Section 3.2. The global motion field used in the comparison

in comparison with the ISW vectors. The estimated mo-

is obtained by converting the motion field from pixel coor-

tion field in the images below have been computed using

a 3232 window and then overlaid, using linear interpola-

dinates to the Special Sensor Microwave Imager (SSM/I)

grid coordinates and plotting them in tandem with the ISW

tion, on a 5 km SSM/I grid for comparison with the ISW

motion vectors.

vectors. Scatter plots show the magnitude and phase vari-

ation between our estimates and the ISW vectors for the

To maximize the throughput of the FFT modules the

spatially collocated positions.

phase correlation is performed on a window size with pow-

Figure 1 is an illustrative example of the comparison be-

ers of 2. Depending on the spatial resolution required for

tween the ISW ground truth vectors (in blue) and the esti-

the interpolation of the motion field, the block size can be

adjusted at 88, 1616 or 3232 leading to an output mo-

mated vectors (in red). The bottom panel in Figure 1 shows

scatter plots of the magnitude and directional components

tion field at 0.8 km, 1.6 km or 3.2 km resolution.

of the estimated vectors with the ISW vectors.

Two statistical measures of the similarity, the Root Mean

Square Error (Eq. 2) and the index of agreement (Eq. 3)

have been computed.

1

kK

(pk - ok )2

RM SE =

(2)

K

=1

K

ωk (pk - ok )γ

k=1

dγ = 1 -

K

(3)

γ

k=1 ωk (|pk - o| + |ok - o|)

where pk are the predicted samples, ok are the observed

ground truth vectors, wk are the weight functions which

are assumed uniform for this study and o is the mean of

the observed data. γ is the order of index and according to

Willmott [43], γ = 1 is most robust for comparing results

because of its linear approach to a perfect match.

Analysis of the image pairs using higher resolution

analysis windows (Figure 2) reveals precise demarcations

corresponding to the regions in the ice-flow undergoing sig-

nificant amounts of non-rigid dynamics. Based on the vari-

ance of the magnitude and direction of the motion field, the

cluster map as shown in Figure 2 was created using a quad-

tree model.

This result reveals the usefulness of local higher order

motion in the vicinity of the regions of discontinuity. Given

the global motion compensated images, local non-rigid dy-

namics was first extracted using the simplest model of the

local motion. Under the assumption that magnitude of the

differential motion is small, a piecewise linear approxima-

tion of the non rigid motion using phase correlation was

applied. As seen in Figure 3, the estimated local motion

vectors are overlaid upon the correlation map to verify the

goodness-of-fit as are the ISW vectors in validation. Exper-

imentally, a threshold correlation of < 0.2 is found to be the

most appropriate for demarcating between continuous and

discontinuous regimes. This low correlation corresponds to

regions where the magnitude of deformation far exceeds the

piece-wise approximation.

The dynamic region analyzed and described earlier in

The subsequent results in Figure 1 show the accuracy of

(Figure 2) is shown again in Figure 4 in the same format

the estimates obtained by the phase correlation technique

as Figure 3 for comparison. This dynamic region contains

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