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Wavelet-based image fusion using "A trous" algorithm
where state for the mean value of the corresponding data set. High amount of the correlation shows that the spectral chracteristic of the multispectral image has been preserved well. Table 1 shows the correlations coefficients between the different solutions and the original multispectral image at 30m resolution.
Table 1: correlation coefficients computed between different solutions and original multispectral image at 30m resolution.
| Method |
Blue |
Green |
Red |
| AWI |
0.8220 |
0.8189 |
0.8117 |
| AWRGB |
0.7950 |
0.7993 |
0.8046 |
| SUBRGB |
0.6899 |
0.6968 |
0.7046 |
| Brovey |
0.5988 |
0.6511 |
0.7011 |
| PC |
0.5533 |
0.5445 |
0.5663 |
| HIS |
0.6534 |
0.6431 |
0.6218 |
As you can see the correlation coefficients of different methods in the table 1, wavelet-based fusion methods (AWRGB, AWI, SUBRGB) can perserve the spectral characterictics of the image more than the others, because their related correlations have the highest values .
Also comparing the resultant images visually, you can find that these wavelet -based fusion methods perfom betther than the others (fig. 1-b).
Figure 1 shows the original R band as an example and the merged one using AWI and a standard method like Brovey method.
Fig. 1. (a) The original R band of ETM (low-resolution multispectral image).(b) Result of the fusion using AWI method(Additive wavelet on Intensity compoenet) . (c) Result of the fusion using the Brovey method.
Conclusion:
The advantages of using wavelet-based methods are:
- The spectral quality of the images is preserved better than using the other approaches (you can see that from the table 1).
- In the additive wavelet-based method the detail information of both of images (panchromatic and multispectral) are used and non of them is discarded.
- For image processing, to work in the frequency and spatial space to gether can be more efficient instead of to work in one space. So using wavelet-based method which use both of space to process the image is recommended.
- Since the wavelet-based method use multiresolution analysis, it's more useful than the other transform in frequency space like Fourior transform.
- In HIS/LHS method the Intensity component is substituted by panchromatic image completely ,so the detail information in the Intensity is discared but in the additive wavelet-baed method using Intensity (AWI) ,the highest resolution features not presented in the multispectarl image are added to the fused image by adding the panchromatic wavelet coefficients to the Intensity component.
- Since the wavelet coefficients (except the residual image) have zero mean, the total flux of the multispectral image is preserved.
- "a trous" algorithm uses dyadic wavelet to merge non_dyadic data in a simple and efficient procedure.So it is better than the other algrithm such as "Mallat". By using this algorithm to decompose the images all wavelet planes in addition to the residual image have the original image pixel size ,so we can use this algorithm to merge non-dyadic images.
References :
- R.C. Gonzalez and R.E. Woods,"Digital Image Processing",Addison_wesley publishing company.
- J.Nunez, X.Qtazu, O.Fors, A.Prades, V.Pala and R.Arbiol ,"Multiresolution-Based Image Fusion with Additive Decomposition",IEEE Trans. On Geoscience and Remote Sensing, vol. 37, no. 3, MAY 1999
- M.Aziz Mohammadi,"Assessment Of Image Fusion Methods Applied to SPOT (PAN&XS) Image using Wavelet Decomposition " , MSc. Thsis , K.N.T. university of Iran
Bibliography
Maryam Dehghani is a student of M.Sc. degree in remote sensing at K. N. Toosi University of Technology. She got her B.Sc. degree from Geodesy and Geomatics Engineering in Elmo San'at university. The area of her interests are: Digital Image Processing , Wavelet Transformatuon.
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