capture large translation but these large windows encom-
mid which amplified to large translations at the finer scales
pass a combination of various motions such that accuracy
of the image pyramid. Experience with ERS-1 SAR im-
of the estimation procedure is limited to a spatial resolu-
ages shows that a three level pyramid ranging in resolutions
from 1536 1536 to 384 384 is sufficient to capture the
tion much larger than the image resolution. Additionally,
SAR is an active microwave system with an emitting sig-
observed large translation.
nal in the range of centimeters (e.g., C-band has 5.7 cm
Having obtained the global motion compensated image,
a local piece-wise linear motion model is applied using
wavelength). Materials like sea ice with crystalline features
the same size as the emitted signal introduce considerable
phase correlation. This local motion model then provides
backscatter which, in turn, alters and blends the return sig-
two important pieces of information to the affine paramet-
nal between pixels. Phase correlation has the basic property
ric model: (1) an initial estimate for the affine motion and
of being illumination invariant and can therefore be used ro-
(2) a correlation map.
bustly to estimate the large motion at a low computational
For this experiment, the affine model chosen is a least-
burden.
square regression technique. It is applied making use of a
known limitation of correlation methods, namely, their in-
As a preprocessing step prior to the estimation, the ERS-
ability to resolve regions of discontinuity [41]. Low values
1 images were modified using histogram equalization in
of correlation coefficient on the correlation map are thus
tandem with mid-tone modification to obtain "visually sig-
used to isolate discontinuities so that the motion model can
nificant regions" [7]. Experiments with various equaliza-
track the deformations in the vicinity of these long narrow
tion methods indicated that the estimated motion field had
crack-like features but avoid computations right at the dis-
the smallest error variance when mid tone expansion was
continuities.
applied.
To tackle the large translational motion, the motion field
3.2. Validation Data Set
was estimated using a multi-resolution hierarchy of images
obtained by decimating the image signal using a median fil-
The European Space Agency's ERS - 1 and ERS - 2 C-
ter. The median filter was used instead of a Gaussian filter
band (5.3 GHz, 5.7 cm) Active Microwave Instrument are
because of the poor response of Gaussian Kernels in regions
currently being used to generate weather independent (day
with heterogeneity, which constitute the differential features
or night), frequent repeat, high resolution (10 m) 100 km
such as leads, families of slip lines, cracks, and ridges.
swath radar images globally and, in this particular case, for
Each image resolution hierarchy obtained from an image
the Weddell Sea in the Southern Ocean around Antarctica.
pairs is used to estimate global motion by performing phase
The 5 month Ice Station Weddell 1992 (ISW) is the only
correlation at each level of the hierarchy and then passing
winter field experiment to date conducted in the Western
that coarse estimate on as an initial estimate to the next finer
Weddell Sea. The orbit phasing of the ERS - 1 was fixed in
level of the pyramid. The global motion is obtained at a par-
the 3-day exact repeating orbit called the "ice-phase" orbit
ticular level of the pyramid by binning the motion vectors at
providing uninterrupted SAR imagery of spatial coverage of
that level into a histogram. The histogram bucket containing
100 100 km2 during the entire duration of the experiment.
the maximum number of candidates is taken as the estimate
The SAR images obtained from ERS -1 are projected
at that level of the hierarchy and submitted to the next level
onto the polar stereographic Special Sensor Microwave Im-
as the initial guess. This process is repeated down to the
ager (SSM/I) grid. The images are then block averaged to
finest resolution image in the pyramid hierarchy where the
100 m resolution (88 pixel block averaging) to speckle fil-
final estimated solution is chosen as the global translation.
ter the images to minimize intensity errors to 1 dB (>90%
To improve robustness of the method, potential median can-
confidence interval) leading to images with dimensions of
didates at each level in the pyramid hierarchy are selected
1536 pixels in the horizontal and vertical direction.
and passed through a "Lorentzian estimator" [9] to deter-
Motion vectors for each 100100 km2 SAR image are
mine the best possible estimate.
resolved using a nested cross-correlation procedure [16],
Due to the periodic nature of the Discrete Fourier Trans-
[15] to characterize 55 km2 spatial patterns. A total of 11
form, the maximum measurable estimate using the Fourier
such image pairs exist from this processing with an RMSE
Transform of a signal within a window of size W is W/2.
less than 0.5 cm/s for 3-day tracking compared against six
Thus, to capture translations of magnitude (u, v), the win-
buoy measurements from the ISW [16].
dow size should be at least 2 ∗ max(u, v). For the ERS-1
experimentation, the block size was taken as 3232 and the
4. Results and Analysis
window size was taken as 128128. The sizes of the win-
dow and the block are maintained constant throughout the
The global estimates obtained using our processing
entire pyramid hierarchy. This provided a method of ob-
method are compared against the ISW results described in
taining accurate estimates at the coarsest level of the pyra-
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