IAPRS & SIS, Vol.34, Part 7, *Resource and Environmental Monitoring", Hyderabad, India,2002 
THE REGISTRATION OF SAR IMAGES FOR INTERFEROMETRY USING 
CUBIC B-SPLINES 
S. Mukherji 
Centre of Studies in Resources Engineering, Indian Institute of Technology, Bombay, MUMBAI — 400 076, INDIA. 
shyamali@csre.iitb.ac.in 
KEYWORDS: Image Registration, SAR, Interferometry. 
ABSTRACT: 
We present a fast algorithm for registering SAR images for interferometry. The algorithm computes the cross-correlation function 
only at the offsets in the neighbourhood of the possible range and azimuth displacements between the images. This speeds up the 
computation significantly. À single cell of the cross-correlation matrix is then interpolated using cubic B-splines in order to achieve 
sub-pixel accuracy in the registration. After computing the affine transformation relating the images, the points, at which the slave 
image needs to be resampled, are found by interpolating the residuals, in the co-ordinates of the tie-points in the slave image, using 
cubic B-splines. A fast algorithm that exploits the local support property of cubic B-splines is used for the interpolation. The results 
of registering an ERS-1/2 tandem pair of images using this algorithm are presented in this paper. 
1. INTRODUCTION 
Interferometry uses the phase information in radar images to 
estimate the height of the terrain. A pair of images of the same 
area are taken from satellite orbits located slightly apart. The 
difference in the phase values of the images (at a point in the 
images) is related to the elevation of the corresponding point in 
the scene. Therefore, it is necessary to identify the positions in 
the two images that correspond to the same point on the ground. 
This process, by which the images are geometrically aligned, is 
called registration. In this paper, we present a fast algorithm for 
registering SAR images for interferometry. 
The process by which radar images of an area on the ground are 
formed is described in Section 2. Section 3 justifies the use of 
cross-correlation to identify pairs of corresponding points in the 
images. In Section 4, the viewing geometry for a pair of 
interferometric SAR images is explained and estimates of the 
resulting displacement between the images are found therefrom. 
Section 5 describes the sub-pixel interpolation that is necessary 
for the range of displacements between interferometric SAR 
images. Section 6 describes how the mapping function for 
registration is found. Section 7 deals with re-sampling the slave 
image while Section 8 deals with the verification of the 
registration procedure. Finally, Section 9 concludes the paper 
with a discussion of the factors that have contributed to the 
speed-up of the registration, in the algorithm that has been 
developed by us. 
2. FORMATION OF RADAR IMAGES (Leberl, 1990) 
A radar image is formed by a sensor on a satellite by 
transmitting and receiving radar pulses along the track of the 
satellite. Thus, the formation of a radar image by the motion of 
a satellite over the area is a dynamic process as opposed to the 
production of an image in an instantaneous exposure by a 
common camera as in optical imaging. Therefore, the baseline 
separation for a pair of radar images of the same scene is the 
distance between the corresponding satellite orbits. 
3. FINDING PAIRS OF CORRESPONDING POINTS IN 
THE IMAGES 
Interferometric SAR images have baselines of the order of a 
few hundred meters at a height of 800km. above the earth’s 
surface. Registration or point-to-point correspondence between 
the two images is needed in order to obtain the interference 
patterns. Since the baseline is very small compared to the 
distance of the sensors from the scene, the difference in the 
viewing angles is small and cross-correlation can be used to 
find corresponding pairs of points in the images. We have used 
normalized cross-correlation to identify these pairs. 
Fig. 1 shows the ERS-1 image of an ERS-1/2 tandem pair of 
images (of the Thane Creek and Navi Mumbai area) with a 
baseline of 180 m., slant range resolution of 7.8m. and azimuth 
resolution of 4m.. 
  
Figure 1: ERS-1 Image of Thane Creek and Navi Mumbai Area 
The pairs of corresponding points in the images (for points at 
intervals of 200 pixels in the azimuth and range directions in 
the master image) were computed using cross-correlation. The 
displacement between the images along the range direction was 
found to be 7 pixels (accurate to an integer) almost throughout 
the image. The displacement in the range direction was found 
to be 8 pixels at the right-hand end of the image. The 
displacement between the images in the azimuth direction was 
found to be either 2 or 3 pixels throughout the image. 
   
    
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