The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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The nearest neighbor, bilinear, cubic convolution, and sine 
interpolators for resampling the slave image were all 
investigated. The 2D sine lengths include both odd and even 
numbers, varying from 2 to 8. Both sine add-ons: modulation 
and Hann window were demonstrated and applied. 
The coregistration performance was evaluated against the 
coherence of the two coregistered SAR images and the 
accuracy of the InSAR DEM. Our own program was developed 
to compute coherence. The results were compared to the 
coherence as computed by commercial software. The InSAR 
DEM was generated through commercial software. 
4. RESULTS AND ANALYSIS 
The average coherences computed from the master SAR image 
and the resampled slave SAR images were recorded into tables. 
The coherence comparison and analysis were conducted side by 
side. 
4.1 Coherences of Original and Coarse Coregistered SAR 
Images 
Searching Subpixel Tie Points and 
Offsets 
# of 
Pars 
Interpola 
tor 
Coherence 
Method 
Rate 
Kernel 
North 
South 
Original 
N/A 
N/A 
0 
N/A 
0.2554 
0.2542 
Coarse 
N/A 
N/A 
2 
N/A 
0.3181 
0.3517 
Table 1 Coherences of coarse coregistered SAR images 
Table 1 contains the coherences out of the original SAR images 
and coarse coregistered SAR images. If the coherence image is 
computed from the original master and slave images, the 
average coherence is 0.2554 for northern Indiana and 0.2542 
for southern Indiana. After the slave SAR image was shifted 
based on coarse coregistration, the average coherence became 
0.3181 for northern Indiana and 0.3517 for southern Indiana, a 
little higher than original SAR images. 
4.2 Coherences of Fine Coregistered SAR Images 
More factors were examined in fine coregistration for 
coherence evaluation. First, the approach of oversampling 
cross-correlation function peak was tested. The oversampling 
rate was 10. The oversampling kernel was Spline. 4-parameter 
transformation equations were used. The interpolators included 
Nearest, Bilinear, Cubic, and Sine with the lengths from 2 to 8. 
Modulation was applied to all sine interpolators. 
Searching Subpixel Tie Points and 
Offsets 
#of 
Pars 
Interpolat 
or 
Coherence 
Method 
Rate 
Kernel 
North 
South 
Fit Peak 
10 
Spline 
4 
Nearest 
0.4297 
0.3980 
Fit Peak 
10 
Spline 
4 
Bilinear 
0.4390 
0.4596 
Fit Peak 
10 
Spline 
4 
Cubic 
0.4450 
0.4461 
Fit Peak 
10 
Spline 
4 
Sinc2x2 
0.4482 
0.4177 
Fit Peak 
10 
Spline 
4 
Sinc3x3 
0.4500 
0.4201 
Fit Peak 
10 
Spline 
4 
Sinc4x4 
0.4507 
0.4217 
Fit Peak 
10 
Spline 
4 
Sinc5x5 
0.4506 
0.4218 
Fit Peak 
10 
Spline 
4 
Sinc6x6 
0.4500 
0.4213 
Fit Peak 
10 
Spline 
4 
Sinc7x7 
0.4499 
0.4213 
Fit Peak 
10 
Spline 
4 
Sinc8x8 
0.4498 
0.4211 
Table 2 Coherences of oversampling cross-correlation function 
After fine coregistration, the coherence increased significantly, 
even with only nearest neighbor interpolator. The coherence of 
nearest neighbor is 0.4297 for northern Indiana, much better 
than the coherence out of coarse coregistration (0.3181). The 
coherence of nearest neighbor is 0.3980 for southern Indiana, 
also better than the coherence obtained from coarse 
coregistration (0.3517). Bilinear yields higher coherence than 
nearest neighbor for both northern and southern Indiana 
(0.4390>0.4297 and 0.4596>0.3980). Cubic yields slightly 
higher coherence than bilinear (0.4450>0.4390) for northern 
Indiana, but slightly lower coherence than bilinear 
(0.4461 <0.4596) for southern Indiana, so there is not much 
difference in performance between bilinear and cubic in 
interpolation. 
Theoretically, sine interpolation should have higher coherence 
than cubic, bilinear, and nearest neighbor methods; and the 
longer sine length should have the higher coherence, but those 
are not always true. For northern Indiana, all sine interpolations, 
even the shortest one, 2-point sine (0.4482), have higher 
coherence than cubic and bilinear. The longer length has 
slightly higher coherence. After Sinc4x4 (0.4507), the 
coherence is reduced as the sine length is increased, i.e. sinc4x4 
seems to be the best interpolator in this table. If sine length is 
longer than 8, the coherence starts to fluctuate, although the 
overall trend is rising. For southern Indiana, the coherences of 
bilinear (0.4596) and cubic (0.4461) interpolation are 
significantly higher than all sine interpolation with bilinear 
providing the best results. The trend of sine interpolation is the 
same as northern Indiana, though the length of the highest sine 
coherence is 5. 
Table 3 shows the comparison between oversampling the cross 
correlation function by 10 times and by 100 times. 
Searching Subpixel Tie Points and 
Offsets 
#of 
Pars 
Interpolat 
or 
Coherence 
Method 
Rate 
Kernel 
North 
South 
Fit Peak 
10 
Spline 
4 
Sinc4x4 
0.4507 
0.4217 
Fit Peak 
100 
Spline 
4 
Sinc4x4 
0.4507 
0.4217 
Table 3 Coherences of different oversampling rates 
100 times oversampling rate does not have higher coherence 
than 10 times oversampling rate. The results confirm the 
average random phase error could be much bigger than 1/100 of 
a wavelength and the higher oversampling rate may not benefit 
significantly. 
Table 4 is the comparison among different number of 
parameters. 
Searching Subpixel Tie Points and 
Offsets 
#of 
Pars 
Interpola 
tor 
Coherence 
Method 
Rate 
Kernel 
North 
South 
Fit Peak 
10 
Spline 
4 
Sinc4x4 
0.4507 
0.4217 
Fit Peak 
10 
Spline 
6 
Sinc4x4 
0.4514 
0.4217 
Fit Peak 
10 
Spline 
12 
Sinc4x4 
0.4511 
0.4218 
Table 4 Coherences of different number of parameters 
From Table 4, one can find the number of parameters has no 
significant effect on the coherence. 4-parameter has been 
sufficient. 6 parameter transformation equations can model the 
small deformation with respect to azimuth pixels. The 2 nd 
ranked 12 parameter transformation equations could model 
more distortion for SAR images, although that is not necessary 
for this ERS SAR data.