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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