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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
Sub-pixelic Image Registration for SAR Interferometry
Coherence Optimization
Riadh Abdelfattah
Département MASC
École Supérieure des Communications
Route de Raoued Km 3,5
2083, El Ghazala-Ariana, Tunisia
Email: riadh.abdelfattah@supcom.rnu.tn
Telephone: +216 1 857 000
Fax: +216 1 856 829
Abstract— This paper presents a methodology for the registration of
an Interferometric Synthetic Aperture radar (InSAR) pair images with
a sub-pixelic precision performed in the Fourier domain, using the Fast
Fourier Transform (FFT). We look for the maximum of the modulus of
the cross-correlation coefficient of both images on a window dimensions
of 2x2 pixels using an iterative process. This will be possible in the Fourier
domain, since a shift in the spatial domain is achieved by a multiplication
with an exponential factor (which is the real shift less than one pixel) in
the frequency domain. It is shown that the proposed sub-pixelic approach
allows the coregistration of the images with an accuracy up to a tenth
of a pixel (and even less).
I. INTRODUCTION
SAR interferometry has become one of the most important tech-
niques of relief mapping [1], [2], [3], [4]. The accuracy of digital ele-
vation models (DEMSs) produced by SAR interferometry are generally
comparable to reference DEM [6](obtained from a SPOT stereo pair
or from an official data base) and ground control points taken over
the relief. However, this is true under certain conditions of the ground
scattering characteristics and the acquisition (sensor, baseline, ...)
geometry which could be measured via the interferometric coherence
[9], [10], [17].
In practice, the coherence has to be estimated on a coregistrated
images from the combination of several pixels (N independent
samples correspond to the pixel or to an area around this pixel)
to limit statistical errors [7], [8]. In order to tend to unbiased
coherence estimation, a large estimation window is required at low
interferometric correlation. We must coregistrate one image (the slave
one) with respect to the other (the master one). As a result of the
coregistration, we get the best bilinear transform that must be applied
to the slave image to make it superimposable to the master one. In
generally, the coregistration process is performed on two steps : a
coarse one, where the shift (integer number of pixels) between the
two images in range and azimuth is computed, and than a fine one,
where the computed shift is less than one pixel.
In this paper, we present a new procedure for sub-pixelic fine
coregistration performed in the Fourier domain, using the Fast Fourier
Transform (FFT). We look for the maximum of the modulus of the
cross-correlation coefficient of both images on a window dimensions
of 2x2 pixels using an iterative process. This will be possible in the
Fourier domain, since a shift in the spatial domain is achieved by a
multiplication with an exponential factor (which is the real shift less
than one pixel) in the frequency domain. It is shown that the proposed
sub-pixelic approach allows the coregistration of the images with an
accuracy up to a tenth of a pixel (and even less).
Jean-Marie Nicolas
Département TSI, École Nationale
Supérieure des Télécommunications
46 rue Barrault
75634 Paris Cedex 13, France
Email: nicolas@tsi.enst.fr
Telephone : +33 1 45 81 81 29
Fax: +33 1 45 81 37 94
The proposed algorithm is tested on two different areas: a highly
energetic relief zone (Mustang-Nepal) and a flat zone (Orgeval-
France). It is shown that on stationary region, the algorithm is well
adapted and gives important results. However, non stationary regions
are time consuming and the result is random.
II. INSAR IMAGE CO-REGISTRATION
To obtain a high quality DEM from InSAR, the complex images
need to be registered to sub-pixel accuracy. Image coregistration
techniques allow the determination of a geometric transformation
which may exist between two images s and 7n. In general cases,
image matching depends on three parameters : translation, rotation
and scaling. For interferometry SAR (InSAR), we generally obtain
satisfactory results with only sub-pixel translation registration.
An InSAR image couple is a pair of two SAR images where every
image is a bidimensional array of single look complex (SLC) data
(focused data) resulting from the processing of raw data in range and
in azimuth. These two SLC images result from the raw data focusing.
Their registration implies compensation of azimuth and range pixel
displacement. Note that the slant range and azimuth offsets change
along track and across track in the SAR SLC images.
The InSAR coregistration process is performed on two steps using
local statistical information (magnitude or phase) computed with
selected windows on both images [5], [2], [15] :
e Coarse matching, where the integer shifts (translation) between
the two images in range and azimuth are computed. This could
be done by cross-correlating the amplitudes of the images [5]
or maximizing a spectral signal to noise ratio (SNR) [2] on a
selected windows with integer positions [13], [14].
Fine matching, where the computed shifts (in range and azimuth)
are sub-pixelic.
However, in the case of fine matching, the sub-pixel cross-
correlation and S/N R maximisation is not robust in the spatial domain
against correlated noise and disturbances [15], [16], [18].
III. SUB-PIXELIC INSAR REGISTRATION
Let s(xs,ys) and m (2m, Ym) represent the two complex images
of the InSAR pair to be coregistered. If s(xs,ys) is a translated
replica of m(x;, y), then the transformation matrix can be written
as follows:
s Em Ne + Ex
(rye oA a fn
Ys Ym ny + Ey
BE