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Digital Image Processing 2
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A method for cloud of classification of AVHRR image data with fractal dimension
Fractal dimension
- Calculation method of fractal dimension in this study
There are several ways of calculation of fractal dimension (hereafter FD). Procedure we used is described below:
Calculation is performed along two lines whose middle point is the pixel considered (FD is estimated pixel by pixel)-----------i.e. local latitude and longitude lien. (See fig.1 (a).) values of pixels along those two lines are calculated into the estimated fractal dimension. Mean of two calculated fractal dimensions along each line is considered to be the fractal dimension belonging to the pixel.
Fractal dimension along a lone is calculated in this way. See Fig. (b), where I is values of pixels and I is the length of domain C. First, we calculate n (r) below for all a in (0,l - b + a).
n(r) = ( | I(a) - I (b) | / r ) + 1 .................(1)
Next, using mean n(r) for all a, N (r) is derived.
N(r) = n(r) I / r ..........................(2)
N(r) is calculated for all r in (0,I), and the gradient of the regression line of log N(r) and log r is the estimated fractal dimension.
Figure 1: (a)The lines along which fractal dimension is calculated.
(b) Calculation of fractal dimension along a line.
- Examples of FD calculation
As written in chapter 1, fractal dimension of coast liens and tidal fronts is not so large as that of cloud. That is a merit of using fractal dimension for texture representation of variance or difference.
Fig. 3 (a) and (b) shows values of difference and fractal dimension of each pixel in the image shown in fig. 2. (Local differences assigned to each pixel in this image is defined as follows[5]:
S = |a0 - a1| + |a0 - a2|+ |a0 - a3|+ |a0 - a4| / 4 ..........................(3)
Where a0 is the values of ch4 temperature of the pixel considered, and a1- a4 are those of the neighborhood pixels show in Fig. 4) in Fig. 3(a), coast and tidal fronts have large value of difference like clouds, while in fig 3 (b), they are not clearly seen.
Figure 4 : Neighborhood pixels considered when calculating difference
These results suggests that if we use fractal dimension to represent different textures, we can distinguish low clouds and coast liens or tidal fronts more effectively than when using difference.
Figure 2: Original image (NOAA-10. 1987.5.9.1sh. ch1).
Figure 3: (a) The brightness of each pixel in this image represents the
value of local difference around the pixel in fig.2 image.
The difference is calculated by eq. 3.
(b)The brightness represents fractal dimension of fig. 2.
Figure 4: Neighborhood pixels considered when calculating difference.
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