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Mingsheng Liao 
  
24 The Criteria for LS Matching Iterative Procedure 
Since the LS matching is an iterative procedure, the criteria for the matching should be selected to decide whether the 
iterative is stopped. Herewith the correlation coefficient of the SLC images is used as the criteria, which is usually 
adopted as the coherence measurement of fringe. The correlation coefficient is calculated according to 
E 
| E[u,u» ]! (8) 
Ve 
JED u, 12 Er uy 2] 
Its estimation holds 
uj (n, mu, (n, m)e Jp(n,m) | (9) 
0 
  
N M > N M 5 
Y Y lu) (n,m) | NV € lu, (n,m) | 
n=0m=0 n=0m=0 ^ 
where u;, u, are the SLC images to be registered, NxM is the size of the estimation window. 
But it should be noted that even if the ergodicity hypothesis holds, the accurate interferometric phase should be 
estimated and compensated in expression (9). The complexity is highly increased. Therefore the frequency independent 
estimator is introduced. So the absolute value of the complex coherence can be calculated as 
  
2p -1 p »0. 
y, Hi Lis ao) 
0 ps0. 
where 
N M . 
E S X uj (n, m) Fluz(n,m) 17 (11) 
p= n=0m=0 
N M 4 N M 
X X lug (n,m)| NV Y lus (n,m 
n=0m=0 n=0m=0 
The estimator described in expression (10) and (11) is much more efficient in computational costs than the usual 
estimator, despite a reduced statistical confidence. If the coherence is not very low and the estimation window is large, 
the accuracy will be good enough as the matching criteria (Guarnieri 1997). 
3 EXPERIMENTS 
The multi-step matching method is applied on the registration between an SLC image pair of SIC-C/C&L-band. 
All the procedures were implemented automatically. The images cover the Hawaii area as shown partly in Fig.2. The 
portion with image size 2500x2500 is used as the test site. The image pair of L-band is shown in Figure 2. 
More than 100 point pairs have been determined within a short period of time with about 0.5 to 1 pixel RMS by 
global relaxation algorithm. The cross cursors marked in Fig.2 indicate the conjugate point pairs. Then the point pairs 
were input as the initial values for the Least Square Matching. After about 5 LS iterations, the RMS of the global 
polynomial transformation is less than 1/10 pixel. The Table 1 and Table 2 show the results from L-band image pair and 
C-band image pair respectively. The window size for matching and coherence estimation is 63x63. So some points were 
cancelled because they were very close the image edge. The geometric registration was performed by means of 2nd 
order polynomials. The accuracy after LS matching is less than 1/10 pixel and available for InSAR data processing. 
Finally the fringes and coherence images were multi-look processed with 2 looks in range and 2 looks in azimuth. The 
fringes and coherence images are shown in Figure 3 and Figure 4 respectively. About 7 minutes was required for one 
image pair with image size 2500x2500 on Indigo-2 workstation. The program code will be optimized further. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000. 189