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

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

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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