The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
DWT 
P (P=9 in 
signal at 
or a high- 
/2 
/2 
(8) 
d,j-i( n ’ k ) 
input signal 
the filtering 
(9) 
. We 
ring if b is 
boundary 
extension, 
padding, 
e shows the 
and the 
6 
The output values are computed by performing the inner 
products of the accessed pixel and the filter kernel coefficients 
(h and g). An indirect address table is designed to store the 
address of the input signals at different level. The width of table 
for a data sequence is w=l+K 0 -l, where / is the maximum length 
of the data sequence, K 0 is the width of the filter kernel. Figure 
6 shows the indirect address table (/=16, K 0 =5). 
f 0 
\T 
0 
nr 
4 
5 6 7 8 
i 
0 
Ï 
2 1 
LU 
3 ] 
LiJ 
5 6 7 8 
Figure 8. Grouping 
0 
I 
2 
3 
4 
5 
6 
T 
1 
T 
3 
Y 
5 1 
6 
T 
1 
T 
3 
m 
0 
T 
0 1 
F I 8 I 9~ 
ED 
I io! 
11 12 
0 
0 
0 
14 13 
Figure 6. The indirect address table 
The texture is organized with each row holding boundary 
extension, a and b values for one particular level of DWT. 
Inside each texel, channel R stores the indirect address of pixel 
with boundary extended. Channels G and B store a and b 
respectively. 
The 2D inverse DWT can be achieved by applying ID inverse 
DWT horizontally and then vertically. Let («)| and 
\y'j_ x («)} be the low-pass and high-pass signal at level j-1. The 
reconstruction of |/l (>?)} is given by 
Aj(n) = Yj h '^ À j-^ n ~ + Hs'( k )r'j-^ - k) ^ 
k k 
2) Upsampling and boundary extension as in figure 9. 
1 
2 
3 
4 
—4 
1 
0 
3 
4 
3 
5 6 7 8 
H PI II 11 El 
B Q H B H 
Figure 9. Upsampling and boundary extension 
3) Interleaving two groups of signal as in figure 10. 
Figure 10. Interleaving 
where h (k) and g\k) are low-pass and high-pass 
reconstruction filters respectively. Similar to the forward DWT, 
(10) can be rewritten as 
Once the indirect address table is ready, values in the next level 
can be reconstructed by convolution. Note that low-frequency 
elements must be multiplied to the low-pass reconstruction filter, 
while high-frequency elements must be multiplied to high-pass 
reconstruction. 
¿j( n ) = 2X-. 
k 
where f Z j_ x (j%k) returns the corresponding data in the up- 
sampled boundary-extended signal at level j-1. Express the ID 
inverse DWT to the form of signal input and output: 
input: 
Output: 
Figure 7. Mapping to the base position in ID invert DWT 
1) Halve the input signal as in figure 8. 
Now we get the method to realize the DWT on one image, but 
remote sensing image fusion has to deal with two images (the 
case that the number of images is more than two is based on the 
case of two images, so this paper analyses two images fusion), 
the storage and management of the intermediate data is the key 
point. 
This paper set a FBO for each of the image to be fused. Two 
texture objects are bind to the FBO of the first image: 
m_fbortl[0] and m_fbortl[l], the binding points are set to 
GLCOLORATT ACHMENTOEXT and 
GLCOLORATTACHMENT1 EXT. When DWT applied to 
the first image at level 1, the destination buffer is first set to 
GL COLOR ATTACHMENT 1 EXT, and load the image data 
to texture m_fbortl[l] which is bind to 
GLCOLORATT ACHMENT 1 EXT; then set the destination 
buffer to GLCOLORATTACHMENTOEXT, perform the 
horizontal ID DWT fragment shader and store the result to 
texture m_fbortl[0]. Then set the destination buffer to 
GLCOLORATTACHMENTIEXT, perform the vertical ID 
DWT fragment shader and store the result to texture 
m_fbortl[l]. At level 2, the source data is the data in texture 
m_fbortl[l], the destination buffer of horizontal ID DWT is set 
to GL COLOR ATTACHMENTO EXT and then the vertical 
is set to GL COLOR ATTACHMENTI EXT. So the result of 
the 2D DWT is stored in m_fbortl[l] too. Because the 2D 
DWT is achieved by exchanging the buffers twice at each level,