ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
  
images pairs. In our experiment, we have found a rule between 
RMSE and energy value: the RMSE drops as the energy 
value increases. Therefore, the energy value can be regarded as 
another measure for evaluating the accuracy of registration, 
replacing RMSE . The rule will be found in the following part 
A. In order to evaluate registration differences between our 
approach and manual methods, we replace 
(G, (x, y) G, (x, »)) in equation (13) with the transformed 
coordinate by using manual methods to compute the measures 
RMSE and max D in equation (12) and (14). All 
experimental results from our approach and manual methods 
are shown in Table I. 
In our experiment, the size of the experimental images is 
512x512 and the predefined thresholds are the same in all 
examples. In C, , the range of the translation coefficients is 20, 
and the range of the first and the second order coefficients is 
0.2. The number of the iteration times in GAs is 15, and € in 
inequation (9) is 0.5. 
3.1 Evaluating the accuracy of registration 
To evaluate the accuracy of our algorithm, we use PhotoShop 
software to clockwise rotate an image by 90 degrees. It is 
shown in Fig.l (a)-(b) Thus, we can know their optimal 
transformation parameters in advance. Two pairs of control 
points ((159,63), (451,163)) and ((423,468), (43,423)) are 
manually selected from the two images to compute initial 
guesses. 
   
(b) 
Fig.1. (a) initial image, (b) transformed image by 
clockwise rotating 90 degree of (a). 
For the manual registration method, 20 pairs of control points 
are manually selected to register the two images. 
From Table I we find that even though the initial guesses given 
are far from the optimal values; for example, RMSE is more 
than 3 pixels. Our approach can still yield a good result that is 
very close to the optimum; its accuracy is much higher than 
that of the manual method. 
3.2 Multi-temporal Image Registration 
Fig.2 (a)-(b) shows a pair of SOPT images acquired on 
different dates. 17 pairs of control points are manually selected 
to register two images, and its result is shown in Fig.2 (c). The 
result of our approach is shown in Fig.2 (d). Because this pair 
of images was taken from the same sensor but on different 
dates, an operator can easily select control points with 
reasonably high accuracy. From table I, the transformation 
parameters obtained by the manual method are very close to 
those by our approach, and the RMSE between them is less 
than one pixel. However, 
  
(c) (d) 
Fig. 2. Ca) the reference image (b) the sensed image; 
(c) registration by manual; (d) registration by our method. 
the registration results by our approach are better than those by 
the manual method because the energy value obtained by our 
approach is higher than those by the manual method. 
  
(e) (yc onrim ye. eni o hi 
Fig. 3. (a) SPOT image; (b) SAR image; (c) registration 
by manual; (d) registration by our method; (e) and (g) 
are two sub images cut from the image shown in ( c ); 
(f) and (h) are two sub images cut from the image 
shown in (d). 
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