A Fusion Approach of Multi-sensor Remote Sensing Data Based on Wavelet Transform
Methodology
The TM and SPOT-PAN data in this paper were acquired on 27 March 1997 by Landsat Thematic Mapper and on 25 August 1996 by SPOT (Satellite Pour I' Observation de la Terre) respectively.
(1) The "FWT" Wavelet Fusion Model
The procedure of "FWT" model can be described as followed:
Step(1): To produce three new SPOT PAN images whose histograms are specified according to the histogram of each TM3, TM4, TM7, namely SPOT-PAN/TM3, SPOT-PAN/TM4, SPOT-PAN/TM7.
Step(2) : choose the wavelet basis for the transform, and perform the wavelet decomposition analysis to generate (from SPOT-PAN/TM3, SPOT-PAN/TM4, SPOT-PAN/TM7) detail information (vertical, horizontal and diagonal) and the approximation images of 20-m spatial resolutions (presented as SPOT-PAN/TM3', SPOT-PAN/TM4', SPOT-PAN/TM7').
Step (3): The original TM3, TM4, TM7 are spatially registered to the approximation images of 20-m spatial resolutions.
Step (4): Replace the approximation images (SPOT-PAN/TM3', SPOT-PAN/TM4', SPOT-PAN/TM7') with the registered original TM3, TM4, TM7 respectively.
Step (5): Introduce the detail information into the registered original TM3, TM4, TM7 through the inverse wavelet transform, and generate the fused 10-m fTM3, fTM4, fTM7 images respectively.
Upper procedure is only for one level wavelet decomposition. In other application purpose, you may choose the different final resolution and perform more than one time wavelet transform.
(2) About the choice of the wavelet basis.
In this study, we have found that the choice of the wavelet basis does affect the fused images. Having implemented the image fusion using the wavelet basis (Daubechies, 1988) from the length of 4 to 20, we compare these fused images and obtain the best result derived from wavelet transform in the wavelet basis of 10. Figure 2a is the result of color combination of fTM3, fTM4, fTM7 in R,G,B channel.
(3) Quality Assessment of the Resulting Images
In order to evaluate the improvement of the fused images, in both spectral and spatial features, the result images are compared with the original TM bands (TM3', TM4', TM7- Figure 2D) which were geometrically corrected to 10 SPOT-PAN, and also compared to the synthetic images merged by HIS transform (Figure 2B) and PCA approach (Figure 2C). The comparison is performed by statistical method and by visual interpretation.
(i) A comparison Based on Statistical Method
The factors computed to qualify the fused results are as followed: mean, standard deviation, entropy, percentage presentation of no value changed pixel for each band and the best combination index for fused color image respectively. The statistical results are shown in TABLE 1.
| Fusion Approach | Band | Mean | Entropy | Standard Deviation | Not changed pixel(%) | Best index factor |
| FWT | fTM3 | 74.80 | 5.74 | 9.12 | 13.38 | 13.9 |
| FTM4 | 63.13 | 5.45 | 8.30 | 14.74 |
| fTM7 | 80.20 | 5.92 | 8.60 | 12.13 |
| IHS | TM31 | 75.15 | 5.37 | 9.18 | 10.82 | 10.8 |
| TM41 | 63.51 | 5.22 | 8.37 | 12.35 |
| TM71 | 80.74 | 5.33 | 8.63 | 10.60 |
| PCA | TM31 | 74.14 | 5.26 | 9.55 | 9.65 | 10.8 |
TM41 | 63.22 | 5.27 | 9.61 | 6.90 |
| TM71 | 80.23 | 5.16 | 8.86 | 7.40 |
| Corrected original image | TM3 | 74.37 | 4.61 | 5.84 | ……. | 8.1 |
| TM4 | 62.87 | 4.61 | 5.82 | ……. |
| TM7 | 79.86 | 5.02 | 7.96 | ……. |
Table 1
Note: the formulas used to compute entropy is as
The entropy presents information measurement involved in single band, while the best index factor shows the information presentation of complex color image. The larger the entropy or the best index factor is, the more information quantity the image has. From the TABLE 1, it is obvious that the entropy and the best index factor of the fused images, not only by FWT approach but the entropy and the best index factor of the fused images, not only by FWT approach but also by HIS and PCA methods, have improved a lot when compared to original images. It has directed the explanation that the information of the fused images has accumulated, and FWT model does the best job.
The analysis from the factors of standard deviation and percentage of no value changed pixel for each band result in the fact that the FWT approach possesses the advantage of minimal distortion of the spectral characteristic of the data. This is because that the wavelet algorithm acts as a double function filter: high-pass and low-pass filter, and the spectral Changes of the fused images only cause by high frequency information -the detail image.
