrm{s}\) indicates the contrast difference between images; the smaller the value is, the smaller the contrast difference is. Table 5 shows the statistical results of the above four areas. It can be seen from the results that the \(\Delta\mathrm{m}\) values obtained by the general histogram specification and Wallis methods are larger than the \(\Delta\mathrm{m}\) values of the original images in some regions, indicating that the two general methods do not significantly improve the color difference in these regions. However, the \(\Delta\mathrm{m}\) value by the method of this paper in the four areas is significantly smaller than that of the original image, which indicates that the color difference between the images after color matching is obviously less than the color difference between the original images, and the algorithm effectively eliminates the color difference between the images. According to the statistical results of \(\Delta\mathrm{s}\), the general histogram specification method reduces the contrast difference in region A, and the Wallis method decreases the contrast difference in region B. For the method adopted in this paper, the \(\Delta\mathrm{s}\) result for images B and D is smaller than that of the original image, which indicates that the contrast difference between regions B and D after color matching is small. The \(\Delta\mathrm{s}\) result for images A and C is greater than that of the original image, indicating that the contrast difference of the image after color matching is increased. The main reason for this is that the reference image used for color-matching processing increases the gray difference between low-reflectance objects (such as sea, bare rock, or shadows) and high-reflectance objects (such as glaciers). However, there are mountain shadows and bare rock areas in region A and a large amount of water \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Image 1** & **Image 2** & **Image 3** & **Image 4** & **Average** \\ \hline Image size & 0.87 Gb & 0.95 Gb & 1.03 Gb & 0.98 Gb & \\ Histogram specification & 131.80 s & 174.47 s & 193.09 s & 176.69 s & 169.01 s \\ Wallis & 22.93 s & 25.91 s & 27.41 s & 26.94 s & 25.80 s \\ Proposed method & 133.11 s & 149.18 s & 189.59 s & 173.71 s & 161.39 s \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Running times for different color-matching algorithms. area in region C, which have lower gray values than glaciers.