THE CURVELET TRANSFORM FOR IMAGE FUSION

4(a)(b)(c)(d)Fig. 2.(a) Original Landsat ETM+ color image. (b) IHS-based fusion result. (c) Wavelet-based fusion result. (d) Curvelet-based fusion result.the spatial and the spectral resolutions have been enhanced, incomparison with the original colour image. That is, the fusedresult contains both the structural details of the higher spatialresolution panchromatic image and the rich spectral informationfrom the multispectral images. Moreover, compared withthe fused results obtained by the wavelet and IHS, the curveletbasedfusion result has a better visual effect, such as contrastenhancement.B. Quantitative analysisIn addition to the visual analysis, we conducted a quantitativeanalysis. The experimental results were analysed basedon the combination entropy, the mean gradient, and the correlationcoefficient, as used in [2], [15]–[17].Table I presents a comparison of the experimental results ofimage fusion using the curvelet-based image fusion method,the wavelet-based image fusion method, and the IHS methodin terms of combination entropy, mean gradient, and correlationcoefficient.The combination entropy of an image is defined as∑255H(f 1 , f 2 , f 3 ) = − P i1,i 2,i 3log 2 P i1,i 2,i 3,i=0where P i1 ,i 2 ,i 3is the combination probability of the imagef 1 , f 2 and f 3 , in which pixel values are i 1 , i 2 and i 3 , respectively,for the same position. The combination entropy (C.E.)represents the property of combination between images. Thelarger the combination entropy of an image, the richer theinformation contained in the image. In Table I, the combinationentropy of the curvelet-based image fusion is greater thanthat of other methods. Thus, the curvelet-based image fusionmethod is superior to the wavelet and IHS methods in termsof combination entropy.The mean gradient is defined asg = 1MNM∑N∑i=1 j=1√(∆I 2 x + ∆I 2 y)/2,∆I x;i,j = f(i + 1, j) − f(i, j), ∆I y;i,j = f(i, j + 1) − f(i, j),