matching is also popular. According to the nodal
scheme, mesh is generated such that nodes lies
across object boundaries and a simple search of
linear motion of these nodal position from the anchor
frame to the destination frame will be able to sufﬁce
deformation (O.Lee and Y.Wang, 1995). In this
paper, we shall highlight a framework that integrates
a vector quantization based block partitioning method
to an genetic algorithm based search scheme with
afﬁne parametrization to accomplish robust, accurate
motion estimation with deformation handling. The
model is built on a multi-resolution platform with
performance feedback.
2 PROPOSED MODEL
The proposed model constitutes of different phases.
The ﬁrst phase is the multi-resolution platform that
the framework is based on. The platform combines
a scale space representation of data with a multi-
resolution level analysis. A multi-resolution model
aims at capturing a wide range of levels of detail of an
image and can in-turn be used to reconstruct any one
of those levels on demand. The distinction between
different layers of an image is determined by the res-
olution. A simple mechanism of tuning the resolution
can add ﬁner details to coarser descriptions providing
a better approximation of the original image. Mathe-
matically, we can represent the above analysis in the
following way. If the resolution is represented using
λ, then the initial level is associated with λ = 0 is 1
and that with any arbitrary resolution λ is
1
2
λ
. If f
λ
is
the image at resolution λ, then at resolution λ+1,
f
λ+1
= f
λ
+ Γ
λ
(1)
where Γ
λ
is the details at resolution λ. In con-
trast, the scale space representation of data deals with
representing images in such a way that the spatial-
frequency localizations are simultaneously preserved.
This is achieved by decomposing images into a set
of spatial-frequency component images. Scale space
theory, therefore, deals with handling image struc-
tures at different scale such that the original image can
be embedded into a one-parameter family of derived
component images thereby allowing ﬁne-scale struc-
tures to be successively suppressed.Mathematically,
to accomplish the above, a simple operation of con-
volution can be used. However, it is important to
note that the overhead of using the convolution op-
erator is kept low. For any given image I(x, y), its
linear scale space representation is composed of com-
ponents L
ϑ
(x, y) deﬁned as a convolution operator of
the image I(x, y) and a Gaussian kernel of the form:
G
ϑ
(x, y) =
1
2πϑ
e
−
x
2
+y
2
2ϑ
(2)
, such that
L
ϑ
(x, y) = G
ϑ
(x, y) ∗ I(x, y) (3)
where ϑ = σ
2
is the variance of the Gaussian. Per-
formance based feedback automates the selection of
relevant resolution and scale for any particular frame
pair. A brief algorithm describing the process is as
follows.
• Initialize the resolutions λ
[1:q]
to [0, 1, 2, ..., q] and
scales ϑ
[1:q]
to [1, 2, 3, ..., q + 1] for any value of
q (4 chosen for this experiment).
• Select the median of resolutions as the initial start-
ing resolution and scale. The median is 2 in our
experiments and the chosen values of (λ, ϑ) are
(2, 3)
• Input at any time instant t, two successive frame
pairs of a video sequence, (f
t
, f
t+1
).
• Re-sample the images f
t
and f
t+1
into the se-
lected resolution using bi-cubic interpolation
• Convolve the image at selected scale (in matching
positions with the resolution) with a Gaussian ker-
nel to obtain a ﬁltered output (G
ϑ
∗ f
t
, G
ϑ
∗ f
t+1
)
• Perform Motion Estimation of these input images
at this scale-resolution using the motion estima-
tion algorithm speciﬁed in the subsection below
and reconstruct the target frame using the esti-
mated motion parameters.
• Evaluate the performance of the model using
the metrics: PSNR, Entropy and Time as in
(H.Bhaskar and S.Singh, 2006)
• If the frame pair processed is (f
t
, f
t+1
) at t = 1
then automatically slide up to a higher resolution
and repeat process by incrementing t. Otherwise,
if t > 1 then if P SNR
t
> P SNR
t−1
then slide
down to lower resolution - scale otherwise slide
up to higher resolution - scale combination.
• Repeat the process for all frame pairs
The second phase of the algorithm deals with
motion estimation. For the purpose of motion
estimation we extend the technique of deformable
block matching that combines the process of block
partitioning, block search and motion modeling. A
vector quantization based block partitioning scheme
is combined with a genetic algorithm based search
method for robust motion estimation (H.Bhaskar
and S.Singh, 2006). We extend the basic model in
such a way that block deformation is handled using a
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