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# Full text

Title
The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics
Author
Chen, Jun

ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001
376
1) is chosen
(p(x) = 1 - |x|
if
x e [- l,l]
(/)(x) = 0
f
x <£ [— l,l]
Figl : linear interpolation
By computation, we can get h(-1) = 1/4, h(0) = 1/2, h(1) = 1/4.
) = \^ x+ ')+- 0
C+i (x ) = — C, (x - 2 ' ) +—C, (x ) + — C, (x + 2 1 )
Therefore we have
The figure 2 shows the wavelet associated to the scaling
function.
Fig2: wavelet ijj(x)
The above £ trous algorithm is easily extensible to the two
pixels for the wavelet connected to linear interpolation. The
At each scale j, we obtain a set of Wj(x) (we also call it wavelet
plan) which has the same number of pixels as the image.
If a B 3 -spline for the scaling function is chosen, the coefficients of
convolution mask in one dimension are (1/16,1/4,3/8,1/4,1/16),
and in two dimensions
1
1
3
1
1
256
64
128
64
256
1
1
3
1
1
64
16
32
16
64
3
3
9
3
3
128
32
64
32
128
1
1
3
1
1
64
16
32
16
64
1
1
3
1
1
256
64
128
64
256
3.Detecting Edges Using the A Trous Algorithm
From above analysis, it is found that an image can be
decomposed into several wavelet planes at different scales,
some of high frequency information is included in the
wavelet planes. Therefore we can detect edges of a remote
sensing image by using the following procedure
1) Initialize i = 0, and input an original image fi(x,y);
2) Convolute the image with the low pass filter h(x,y)
fi+i(x,y) = fi(x,y) * h(x,y)
3) Get a wavelet plan
w i+ i(x,y) = fi(x,y)-f i+1 (x,y)
4) If i < n (the n is defined the decomposition number)
5) Repeat the steps 2), 3), 4) until i = n.
In order to process the image borders, the mirror symmetry