The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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among images (Kilic, S. et al, 2006). This method firstly 
calculates a standard transformation matrix. Then, the new 
image, namely principal component data, is obtained from the 
input image based on the transformation matrix. At last, the 
results of change detection may be acquired using image 
difference method. 
Figure 1. The constitution of the change polygon system 
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Suppose a vector of n dimension image X = [*,, x 2 , • • •, x n ] 7 , 
which is performed using a linear transformation. Namely, 
Y = Q T X 
(1) 
Where, Q = [Q,,Q 2 ,-. 
. q ] is an orthogonal 
matrix. The 
covariance matrix is: 
* 
II 
* 
-E(X)I(X-E(X)r} 
(2) 
Because G. is a real and Symmetrie matrix, an orthogonal matrix 
Q =[ß,,ß 2 , .ßj 
consequentially exists, 
and makes 
0GQ become a diagonal matrix. That is: 
orthogonal transformation is performed on original image, the 
principal component Y = \Y ,Y ,-,Y ] T is obtained. The 
12 M 
change detection may be used to the second components 
because the change targets are mainly displayed in the second 
components transformed. 
Canonical correlation analysis is a kind of the statistical 
analysis methods that analyzes the linear relationship between 
two random variables (Chen Lei et al, 2007). The idea means 
that canonical transformation is applied to the image using the 
different linear combination transformation, in which a 
transformation of the largest correlation coefficient can be 
found. In fact, the method can be converted to the problem of 
solving eigenvalues and eigenvectors. 
Suppose that the covariance of the random variable [x Y] 
is£, andf/ = a T X V = b T Y. X ma Y be separated and written 
as: 
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prob 
the < 
detei 
QCO = 
x i 0 
X 
(3) 
Solve the eigenvalues of the image matrix G, 
and calculate the correspond eigenvectors Q . After the 
(4) 
Canonical correlation analysis means that the linear 
transformation is performed to the random variable [jf Y\, 
and make the coefficient vectors a and b of U = a T X and 
V = b T Y meet: