as obtained from the correlation map. The affine parameter

Magnitude (kms)

30

estimation chosen is a least-squares fit to the locally trans-

RMSEcomplete = 0.88498

lated patch. The Peak Signal to Noise Ratio (PSNR) values,

RMSEgood = 0.13614

d

= 0.98145

25

complete

calculated using Eq. 4, are provided in Table 1.

d

= 0.99318

good

n

= 2650

complete

n

= 1930

good

n

= 548

20

255

deformation

]

P SN R = 20 ∗ log10[

(4)

σ|Image1-Image2|

15

where σ is the standard deviation, I mage1 and I mage2 is

10

the image pair under consideration. From the table it is ev-

ident that the PSNR value between I mage2 and the mo-

5

tion compensated images increases with increasing motion

0

model complexity.

0

5

10

15

20

25

30

ISW Vectors

Direction (degs)

280

RMSEcomplete = 7.7171

RMSEgood = 1.268

Localizing and parameterizing discontinuities is an im-

260

dcomplete = 0.97229

d

= 0.98891

good

portant landmark for sea-ice research. Due to the low tem-

240

ncomplete = 2650

ngood = 1930

poral resolution of the SAR images, this type of information

220

n

= 548

deformation

is paramount input into numerical models for interpretation

200

of events between SAR scenes. This paper describes a hi-

180

erarchical method to estimate the parameters of a discon-

160

tinuous motion field such as the ones captured by the ERS-

140

1 SAR imagery in three stages. The hypothesis of using

120

a finer sieve to filter out coarse motion models iteratively

100

seems to be validated with the observed improvement in the

80

PSNR values of the motion compensated images.

80

100

120

140

160

180

200

220

240

260

280

The comparative results between the estimated vectors

ISW Vectors

and the ISW ground truth vectors indicate that hierarchical

phase correlation is ideal for the estimation of the global

motion. This is mainly due to the inherent robustness of

phase correlation to illumination variation and its ability

to capture large translational components without getting

caught in local minima. Additionally, the usage of the Fast

Fourier Transform in the calculation of the phase correlation

term makes the computation significantly faster then optic

flow methods.

The second stage involves isolation of discontinuous re-

to ISW vectors. Including flagged points undergoing de-

formation we can account for 93.5% of all the data points.

gions using local piecewise linear model followed by the

The remaining 6.5% of data are displacement results greater

third stage of estimating affine parameters along regions of

discontinuities. Under the assumption that the net motion

than 400m which we can not account for using a correlation

is actually composed of a large global motion component

map. These points mainly correspond to regions where the

and small local deformations, this method captures the large

gradient of the velocity is high and, in principle, requires

global motion component and the local deformation using

a higher-order motion model to localize the position of the

an affine motion model.

discontinuity accurately. Also indicated in the scatter plot

are the RMSE (Eq. 2) and index of agreement (Eq. 3) for

As a subsequent stage to the current research, the esti-

the complete data set and the "good" data set indicating a

mate of the local deformation could be improved using ro-

high accuracy between the ISW vectors and our estimated

bust parameter estimation techniques and also inclusion of a

motion vectors.

motion model such as the quadratic. Another possible track

To improve upon the estimated parameters, an affine mo-

for future research would be a feature-based approach in

tion is imposed onto the local piece-wise linear motion.

tandem with global motion estimation in order to improve

This is performed specifically in the regions of discontinuity

the overall robustness of the estimated global motion.

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