International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
  
m-}n-}l 
H(X |Y)=-} > p(b,)p(a, | b,)log p(a, | b;) 
7=0 j=0 (2) 
n-lm-l 
HULK) = => > p(a;)p(b; | a;)log p(b, | a;) 
j=0 i=0 
where, p(ajb) and p(bja;) are conditional probability, 
respectively. Using these information content, Rajski distance 
p (X, Y) is defined by the following formula. 
MX H(X Yy* HQ X) 3) 
H (XY) 
In addition, the range of this Rajski distance is 1 or less and 0 or 
more, it takes 0 when two probability phenomenon systems are 
in agreement, and it takes 1 when these are independent. 
  
2.2 Calculation Technique of Rajski Distance from 
Polarimetric SAR Image Data 
As the technique of calculating Rajski distance using 
polarimetric SAR amplitude image data, the method by co- 
occurrence matrix used in texture analysis is applied. This 
matrix constructs a square matrix with the size of N x N, when 
the gray level in a partial image is set to N. In this matrix, when 
a pixel value is taken in the position with row and column, the 
clement is appearance probability of pixel with the combination 
of the pixel value. This matrix is called gray level co- 
occurrence matrix (GLCM). When GLCM is used for texture 
analysis, the pixel value of the circumference pixel which takes 
the pixel value of an attention pixel in the row direction of a 
procession, and is about an attention pixel and its contiguity 
pixel in the same picture at the place which only a specific 
distance separated from the attention pixel with the specific 
angle in the direction of a sequence is taken. Generally the 
distance between attention pixel and contiguity pixel is one, and 
an angle is taken at 0, 45, 90, and 135 degrees (Haralick, R. M., 
et al., 1973). 
In this paper, it considers constituting GLCM from combining 
two kinds of polarization from the amplitude image to HH, HV, 
and VV polarization used in many cases for visualizing of 
polarimetric SAR data. When the gray level of one of amplitude 
image is set /, and that of another amplitude image is set /, the 
frequency of appearance of the combination of the gray level is 
expressed with P(7, j, q). Where, q expresses the combination of 
transmit and receive polarization. The element of GLCM p(i, j, 
q) can be expressed as follows. 
c P(i, j.q) (4) 
PU, j.q) = Y Nd P . 
i=0 j=0 AS 
[n this formula, N is the number of gradation. GLCM [G(4)] for 
combination of polarization q is expressed as follows. 
p(0,0,4) p(0,N —1,q) 
[G(q)] = : d 
pON —1,0,4) pON —1, N —-1,q) 
In the case of SIR-C, combination of polarization q ^ 3; HH- 
VV, HH-HV, and HV-VV. 
Next, the technique of calculating co-occurrence matrix to 
Rajski distance is described. In the two kinds of transmit and 
receive polarization amplitude images, the probability that the 
pixel value will appear in one of images is corresponded to the 
probability phenomenon system X, and the probability that the 
pixel value will appear in another image is corresponded to the 
probability phenomenon system Y, respectively. Using the 
elements of co-occurrence matrix, joint entropy for the 
combinations of transmit and receive polarization q is obtained 
as follows. 
22 
N-IN-I 
HY ) 2 - 3. pli,j.q)log pli, j,q) (6) 
i=0 j=0 
And the conditional information contents are also obtained as 
follows. 
N-IN-I 
je pG, j. 4) 
H,(Xx|Y)=- pj. log Usi 
à 2 2 p,(J) (7) 
N-IN-I p, j.q) 
HQ | X) 2 - 3 Y. pi. j.q)log 25 
j=0 i=0 pi) 
Using these information contents, Rajski distance p(g) for the 
combinations of transmit and receive polarization q is obtained 
the same as equation (3). 
2.3 Creation of Rajski Distance Image 
The algorithm that creates Rajski distance image constructed by 
assigning Rajski distance obtained from two kinds of single 
polarization amplitude image to pixel value is described. Main 
processing that creates Rajski distance image is as follows. 
2.3.1 Extraction of Sub Area: To construct co-occurrence 
matrix, sub areas are extracted with M x M pixels. Note the size 
of sub areas because reliability of co-occurrence probability 
will decline with too small size and influenced area of tiny 
noise that appears in sub area will be spread with too large size. 
2.3.2 Construction of Co-occurrence Matrix: In the 
extracted sub area, the appearance frequency for the 
combinations each pixel value of two amplitude images are 
calculated and co-occurrence frequency matrix is constructed. 
Each element in the frequency matrix is transformed to 
probability using the size of sub area. 
2.3.3 Calculation of Information Contents: Joint entropy 
and conditional information contents are calculated using the 
constructed co-occurrence matrix. 
2.3.4 Calculation of Rajski Distance: Rajski distance is 
calculated for attention pixel using obtained joint entropy and 
conditional information contents. 
2.3.5 Quantization of Rajski Distance to Pixel Value: 
Calculated Rajski distance is quantized to pixel value that set a 
limit from 0 to 255. The range of Rajski distance corresponds to 
one gray scale of pixel value is 1/256. 
Reiterating a series of these processing for whole pixels with 
scanning to x and y direction in two images, Rajski distance 
image is created. The outline of this process is illustrated in 
Figure 1 (Yamada, T. and Hoshi, T., 2002a). 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Amplitude [ | Rajski distance 
image 1 image 
(Polarization A) 7 J 
Z N 
| Attention pixel 
Amplitude 
image 1 i 
<< Sub area to construct 
  
(Polarization B) 
  
  
  
  
  
  
  
  
co-occurrence matrix 
  
  
  
  
Figure 1. Creation process of Rajski distance image 
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