Thë International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beiiing 2008 
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matches are always given by Model-I for all three matching 
methods, and Model-IIB gives the second best matches. 
Model-IV is the worst model for matching treetop point 1 and 
ground point 2. The correlation coefficients also show that the 
treetop point is more difficult to be matched in comparison with 
the ground point. The reason may be due to the mixed texture 
and complicated geometry at the treetop. 
More QuickBird matching experiments (not presented in this 
paper) also confirm that, due to the view angle changes of 
QuickBird sensors and the changing angle between an object 
and its shadow (in particular between tree shadow and tree), 
high-resolution satellite imagery such as QuickBird requires a 
well-defined geometric model for their image registration and 
matching; in this case, Model-I seems the appropriate choice. 
Incorporating a quadratic line search with GCC or LSM 
matching often improves the convergence and leads to a higher 
matching correlation. From both GCC and LSM line search 
results, it shows a very slight improvement of matching (cross 
correlation coefficient) within a few extra iterations. 
The function maximisation procedures require a tolerance 
which indicates when successive function values are sufficiently 
similar. Tables 1-3 also list the number of iterations (maximum 
is 50). This very limited comparison suggests that a tolerance 
of 0.002 gives similar results to those obtained from a more 
stringent convergence tolerance, in about one third of the 
number of iterations. 
Figure 1: Segments of Landsat scenes (path 111, row 84). Left 
image: segment of the rectified TM scene for Band 3, March 
1995 (map grid: AMG, pixel size: 25m). Middle image: 
segment of the raw TM scene for Band 3, February 1992 (pixel 
size: 30mx30m). Right image: segment of the raw MSS scene 
for Band 2, January 1987 (pixel size: 57mx79m). 
Figure 2: Left and right images are two segments from a raw 
QuickBird stereo pair for multiple-spectral band 4, June 2003 
(pixel size: approximately 3mx3m). 
GCC 
LSM 
Point 
Model 
Corr. Score 
Iter. 
Corr. Score 
Iter. 
1 
Model-I 
0.87377 
50 
0.87377 
11 
Model-HA 
0.87245 
11 
0.87245 
11 
Model-IIB 
0.86975 
10 
0.86975 
11 
Model-IH 
0.86961 
12 
0.86961 
50 
Model-IV 
0.86844 
10 
0.86844 
11 
2 
Model-I 
0.89668 
14 
0.89669 
13 
Model-HA 
0.89618 
12 
0.89618 
12 
Model-IIB 
0.89665 
16 
0.89665 
14 
Model-III 
0.89609 
13 
0.89609 
15 
Model-IV 
0.89367 
10 
0.89367 
11 
3 
Model-I 
0.97144 
11 
0.97144 
11 
Model-IIA 
0.97139 
11 
0.97139 
11 
Model-IIB 
0.97034 
9 
0.97034 
9 
Model-III 
0.97041 
12 
0.97030 
8 
Model-IV 
0.96727 
10 
0.96727 
10 
Model-IV 
0.74198 
3 
0.74198 
2 
Table 1: GCC and LSM sub-pixel matching a raw Landsat TM 
image from February 1992 (centre image in Figure 1) to a 
rectified and resampled TM image March 1995 (left image in 
Figure 1) for three ground control points (average computing 
time is 0.03 second per point). 
GCC 
LSM 
Point 
Model 
Corr. Score 
Iter. 
Corr. Score 
Iter. 
1 
Model-I 
0.88635 
20 
0.88635 
18 
Model-IIA 
0.88634 
20 
0.88634 
18 
Model-IIB 
0.84573 
31 
0.84575 
31 
Model-IH 
0.84558 
28 
0.84558 
19 
Model-IV 
0.75940 
22 
0.75940 
22 
2 
Model-I 
0.84540 
44 
0.84540 
23 
Model-IIA 
0.84542 
21 
0.84542 
20 
Model-IIB 
0.82646 
21 
0.82647 
23 
Model-HI 
0.82466 
40 
0.82467 
29 
Model-IV 
0.75606 
32 
0.75604 
31 
3 
Model-I 
0.93416 
15 
0.93416 
15 
Model-HA 
0.93360 
15 
0.93360 
15 
Model-HB 
0.88439 
16 
0.88439 
16 
Model-HI 
0.88151 
17 
0.88149 
16 
Model-IV 
0.85979 
19 
0.85979 
19 
Table 2: GCC and LSM sub-pixel matching an original Landsat 
MSS image from January 1987 (right image in Figure 1) to a 
rectified and resampled TM image March 1995 (left image in 
Figure 1) for three ground control points (average computing 
time is 0.04 second per point). 
GCC 
LSM 
Point 
Model 
Corr. Score 
Iter. 
Corr. Score 
Iter. 
1 
Model-I 
0.75367 
9 
0.75367 
13 
Model-HA 
0.63904 
50 
0.63933 
50 
Model-HB 
0.67154 
7 
0.67205 
50 
Model-III 
0.58464 
50 
0.58461 
13 
Model-IV 
0.48116 
5 
0.48116 
4 
2 
Model-I 
0.93372 
22 
0.92689 
14 
Model-HA 
0.92933 
50 
0.92693 
50 
Model-HB 
0.92534 
50 
0.92358 
50 
Model-HI 
0.92357 
50 
0.92320 
50 
Model-IV 
0.89629 
4 
0.89629 
5 
Table 3: GCC and LSM sub-pixel matching of two QuickBird 
bush images for treetop point 1 and ground point 2 (average 
computing time is 0.03 second per point). 
6. CONCLUSION AND DISCUSSION 
The correlation results from the gradient cross correlation are 
nearly identical (both the matching results and iterations) to 
those of the least square matching. However, the gradient cross 
correlation method combines radiometric correction and 
geometric correction into a single step, which makes its 
parameter estimation and practical computation implementation