3. Motion Estimation Technique
the availability of high-spatial resolution, all-weather Syn-
thetic Aperture Radar (SAR) images [15], [16], [17], [19].
This paper delves into the estimation and validation of sea-
In this paper, we use phase correlation as the technique
ice motion using SAR images from the European Space
to estimate sea-ice motion. Extensive studies on the phase
Agency's (ESA) first European Remote Sensing (ERS-1)
correlation process for motion estimation have been pro-
satellite, specifically, imagery from C-band (5.7 cm) mi-
vided in [40], [41]. Various image registration techniques
crowave SAR. Among the algorithms for motion tracking
using the Fourier Transform exist in current literature [12],
in the Antarctic, the method by Drinkwater and Kottmeier
[38], [32]. Alliney, et al. [2] estimate object motion under
[18] is one of the more successful ones. The data set ob-
the constraint that the background does not undergo signif-
tained using their method from Ice Station Weddell (ISW)
icant changes. Stone, et. al., [39], and Foroosh, et. al.,
1992 [16], [15] is the one we chose to validate our algo-
[22] provide algorithms to perform subpixel image regis-
rithm.
tration using the phase correlation technique. Phase cor-
relation as described in research literature is derived from
2. Relevant Background
the Fourier Shift Theorem which is a specialization of the
Affine Fourier Theorem as proposed by Bracewell [10].
The affine theorem describes the separation of the dis-
Since the original description of the problem by Horn
placement vector and the affine coordinate matrix in the
and Schunck in the seminal work [24], optic flow estimation
frequency domain. When handling the large motion, as ob-
has been a much researched topic. Under the assumption of
tained in the satellite imagery, the global translation compo-
extremely small temporal resolution the optic flow equation
nents overshadow the differential affine motion parameters
is considered valid and many techniques have been devel-
and thus the affine theorem has an immense potential in es-
oped to estimate the flow field [25], [3], [5]. Robust tech-
timating the motion since the translation component can be
niques [8], [6], [36] have emerged to handle the large noise
estimated independent of the affine parameters.
and/or the failure of the underlying image motion model.
The translational component can be extracted from
Sequential pairs of SAR images capture two important
within the correlation equation using "whitening" zero-
characteristics of sea-ice motion, global translation and dif-
phase FIR filters H1 = |F (u)|-1 and H2 = |G∗(u)|-1
ferential non-rigid dynamics. Due to differences in satellite
[33] leading to a Dirac delta function centered at the trans-
orbits and the earth's rotation, the visual capture of local
lation parameters as in Eq. 1
sea-ice dynamics is overshadowed by the complexity to as-
certain high magnitude global translation (on the order of
F (u) G∗(u)
-1(
about 200 pixels on 100m resolution images separated in
) = δ(x - d)
(1)
H1 H2
time by three (3) days). Traditionally this problem has been
addressed using a hierarchical framework [11], [4]. Specif-
The main advantage of phase-based techniques are its
ically within the field of sea ice, this problem is currently
characteristic insensitivity to correlated and frequency-
addressed using a variety of methods including cross cor-
dependent noise. With the availability of the 2-D FFT [13],
relation and 2D wavelets [21], [28], [29], [20], [16], [15],
the calculations can be performed with much lower com-
[31], [30].
putational complexity. The disadvantage with these tech-
An added complexity in this traditional methodology
niques is that they are applicable only under well-defined
comes from the fact that high-spatial resolution SAR data
transformations and thus require bolstering from other tech-
is limited by low-temporal resolution due to polar orbital
niques, especially in the cases where the transformations are
constraints (typically 3 days). Under the influence of fast
arbitrary. A point of consideration is that phase correlation
moving storms, significant non-linear changes in disconti-
peak may reduce in height under image rotation and scal-
nuities can occur at temporal scales much lesser than 3 days
ing [32]. For sea-ice SAR imagery, these can be assumed
and sea ice can deform rapidly resulting in large changes
negligible since the global translation is large compared to
in the orientation, distribution, and size of continuous and
affine parameters and thus not significantly affected by the
discontinuous regions. Thus estimation of the motion field
magnitude reduction.
in SAR imagery requires an added perspective when com-
pared to the traditional optical flow algorithms. The hy-
3.1. Processing Method
pothesis considered here is that motion can be extracted in
a hierarchical fashion with coarse resolution levels resolv-
Global translations of sea ice in SAR imagery are of
ing large global translation through linear models and finer
order 100 to 200 pixels depending on the temporal dis-
resolution levels resolving smaller local non-rigid dynamics
tance between images. The traditional method of "Normal-
using higher order parametric motion models such as affine,
ized Cross Correlation" requires a large support window to
quadratic, etc.
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