International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
  
where Z,= a center pixel value in the window 
Z = a pixel value except the center 
x. = a center pixel value after filtering 
  
Fig. 1. Filtered SAR image (Path =416, Row =315, Tabajara) 
Next, to extract the only river shapes, we applied binarizing and 
thinning for the images (Fig. 2). First, we obtained the 
coordinates through the river path at every constant interval, 
and calculated each angle from the adjacent line segment (Fig. 
3). We determined this constant length was 20 pixels (500 m) 
because the smallest river wavelength was approximately 500 
m. By this technique, we transformed the river shapes into a 
one-dimensional signal (Fig. 4). This signal showed that a small 
meandering had high frequency and big amplitude, while a 
large meandering had low frequency and small amplitude. 
at 
  
Fig. 2. Binarized image (Path =416, Row =315) 
  
Fig. 3. Method of one-dimensional transformation 
890 
angle [degree] 
90 
60 
-60 
-90 
100 150 200 
Length [pixel] 
Fig. 4. One-dimensional signal (Path = 416, Row = 315) 
Next, to analyze the spatial frequencies or the characteristics of 
the river shapes, we applied the Fourier and continuous wavelet 
transforms for the one-dimensional signals. In this technique, 
we could treat the river shapes in the spatial frequency domain. 
The mother wavelet that we applied was the Gabor wavelet 
expressed as the equation (3), which showed the best fitting 
wave for the original wave (Fig. 5). The wavelet's scale was 
equivalent to the frequency, and then the bigger scale was 
equivalent to the lower frequency. We show the space- 
frequency two-dimensional plane where an x axis corresponds 
to the spatial scale, a y axis corresponds to the wavelet's scale, 
and a z axis corresponds to the spectral intensity (Figs. 6 to 9). 
  
| A 
W(b,a)=— | f(x “1d 
| T. [Aw dx 
(3) 
] x 
w(x) =——=—cxp| —— |expl ix 
y ee p(ix) 
W(b.a) spectrum intensity 
f(x) = original signal 
w(x) = mother wavelet 
a = scale 
b = position 
where 
0.15 
0.1 
0.05 
20 0 10 20 30 
Fig. 5. Real part of Gobor wavelet 
-10 
Moreover, we applied the multi-resolution analysis with a 
discrete wavelet transform to the original signals. In this 
technique, we analyzed which level of that frequency was 
included in which part of the signals. The level corresponded 
to the frequency, and then the higher level was equivalent to 
the lower frequency. This mother wavelet that we applied was 
the Daubechie's wavelet.