Application of Wallis Transform in Wavelet Based Image Fusion

The algorithm of image fusion has developed from traditional image fusion methods such as IHS transform, Brovey transform etc. to nowadays wavelet based image fusion methods. Normally wavelet based image fusion includes three steps: pre-processing(enhancement), registration, wavelet based fusion. From the published papers, we find that most effort is paid to investigate the application of Mallat algorithm and à trous algorithm, some papers have related to registration. It is also easy to understand that image preprocessing methods certainly influence the fusion result, but no paper on this issue has been reported yet. It is worth to investigate how the pre-processing procedure influences the fusion result. Due to Mallat algorithm using orthogonal basis, it therefore distorts the phase of the image, while à trous algorithm using à trous filter overcomes this disadvantage.We prefer to use à trous algorithm in our case. By using this algorithm, we need to extract the wavelet component from the high resolution image after image pre-processing.Through the analysis profile lines of the wavelet components of images after preprocessing such as linear stretch, histogram equalization and wallis transform, it is concluded that if original high resolution image is only processed by linear stretch and histogram equalization, the extracted wavelet component with à trous algorithm will make no difference from the original image, so it can not help much in the image fusion model in the sense of image enhancement algorithms. But the wavelet component from the image after using Wallis transform method is much larger than the original image.