The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
127 
/(*) = 
^ e - N (x- M ) 2/ 2a 2 
Jlncr 
According to local road model in the fig. 1, we define variable 1, 
m, r present the different region from left to right, and have the 
X X X 
mean pixel random variable 1 , m , r respectively, at 
same time we consider they are independent. Then we get the 
ratio random variable that is left region to middle area (road 
. R lm =X./X r 
/ ,m i r) 
region) is 
R l,m 
for example; then the PDF of 
the 
f R , m (y) = ¡Myxjf m (x m )x m dx, 
0 
■IT 
-W 
2o 
la 2 
■dx_ 
jN,N m 
•JIko-JIko 
(.N,y 2 + N m )x m 2 - 2(N,/jy + N m n)x m + (N m + N,)^ 
la 1 
-K 
0 
<jN,N a /i(N m +N,y) ^ 
j2^a{N m + N,y 2 ) 3/2 £XP { 2(N m + N,y 2 )a 2 
2 no 
N,N m S(y- l) 2 
-dx_ 
M 
As SAR image data has its own distribution characteristics, 
2 
and has correlation don’t like ordinary Gaussian 
k = JLl/<J 
distribution. Let 
, then 
f (y) = M^lML exp 
A '- W TU(N m + N,y^ eXP 
2(N m+ N,y 2 ) 
N 
Where 1 present the pixel numbers of the left region in 
N ... 
Figure 1; m is the pixel numbers of the middle region (road). 
We can get Rr m at the same deduction. From above, we 
can get the conclusion that the model performance is relative 
N. N N m , , 
to ' , or r , and k these parameters. 
3.3 Uncertainty analysis of parameters selection 
N N N 
1 , or r , m and k are the key parameters to the results. 
In the paper, we consider these parameters are all random 
variables. Through analyzing how to select value can get better 
roads extracted performance, we should commence on local 
roads model built on statistical theory. Due to statistical theory, 
every local region should include enough pixels to reduce the 
effect of random error. That is to say local region should be as 
larger as possible; this will mislead to the label of other ground 
objects other than roads. So the region should be proper. 
Through theory analysis, we drew the PDF of 
N, N. 
T, 
as 
and k changed separately. 
f R (^) 
Figure 3: The PDF curves of / m with parameters 
changed