The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B7. Beijing 2008 
wavelet coefficients are considered noise and filtered out. The 
original image coefficients are then modified by adding a 
percentage of the corresponding denoised coefficient. This 
percentage was determined based on the percentage of image 
entropy in the image excluding shadow and cloud image and in 
the shadow area, which was found to be 0.305. A final output 
image is produced from the original defected pixel values 
except at identified shadow areas, where the reconstructed 
image was used. The results of one to four decomposition levels 
are demonstrated in Figure 5. A simple edge suppression 
algorithm that utilizes Gaussian filter wad applied to enhance 
the shadow area edges. 
3.4 Results Evaluation and Discussion 
Figure 5 shows the results obtained with different number of 
wavelet decomposition levels. Using two or three levels of 
decomposition gave the best visual results in terms of 
enhancing the high frequency component in the shadow areas. 
This is shown in the marked runway and road areas. Less detail 
were shown in the shadow areas if single decomposition level is 
used. On the other hand, using four levels of wavelet 
decomposition led to significant increase in the introduced 
artifacts in the output image. Figure 5 also shows that although 
shadow areas were significantly enhanced, these areas look 
patchy due to edge problems. Edge problems are mainly the 
result of the limitation of the shadow detection algorithm. 
Enhancement of cloud and shadow detection procedures should 
lead to significant reduction of this problem effect. 
In order to quantify the obtained results two metrics were used. 
The first metric is the RMSE computed for the difference 
between each output image and the reference cloud-free image 
shown in figure 4 above. The second used metric is the entropy 
computed for each output image, the original image, and the 
reference image. Table 1, which summarizes the computed 
metrics, shows that the RMSE computed for the images 
resulting from applying the developed algorithm is less than the 
value computed for the original image, which indicates 
enhancement in image quality regardless of the number of used 
wavelet levels. The RMSE values for the output image obtained 
using 2 wavelet decomposition levels gave the least value of the 
RMSE. The high value of computed RMSE for all images could 
be attributed to the clouds existence in the output and original 
images compared to the cloud-free reference image. 
Table 1 shows an increase in the computed entropy values with 
the increase in the number of wavelet decomposition levels. 
This might be attributed to the increase in the added details due 
to the increase in coefficient values at more wavelet levels. It 
should be noticed here that the increase in the entropy value 
does not indicate enhancement in the image. This is clear for 
the output image that resulted from applying the developed 
algorithm on four decomposition levels. The entropy value for 
this image is large while the image suffers many unwanted 
artifacts. Generally, the entropy values for the output image are 
higher than the entropy for the original image. Again the 
consistence difference between the reference and output images 
entropy may be attributed to the cloud existence in the latter 
images. 
No of wavelet levels 
RMSE 
Entropy 
1 
48.1074 
6.0483 
2 
48.0001 
6.0886 
3 
48.0757 
6.0954 
4 
47.8091 
6.0959 
Original Image 
52.9923 
6.0759 
Reference Image 
6.9761 
Table 1. RMSE and entropy computed for output, original and 
reference images 
Figure 5. Output enhanced image using different wavelet 
decomposition levels: single level (top-left), two levels (top- 
right), three levels (bottom-left), and four levels (bottom-right) 
4. CONCLUSION 
A new algorithm for enhancing cloudy images by eliminating 
cloud-related shadows was developed and tested. The 
developed algorithm was successful in eliminating shadows 
from a single cloudy image while preserving underneath details. 
The algorithm adjusts the high frequency content in shadow 
areas by boosting the image wavelet coefficients before final 
image reconstruction. Several discrete wavelet decomposition 
levels were tested. The increase in image wavelet coefficient 
was determined by inspecting the image entropy in the shadow 
and the rest of the image. Visual and quantitative analysis of the 
results revealed that the ability to enhance details under shadow 
areas increased with the increase in the number of wavelet 
decomposition levels. Nevertheless, the higher this level is, the 
more artifacts in the output image. Generally, two or three 
wavelet decomposition levels were found to be sufficient for the 
analysis used in this study. 
The obtained results, although revealed under shadow details, 
were patchy. One of the factors causing the patchy appearance 
of the shadow areas is the errors in the used shadow detection 
algorithm. Finally, it should be mentioned here that although 
the developed algorithm was tested on cloud-related shadows, it 
is believed that this algorithm can be implemented on large 
patches of shadows casted by features other than clouds given 
that the appropriate shadow detection algorithm is applied. 
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