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The International Archives of the Photogrammetry. Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beiiing 2008 
2>,-y,Xg'-g’.) C'„ (4) 
^(S, -«,)"£(«',“if,)’ V C n C '» 
Replacing g' 2 with c 0 +c,g 2 in (4) and after a series of steps 
can be reduced to: 
g,£(g,-g,)(&-£) _ C, 2 _ p 
} /^(g l -g l ) 2c ^(g2-g2) 2 V C n C 22 
Secondly, the following shows that the least squares matching 
and gradient cross correlation use the same criterion to estimate 
the unknowns. 
Least squares techniques minimise the sum of squares of 
observation errors or image intensity differences (3): 
^ vv = min 
Assuming g t and g 2 are normalised, then the linear 
radiometric correction coefficients can be obtained: 
C o = 0> c i 
= ¿Mi 
= s*; 
(5) 
y.vv can then be expanded using (3) and (5): 
/ jgl / ,gl 
R 2 ) 
both GCC and LSM matching. The further line search suggests 
improved cross correlation coefficients may be achieved with a 
few extra iterations. The duration of computation time is 
recorded for comparison purposes. The experiments were 
conducted on a DELL Pentium III personal computer with CPU 
clock speed of 1.70GHz and memory of 512MB. 
5. EXPERIMENT RESULTS 
The performance of the algorithm is examined for three pairs of 
images. The first pair (Figure 1) relates to the registration of a 
Landsat TM image from February 1992 (the middle image in 
Figure 1) to a rectified Landsat TM image from March 1995 
(the left image in Figure 1). The original TM image pixel size 
is 30m, and the rotation of the original image is about 9° from 
true north. The rectified Landsat TM image is in AMG 
(Australian Map Grid) zone 50, and the pixel size is 25m. 
The second pair relates to the registration of a Landsat MSS 
image from January 1987 (the right image in Figure 1) to the 
1995 Landsat TM image (the left image in Figure 1). The 
original MSS image pixel size is 57mx79m, and the rotation is 
again about 9°. 
Three control points were chosen around the large patch of bush 
in the rectified TM images: Point 1 is at the top right of the 
patch, Point 2 is at the bottom right of the patch and Point 3 is 
at the top left of the patch. Their corresponding points in the 
raw TM and MSS images were roughly located as the initial 
start points for registration. The correlation window size used 
is 41 pixels by 41 pixels. 
The relationship between ^ vv and R can be described using 
the following equation: 
1' 
= 1 -R 2 ,R = 
S' 
(6) 
(6) means that finding the minimisation of the sum of squares of 
intensity differences between the left and right image patches is 
equivalent to maximising the cross correlation coefficient 
between the two patches. 
4. IMPLEMENTATION 
A hierarchy of relationships between the affine transformation 
parameters can be specified in practice: r 
The third pair (Figure 2) relates to the matching of two 
QuickBird high-resolution satellite images, which were flown 
on June 19, 2003; the rotation between two raw images is about 
13°. Figure 2 shows a small isolated forest patch and the 
surrounding shadows. One point was selected on the treetops 
among the forest patch at the middle of the image and another 
point was selected at the shadow edges on the bare ground. The 
correlation window size used is 21 pixels by 21 pixels. 
Table 1 summarises the results for all models for the Landsat 
TM registration. For this example, Model-Ill (common pixel 
scaling and common rotation angle) should be appropriate. 
This is confirmed in Table 1, where the matching correlation 
coefficient for each control point for Model-Ill is similar to that 
for Model-I, Model-IIA and Model-IIB. Model-IV gives the 
worst matches. The results also indicate that GCC and LSM 
give similar results. 
• Model-I: different scale, different rotation (6 unknowns: 
two offsets, two scales, two rotations) 
• Model-IIA: different scale, common rotation (5 unknowns: 
two offsets, two scales, one rotation) 
• Model-IIB: common scale, different rotation (5 unknowns: 
two offsets, one scale, two rotations) 
• Model-Ill: common scale, common rotation (4 unknowns: 
two offsets, one scale, one rotation) 
• Model-IV: fixed scale, fixed rotation (2 unknowns: two 
offsets) 
In order to investigate the behavior of different models for 
various images, the above models were also implemented within 
two matching methods (GCC and LSM). Further, a quadratic 
line search strategy (Adby and Dempster, 1974) is applied to 
Table 2 summarises the results for the Landsat MSS 
registration. For this example, Model-IIA (different pixel 
scaling, common rotation) should be appropriate. This is 
confirmed in Table 2, where the matching correlation 
coefficient for each control point for Model-IIA is similar to 
that for Model-I. Model-IV gives the worst matches. Again, 
GCC and LSM give similar results for the appropriate model. 
The estimated line and pixel scaling are roughly consistent with 
the expected values: the line scaling should be about 25/57 = 
0.44, while the observed values in Table 2 are 0.40, 0.44 and 
0.45; and the pixel scaling should be about 25/79 = 0.32, while 
the observed values in Table 2 are 0.27, 0.30 and 0.30. 
Table 3 summarises the results for the QuickBird image 
matching. For both points (Points 1 and 2 in Table 3), the best