The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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x = {A t A)' A t B 
(4) 
Calculating the gradients in x and y directions of the quadric 
surface and form the equations, 
— = 2 ax + cy + d = 0 
Sx 
S z 
— = 2 by + cx + e = 0 (5) 
5y 
There is an extreme point at (x a , y a ) , 
2 db - ce 2 ae - dc 
where X = — , V = — . If the value at 
" c 2 -4 ab c 1 - 4ab 
this point is maximal in the window, then the precise position of 
the feature point is at (x + X a , y + y a ) . 
2.2 Image Matching 
The matching method is based on normalized cross-correlation 
and conformal transformation techniques. The normalized 
cross-correlation is used to compare the similitude of the 
matching points in the template searching window. The 
conformal transformation technique is used as an assistant when 
the correlation coefficient is not very high (Deng, and Wang, 
2005). Figure 3 shows the flowchart of matching algorithm. 
During feature matching by the method of template matching 
and conformal transform, the thought of matching principle 
based on bridge mode method (Zhang, etc., 1998) on initiate 
matching points was introduced, to eliminate the low precision 
effect on the following matching points. The effect is caused 
by the cumulated error due to the low precision of initiate 
matching points. 
To get four comer s’ coordinates of the target 
To get control points from source image 
i 
To detect the target point in the prediction 
searching window 
To compare the similitude of the points by 
normalized cross-correlation and conformal 
transformation techniques 
To determine the matched points 
To find out the accurate matching site into 
sub-pixel by the surface fitting method 
Fig.3: Flowchart of Matching Algorithm 
3. EXPERIMENTS 
The proposed method has been tested by three pairs of overlap 
SPOT images. Two pairs were captured in the same time, 
located in flat area and mountainous area respectively. One 
pair was captured in different time. The images were 
geometric rectified respectively. Table 1 shows the tie points 
accuracies which were calculated according to the transform 
formula. 
Different image pairs 
Root mean square errors 
Flat area 
0.0641 
Mountainous area 
0.6235 
Different acquisition time 
0.5775 
Table 1: The position matching accuracy of the experimental 
data (unit: pixel) 
In the flat area, the geometric distortion is low. The matching 
points on the overlap area have high correlation and with high 
matching accuracy. In the mountainous area and in different 
acquisition time, the image distortion is high. The matching 
points not only have differences in radiant value, but also have 
distortions in geometry (such as, shift, scale, rotation, etc.). 
Thus the conformal transformation techniques were used to 
improve the matching accuracy. Figure 4 shows the matching 
results of the 3 pair images.