International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
TABLE I 
DATES AND PERPENDICULAR BASELINES OF THE CONSIDERED 
ERS-1/ERS-2 INTERFEROMETRIC TANDEM PAIR. 
  
  
Mission Orbit Date By 
Orgeval ERSI 22956 05/12/95 0 
ERS2 3283 06/12/95 83m 
Mustang ERSI 25422 25/05/96 0 
ERS2 5749 26/05/96 90 m 
  
  
  
where 7). and 7), are the azimuth and the range integer translation 
factors and &, and &, are their corresponding sub-pixel translation 
factors. 
In order to realign images s and m, it is first necessary to determine 
the integer translation vector (na. y). For this, several image regis- 
tration algorithms could be used to solve this problem [11], [12], [19]. 
We used the ISAR software (the CoherRegist subroutine) distributed 
by ESA (European Space Agency) [19] to compute these integer 
coarse shifts. Then, we perform an a priori registration using the 
resulting a priori coarse coefficients. 
The present paper is meant as a contribution to the estimation 
approach of the sub-pixelic translation vector (£x, £y). We consider 
for the following the transformation model of (1) between a two 
InSAR images s(z,, ys) and m(x;, ym) to be matched. Thus, using 
the ISAR software, we perform an integer co-registration of s and 
m, which lead to a new relationship between the coregistred image 
s' and m: 
s'(x,y) = m(x — Ex,Y — Ey) = M(r,y) D Ô(T — Ex,Y — Ey) Q) 
where & is the convolution operator and ó is the dirac function. 
Our idea consists in looking for the vector (£5,£,) that maximises 
the cross-correlation between s’ and m. However, in order to reduce 
the complexity given by the convolution in the spatial domain, we 
consider equation (2) in the Fourier domain: 
S'(u,v) — exp(-2jT(uz« -- vey)) M(u, v) (3) 
where S’ and M are respectively the Fourier transform of s' and 
m. £4 and e, are taken in the interval [—0.9, --0.9] (a window of 
2x2 pixels) with an incremental step of 0.1. The cross correlation is 
computed locally on a window size of 3x3 pixels. The corresponding 
shift matrix is given by: 
1 e 2e eu 
D e ex e S Gsteg) e —-2jn(ea-t2£,) (4) 
e x e SOS +Ey) etT(extey) 
For different values of €, and &, and for each pixel, we operate 
the product of the shift matrix with the corresponding neighborhood 
pixel matrix. Then, we compute the inverse Fourier transform of this 
product which will give the spatial cross-correlation factor. 
On Fig. 1 are plotted an example of histograms of the azimuth and 
range shifts computed with the new algorithms from two different 
SLC images (detailed information on the used images are given in 
next paragraph). 
[V. EXPERIMENTAL RESULTS 
Two test sites representing different geomorphological regions are 
selected in order to test the robustess of the new sub-pixelic matching 
approach. The test areas are Orgeval (France, 48°51" N, 3°08’ E) and 
Mustang (Nepal, 29°12" N, 83°55’ E) (see Table I). 
The Orgeval site is a rather flat area where the elevation varies 
from 120 m to 200 m. In this region, there are many agricultural 
   
: 3 
3x10 35* 10 
25 3 
= = 
E 225 
Rie E 
E 2:32 
£15 € 
E S15 
z 2 
o 
o 
o 
f 
-0.5 0 05 -0.5 0 05 
Sub pixelic range shift Sub pixelic azimuth shift 
(a) (b) 
ax 10 4x10 
35 3.5 
£3 m3 
X Z 
22.5 25 
= 2 $2 
5 s 
Z15 Z5 
1 1 
0. 0.5 
> 2 1 
3:05. 70 05 -0.5 0 0.5 
Sub- pixelic range shift Sub-pixelic azimuth shift 
(c) (d) 
Fig. l. Examples of histograms of the azimuth and range shifts computed 
with the new algorithms from (a) & (b) the Mustang and (c) & (d) Orgeval 
tandem pairs. 
field and few urban areas which are located at the border of the test 
site. About 6096 of the total area is covered by crops (wheat, corn, 
peas, flax, sugar beet) (Fig. 2 (a)). 
The Mustang test area is a highly energetic relief site where the 
elevation varies from 3200 m to 4400 m. Cultivated land is rare 
and particularly low and vegetations are scattered. The villages on 
the selected area are small and without any particular shape. The 
Mustang site is a good test area for InSAR topographic Mapping, 
since it offers a big relief diversity (Fig. 2 (b)). 
The coherence map of Orgeval indicates that more than 70% of 
the area has a coherence greater than 0.7. For the Mustang test site, 
although the ERS SAR data are acquired with | day interval between 
acquisitions, the corresponding coherence map (Fig. 2 (d)) computed 
with a (5x8) pixel window indicates that only 50% of the samples 
have a coherence greater than 0.6. This is due to the energetic relief of 
Mustang. Moreover, after achieving the coarse registration using the 
ISAR software on the two tandem pairs (results are given in TABLE 
Il). 
Thus, we can understand the random results in Fig. 1 (a) and (b) 
where the sub-pixelic shifts are not dominante in range and azimuth. 
However, in Fig. | (c) and (d) in both azimuth and range direction, 
the sub-pixelic translation factors are dominante and we decide to 
co-register the tandem pair of Orgeval using these globale shifts. 
TABLE Il 
THE ESTIMATED MATCHING PARAMETER: THE INTEGER SHIFTS 
COMPUTED WITH THE ISAR SOFTWARE AND THE SUB-PIXELIC ONES 
COMPUTED WITH THE NEW ALGORITHM 
  
  
Orgeval Mustang 
Parameters computed with the ISAR software 
  
Azimuth shift [pixels] I -4 
Range shift [pixels] ] 3 
Parameters computed with the new algorithm 
Global sub-pixel azimuth shift (Ex) -0.2 -0.9 
Global sub-pixel range shift (ey) -0.3 -0.9 
Performance evaluation of the sub-pixelic registration algorithm is 
done by comparing the coherence maps before and after the sub- 
pixelic matching approach. We conclude that the new sub-pixelic 
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