The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part Bl. Beijing 2008 
the transformation equations. The coregistration performance is 
usually evaluated by coherence and the accuracy of the final 
InSAR DEM. Figure 1 is a typical work flow for SAR image 
coregistration. 
Figure 1 Typical flow chart for SAR image coregistration 
2.1 Coarse Coregistration 
Coarse coregistration is the step where two SAR images are 
coregistered at up to one or two pixels accuracy. One of these 
two SAR images must be assigned as the master (reference) 
image and another one is the slave (match) image. Through the 
whole coregistration process, only the slave image will be 
shifted in coarse coregistration and resampled in fine 
coregistration. Usually the image located closer to the target of 
interest is selected as the master image to provide the best 
geometry. (Leical, 2007) 
Cross-correlation (Li and Goldstein, 1990; Liao et al., 2004) is 
the most commonly used approach for coarse coregistration. 
The algorithm is simple to implement, the speed and accuracy 
are acceptable, and it is not data sensitive and can be applied in 
automatic InSAR processing easily. Cross-correlation can be 
calculated in frequency domain for the faster processing. 
After all patch pairs with good cross-correlation are finalized, 
the average peak coordinates are computed and regarded as 
range and azimuth offsets between two SAR images. The slave 
SAR image will be shifted by the range and azimuth offsets. 
2.2 Fine Coregistration 
2.2.1 Searching for Subpixel Tie Points 
The first question about this process that one needs to address is 
how fine the coregistration should be, 1/2, 1/5, 1/8, 1/10, or 
1/20 pixel? In 1990, Li and Goldstein found the phase error was 
about 30 degrees when the signal-to-noise ratio (SNR) was 16 
dB for SeaSAT SAR interferometry (Li and Goldstein, 1990). 
Later, 40 degrees phase random error (equivalent to 20~30 
meters vertical DEM error) was commonly utilized for ERS 
SAR interferometry. Because the phase range for SAR images 
is always 360 degrees (2n), roughly 1/10 pixel has become 
widely accepted for fine coregistration (Hanssen and Bamler, 
1999; Kwoh et al., 1994; Rufino et al., 1996; Rufino et al., 
1998). 
Cross-correlation is not only for coarse coregistration, but also 
a common criterion for fine coregistration. There is 
disagreement as to the best way of obtaining subpixel offsets. 
Some researchers oversampled the coarse cross-correlation 
peaks and looked for the subpixel peaks. Li and Goldstein 
sought the maximum subpixel peaks by a linear fit 3-point 
interpolation, achieved the subpixel accuracy of 0.05 pixel (Li 
and Goldstein, 1990). Other researchers oversampled SAR 
image patches, computed cross-correlation of the oversampled 
SAR images and searched for the peaks. Rufino et al. searched 
for subpixel tie points by oversampling both image subsets by 
10 times with a cubic B-spline algorithm (Rufino et al., 1996; 
Rufino et al., 1998). Kwoh et al. moved one image chip by 0.1 
pixels for each cross-correlation computation, which can be 
considered as equivalent to oversampling images by 10 times 
for subpixel coregistration (Kwoh et al., 1994). 
Using complex data or magnitude only for cross-correlation 
computation is also an issue for fine coregistration. Complex 
data containing both magnitude and phase information, could 
provide more information for cross-correlation computation, 
but could also introduce phase spectrum noise when the 
decorrelation is significant. Prati and Rocca used complex data 
for coregistration (Prati and Rocca, 1990). Kwoh et al. 
concluded that magnitude only cross-correlation was better than 
complex cross-correlation for ERS SAR data (Kwoh et al., 
1994). Rufino et al. used magnitude only as well (Rufino et al., 
1996; Rufino et al., 1998). 
2.2.2 Fitting Transformation Equations 
After coarse coregistration, the remaining offsets between two 
SAR images mainly exist in range direction. That is because the 
parallel baseline component (Z?n) between two platforms varies 
almost linearly from near range to far range. (Li and Goldstein, 
1990). The resulting change of offset is limited to approximate 
two pixels for ERS SAR images. Very small offsets in the 
azimuth direction can be detected after coarse coregistration. 
(Rufino et al., 1996; Rufino et al., 1998) 
Thus a number of researchers apply only the following four 
parameter transformation equations (Eq. (1)) onto subpixel tie 
points. 
X - x + ax + c 
Y = y + dx + f (1) 
(X, Y) are the coordinates of tie points in the slave image, and (x, y) are 
the coordinates of corresponding points in master image. There is no 
first order coefficient for y, because most offsets are only 
proportional to the range pixel location. These equations are 
sufficient for ERS tandem mode SAR images. They are also 
employed in commercial software packages, like ASF SAR 
tools and Leica ERDAS IMAGINE. 
If there is more distortion along the y direction, one can use the 
6-parameter, first order transformation equations: 
JX-x + ax + by + c fX-ax + by + c 
\Y = y + dx + ey + f [Y-dx + ey + f ^ 
Sometimes the 12-parameter second order transformation 
equations for highly distorted SAR images are applied. The 
second order equations are more than adequate for ERS tandem 
mode SAR images. However, in some investigations, even