# A High-Dynamic-Range Optical Remote Sensing Imaging Method for Digital TDI CMOS
## 3 Image Enhancement Algorithm of Entropy-Maximized Adaptive Histogram Equalization (EMAHE)
Hence, in the above case, an excessively concentrated gray value will cause the slope of _CDF_ to be too large, which will lead to excessive shear of the histogram. Although this can improve the contrast of the image as a whole, especially in the shadow-covered area, the negative impact of over-amplifying the noise of the subdomains is fairly serious. However, there is no definite changing principle for the value of entropy with the block increase, because it has an important relationship with the spatial distribution of the gray values. The reason is that for the same image, using different a block method may result in the same target falling into different sub-blocks, as shown in Figure 7. The result of regional HE is strongly dependent on the actual gray distribution of the subdomain. Therefore, for the same image, as the number of blocks increases, it will have uncertain subdomain gray distributions and HE results, and of course, an uncertain variation trend of entropy. Further, for different images it is important to adaptively find the best value of blocks according to the maximum entropy strategy. Through experiments with different images, we come to the conclusion that the typical value of blocks can be set as 8 \(\times\) 8, and the reasonable range of the clip limit is from 0.01 to 0.1. Because there is a certain relationship between the entropy and the clip limit, we firstly keep the blocks fixed and increase the clip limit from 0 by a specified step (here, the step is set as 0.01). As shown in Figure 8, the entropy increases gradually and then decreases. The best clip limit exists where there is the largest entropy on the curve. Then, based on the best clip limit, the number of blocks increases from 2 \(\times\) 2 step by step (here the step is set as 1 \(\times\) 1). In this process, the change of entropy has no clear regularity, as is shown in Figure 9. However, the location of the maximum entropy has a certain law. That is, if we divide the 5-stage image, whose grey level is medium and gray value distribution is relatively concentrated, with an overly large value of blocks, the noise will be excessively amplified. In fact, the ranges from 2 \(\times\) 2 to 10 \(\times\) 10 could be reasonable in this condition. For the 13-stage image of high grey level, the maximum entropy usually appears near the block value of 20 \(\times\) 20. Hence, we can directly find the optimal blocks from 16 \(\times\) 16 to 30 \(\times\) 30. The parameter selection strategy as above can reduce the computational complexity and improve the efficiency of the algorithm. The original 5-stage and 13-stage images are shown in Figure 10. Their enhanced results by the algorithms of the reference [11; 12], and EMAHE are shown in Figure 11. The enhanced 5-stage image by EMAHE contains a large number of details with respect to the medium illumination targets, but the contrast enhancement of the shadow covered area is still not sufficient. Meanwhile, the enhanced 13-stage image shows a great improvement of the grey level and contrast of shadow-covered area, while keeping most of the details of the image as a whole. Figure 5.0 Image block with different parameters. In addition, the entropy and average gradient of the enhanced images are shown in Figure 5.1 Experimental data show that the EMAHE can improve the entropy to some extent while increasing the average gradient of the image. These positive effects lay an important foundation for further image fusion. Figure 5.2 Relationship between entropy and clip limit when blocks = 8 \(\times\) 8. Figure 5.3 Original images. (**a**)The original 5-stage image; (**b**) The original 13-stage image. Figure 5.4 Relationship between entropy and blocks when the optimal clip limit is set. Figure 5.5 Comparison of Enhanced 5-stage and 13-stage images. (**a,b**) Enhanced images by algorithms of [PERSON] [11]; (**c,d**) Enhanced images by algorithms of [PERSON] [12]; (**e,f**) Enhanced images by entropy-maximized adaptive histogram equalization (EMAHE).