In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
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Figure 1(b) Corresponding frequency partition 
Figure 1. Two level Nonsubsampled Contourlet transform 
decomposition 
Different to the CT, the multiresolution decomposition step of 
NSCT is realized by the shift-invariant filter banks satisfied 
Bezout identical equation (perfect reconstruction) not the LP 
filter banks. Because of no decimation in the pyramid 
decomposition, the lowpass subband does not bring frequency 
aliasing, even the band width of the low-pass filter is lager than 
7c/2. Hence, the NSCT have better frequency characteristics than 
CT. The two-level NSCT decomposition is shown in figure 1. 
2.2 Fusion Method Based on NSCT combining with HIS 
(NSCT+HIS) 
The core of the NSCT is the nonseparable two-channel 
nonsubsampled filter banks. It is easier and more flexible to 
design the needed filter banks that lead to a NSCT with better 
frequency selectivity and regularity when compared to the CT. 
Based on mapping approach and ladder tructure fast 
implementation, the NSCT frame elements are regularity, 
symmetric and the frame is close to a tight frame. The 
multiresolution decomposition of NSCT can be realized by 
nonsubsampled pyramid (NSP), which can each the subband 
decomposition structure similar to LP. A fusion method based 
on NSCT combining with HIS is proposed. If the multispectral 
images are registered to the panchromatic image , A general 
scheme for the NSCT+ HIS fusion methods is shown in Figure 
2. 
This method can be performed in the following steps: 
Step 1: Perform HIS on the multispectral image and get 
saturation, hue and intensity components; 
Step 2: Apply histogram matching between the original 
panchromatic image and intensity to get a histogram-matched 
panchromatic image. 
Step 3: Employ NSCT on intensity and the histogram-matched 
panchromatic image, and get low frequent subband and high 
frequent subbands. 
Step 4: Fuse the intensity and the histogram-matched 
panchromatic image. The fused low frequent data employ the 
low frequent coefficient of intensity. The fused high frequent 
coefficient adopt H Maximum the region-energy for every 
coefficient of each subband of panchromatic image and 
intensity get by step 3. 
Step 5: Apply NSCT reconstruction with new coefficient to 
obtain the new intensity. 
Step 6: Perform the inverse HIS transform to obtain the fused 
image. 
The scheme for the CT +HIS fusion method differ only from 
NSCT+HIS method in the applied CT . 
Figure 2. Image fusion flow chart of NSCT+HIS 
3. EXPERIMENTS AND FUSION RESULT 
ANALYSIS 
The tested remote sensing images consist of lm panchromatic 
and 4m multi-spectral IKONOS images. Figure 3 shows the 
fusion results of the IKONOS images. The visual inspection 
shows that the fused images produced by proposed algorithms 
have more details than that of the algorithm CT+HIS. 
Three different measures are used to evaluate the performance 
of the algorithms under investigation. These measures are: the 
normalized correlation, the entropy and the average gradient. 
Detailed equations of these measures can be found in the 
literature. Table 1 shows the results of the fusion experiment of 
the fused images where the correlation is measured between the 
PAN image and the corresponding gray fused image, and 
correlation between gray MS and gray fused image. The 
entropy and the standard deviation are measured for the fused 
images.