Information Technology Reference
In-Depth Information
LLY
K
(
x
,
y
,
t
)
d
t
)
1
|
∑
(
x
,
y
)
LLY
K
(
x
+ d
x
,
y
+ d
y
,
t
MAD
B
(d
x
,
d
y
)=
−
−
(9)
|
B
∈
B
Here
LLY
K
is the
Y
-component of the low frequency subband and
B
is the consid-
ered block. Estimation with pixel accuracy turns to be better, than half pixel because
of shift-variance of wavelets. Then the global affine six parameters motion model is
estimated by robust weighted least squares:
d
x
(
x
,
y
)=
a
1
+
a
2
x
+
a
3
y
d
y
(
x
,
y
)=
a
4
+
a
5
x
+
a
6
y
.
(10)
The outliers with regard to this model with weak weights
w
(
B
) form the motion
mask
M
t
at the top of the pyramid and serve for extraction of objects
O
t
.When
estimating the model of Eq. (10) the coefficients of the HF subbands are used in
order to a priori exclude “flat areas” in a subband LL, which are not reliable for
motion estimation. Here the standard deviation vector
HH
)
T
σ
(
B
)=(
σ
LH
,
σ
HL
,
σ
is computed for each block. If its norm
||
σ
(
B
)
||
∞
is less than a level-dependent
threshold
Th
k
σ
, then the block is considered as “flat”.
The projection of motion vectors to initialize the estimator at the lower levels
of the pyramid is realized with location principle on the subband LL diadycally
increasing block size and vector magnitudes. The outlier blocks, projected with this
scheme are then split into smaller blocks in order to keep precise motion estimation
in areas with proper motion. The motion model of Eq. (10) re-estimated at each
level of the pyramid allows for improvement of PSNR measured on non-outliers up
to 8% on average.
In filtering of outliers from blocks which follow the model of Eq. (10), the abso-
lute difference between optimal values of MAD obtained when a block is compen-
sated with its original vector and with Eq. (10) is computed. If it is greater than a
threshold
Th
k
MAD
, than the “proper” motion of a block is confirmed. Otherwise, it
is incorporated in the set of the blocks following the global motion, the same test
is made for flat blocks. Figure 6 depicts the results of this filtering at the second
resolution level of a Daubechies pyramid. The upper row represents the LL subband
at level 2, the mid-raw is the result of outlier rejection by weighted least squares,
the lower row is the result of filtering.
The merged motion masks and segmentation map at the top of the pyramid form
extracted objects (see an example in Figure 7).
To form a scalable object-based descriptor, it is necessary to get extracted objects
at all levels of the pyramid. The object masks extracted from the top of the pyramid
have to be projected and refined at each level. If the projection across pyramid levels
is naturally guided by wavelet location principle (Figure 5), fitting of object bound-
aries to the LL subband content at the lower pyramid levels is a problem per se. It
is natural try to use already available contour information in HF subbands. This can
be done in the framework of Markov Random Field (MRF) modeling.
