The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part Bl. Beijing 2008 
After windowing, modulation, and normalization, the value of 
the interpolated point is: 
£x(/fc)F(* - m)W(k - m)M(k - m) 
Eq. (9) is only for one dimensional (ID) data, or one 
row/column of a SAR image. To resample the 2D SAR image, 
one can apply Eq. (9) separately: range interpolation and 
azimuth interpolation. If the sine length is S, (S+l) ID 
interpolation computations are needed, S of which are 
performed along the range (rows) around the interpolated point 
and the (5+/)th ID interpolation computation is for 
interpolating the S interpolated range values along azimuth 
direction (columns). One can find more explanation about the 
above equations in the ESA manual (ESA, 1999). 
The non-zero Doppler centroid for ERS SAR images is only 
along the azimuth direction. No modulation is needed for range 
interpolation, and only azimuth interpolation requires 
modulation. 
In this research, two ID sine interpolations were not employed 
separately, but one 2D sine interpolation simultaneously. The 
2D separable sine function is applied: 
computed to evaluate InSAR DEM accuracy, in order to 
evaluate SAR image coregistration. 
3. DATA, TOOLS AND EXPERIMENT 
3.1 Data and Tools 
As the SAR data, two pairs of ERS-1/2 tandem mode single 
look complex images were used. Those ERS SAR data were 
granted through project 3889 by ESA. 
The first pair consists of one ERS-1 image acquired on 
November 8, 1995, and one ERS-2 image acquired on 
November 9, 1995. The rough perpendicular baseline between 
them is 236 meters. This pair covers about 10 counties in 
northern Indiana, USA. This area is a flat area. 
The second pair consists of one ERS-1 image acquired on 
October 20, 1995, and one ERS-2 image acquired on October 
21, 1995. The rough perpendicular baseline between them is 
145 meters. This pair covers about 10 counties in southern 
Indiana, USA, a more hilly area. 
The reference DEM was produced from the “Indiana 2005 
State-wide Orthophotography Project”, which includes a high 
resolution DEM (Orthophoto DEM). The DEM has 5-foot 
(~1.5m) post spacing and 6-foot (~1.8m) vertical accuracy at 
95% confidence level. 
F(n x ,n y ) = Sinc\n{n x + A x )]Sinc[7r(n y + )J, 
2 2 
A,,A, e[-0.5,0.5) 
(S,-l) 
2 
(10) 
Matlab is the main tool that was employed for SAR image 
coregistration and coherence computation. Leica ERDAS 
IMAGINE was used for generating a final InSAR DEM. 
3.2 Experiment 
The sine length S can also be different for range and azimuth 
direction. All the other additional equations also need 
modifying to 2D cases accordingly, except Eq. (8), where the 
modulation is still applied one dimensionally, i.e. in the 
azimuth direction. The computational effort for 2D sine 
interpolation is one ID interpolation less than two separate ID 
sine interpolations. 
The sine length S is an odd number in Eq. (10). It can also be 
even number too. Hanssen and Bamler simulated sine 
interpolation with sine length of even number (Hanssen and 
Bamler, 1999). The paper from the European Space Agency 
proposed a sine length of odd number. In this research, sine 
lengths of both even and odd numbers are applied. 
These algorithms are applied and discussed with real ERS SAR 
data. The advantage and disadvantage of using sine 
interpolation are discussed in this investigation. 
2.2.4 Coregistration Evaluation 
Most InSAR researches apply the coherence image to evaluate 
the performance of SAR image coregistration. In this study, the 
average of the whole coherence image is used as criteria, to 
evaluate the coregistration results from the above coregistration 
functions and algorithms. 
The final InSAR DEM is certainly another good criterion for 
estimating SAR image coregistration. The better coregistration 
performance should result in a higher InSAR DEM accuracy, 
i.e. a lower InSAR DEM error. The Root Mean Square Error 
(RMSE) between the InSAR DEM and the reference DEM is 
The experiments for SAR image coregistration were also 
motivated by the rapidly improving hardware capabilities, 
while it was not easy to implement these computationally 
intensive algorithms before. These SAR image coregistration 
algorithms can now be evaluated in a different computational 
environment. 
The main experiment is to examine and compare interpolators, 
including nearest neighbor, bilinear, cubic convolution and sine 
function, implement and verify sine add-ons for SAR image 
coregistration, using ERS SAR data. 
For coarse coregistration, complex and magnitude only were 
tested and compared for cross-correlation computation. The 
magnitude only should be good enough for coarse 
coregistration. 
More experiments were performed for fine coregistration. To 
obtain subpixel cross-correlation peak, both oversampling 
cross-correlation function and oversampling SAR images were 
tested and compared. Also 1/10 pixel accuracy requirement was 
examined by comparing oversampling cross-correlation 
function by the factors of 10 times and 100 times. 
Four parameter transformation equations, which are sufficient, 
were mostly agreed. Six and 12 parameter transformation 
equations were tested as well, and it is interesting to see how 
much the coregistration can be improved using these higher 
ordered transformation equations, considering computation 
effort is not the issue as it was in the 1990's. 
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