PPFPS - a paraboloid prediction based fractional pixel search strategy for H.26L

Abstract

H.26L is a new recommendation for moving picture coding proposed by ITU-T, in which 1/4-pel and 1/8-pel fractional pixel motion compensation is added to achieve more accurate motion description and higher compression efficiency. However, at the same time the complexity of the fractional pixel motion estimation also increases, requiring a total of 24 fractional-pel positions to be checked in 1/8-pel motion vector search, while some fast integer pixel motion search algorithms have decreased the searching pixels to about ten. Therefore, reducing the computational load for fractional pixel motion search is both necessary and significant. A novel paraboloid prediction based fractional pixel search algorithm is first proposed in this paper. In any case (1/2 pixel, 1/4 pixel or 1/8 pixel resolution), roughly a computation reduction of 62.5% in fractional pixel motion estimation can be achieved compared with the full fractional pixel motion search algorithm. Experimental results prove that the strategy keeps good performance in preserving image quality and has little influence on the bit rate.

Full text

PPFPS-
A
Paraboloid Prediction based Fractional Pixel Search Strategy for
H.26L*
Zhibo Chen Cheng
Du
Jinghua Wang Yun He
State Key Lab on Microwave
&
Digital Communications
Dept.
of
Electronic Engineering, Tsinghua University, Beijing,
100084
{cherub, hey}
@video.mdc.tsinghua.edu.cn
ABSTRACT
H.26L is a new recommendation for moving picture coding
proposed by ITU-T, in which 1/4-pel and 1/8-pel fractional pixel
motion compensation is added to achieve more accurate motion
description and higher compression efficiency. However, at the
same time the complexity of the fractional pixel motion
estimation also increases, requiring a total of 24 fractional-pel
positions to be checked in 1/8-pel motion vector search, while
some fast integer pixel motion search algorithms have decreased
the searching pixels to about ten. Therefore, reducing the
computational load for fractional pixel motion search is both
necessary and significant. A novel Paraboloid Prediction based
Fractional Pixel Search algorithm is first proposed in this paper.
In any case (U2 pixel, 1/4 pixel or 1/8 pixel resolution), roughly
a computation reduction of 62.5% in fractional pixel motion
estimation can be achieved compared with the full fractional
pixel motion search algorithm. Experimental results prove that
the strategy keeps good performance in preserving image quality
and makes little influence
on
the bit rate.
Keywords:
H.26L, fractional pixel motion estimation,
paraboloid prediction, PPFPS, PPHPS
1.
INTRODUCTION
Hybrid coding framework has been successfully adopted in
various moving picture coding standards, such as MPEG-I,
MPEG-2, H.263, and MPEG-4. From 1998, a new ITU-T
moving picture coding recommendation named H.26L is placed
on
the agenda of ITU-T
Q.
15
group (now named VCEG---Video
Coding Experts Group)[l]. The latest version of H.26L, Test
Model Long Term
8.0,
is proposed in Port0 Seguro meeting this
year[2], which is characterised by its high coding efficiency and
more functionalities.
Compared with H.263, some significant changes have been
adopted in H.26L[2]: the residue coding is 4x4 block based,
DCT is replaced by integer transform, universal VLC table is
used, 1/4 and
1/8
pixel accuracy motion estimation is proposed,
etc. A PSNR analysis shows that the H.26L results average more
than 2
dE4
higher in luma PSNR across all test cases than ISO-
MPEG’s chosen MPEG-4 “Advanced Simple” profile anchor
performance[3]. However, H.26L is essentially still based on
hybrid coding framework, and motion estimatiodcompensation
is still important in achieving the high coding efficiency.
Motion estimation is generally conducted into
two
steps: the first
step is integer pixel motion vector estimation and the second is
fractional pixel motion vector estimation. For fractional pixel
motion estimation, 1/2-pel accuracy is frequently used (H.263,
MPEG-I, MPEG-2, MPEG-4) and higher resolution motion
vectors are adopted recently in MPEG-4 (1/4-pel accuracy)[4]
and H.26L (U4 and 1/8-pel accuracy)[2].
Algorithms on fast motion estimation are always hot research
spots, especially fast integer pixel motion estimation, which has
achieved most attention because traditional fractional pixel
motion estimation (such as 1/2-pel) takes only a very small
proportion of the computational load of motion estimation.
However, with the development of fast integer motion
estimation algorithms and the decreasing number of integer
motion search points, computation load of fractional pixel
motion estimation has become more comparable to that of the
integer case. For instance, some center-biased fast integer
motion vector estimation algorithms [6][7][8][9] have reduced
the checking pixel positions averagely down to
10;
while full
fractional-pel motion estimation needs at least
8
1/2-pel
positions to be checked, and more positions to be searched if
higher resolution motion estimation is adopted, e.g. 16 positions
in the case of 1/4-pel and 24 positions in 1/8-pel, even possesses
a much higher proportion than integer pixel motion estimation in
the total motion estimation strategy.
There is still no related work investigating fast fractional-pel
motion estimation algorithms,
so
this paper presents a work both
necessary and significant on the topic.
In this paper, we propose a Paraboloid Prediction based
Fractional Pixel Search (PPFPS) strategy which is characterized
by its excellent ability to reduce computation load as well as its
good quality of preserving the rate-distortion performance.
For the sake of consistency, fractional-pel is used in this paper as
a general designation of all concepts related to fractional pixel
which are indicated by 1/2-pel, 1/4-pel and 1/8-pel, for instance,
1
/2-pel positions, 1/4-pel positions, and 1/8-pel positions are
used to indicate those pixel positions interpolated by a 1/2-pel,
1/4-pel or 1/8-pel filter and are generally referred to as
fractional-pel positions.
The paper is organized as follows: in Section 2, we will describe
the full fractional pixel motion estimation proposed in H.26L.
Section 3 presents our fast fractional motion estimation
algorithm and experimental results are given in Section 4.
Section 5 concludes this paper.
:This project
is
supported
by
National Science Foundation China
0-7803-7448-7/02/$17.00 02002
IEEE
111
-
9

2.
FFPS
-
Full Fractional Pixel Search algorithm in
H.26L
In H.26L[2], for each block or macro-block the motion vector is
determined by a full search on integer pixel positions followed
by fractional-pel refinement which is done by using full
fractional pixel search algorithm. It is reported that a gain up to
1.5 dB of PSNR is achieved with 1/8-pel motion estimation as
compared to 1/4-pel[ lo].
The fractional-pel positions are drawn in Fig.1, where capital
letters represent integer pixel positions, Roman numbers 1/2-pel
positions, lower case letters 1/4-pel positions and Arabian
numbers 1/8-pel positions. In a motion compensated prediction
scheme the motion vector and the block-size pattem (e.g. 16x16,
four 8x8, etc.) have to be estimated for each macroblock, which
is done by the following five steps[9]:
1.
Do integer pixel search to find the best integer pixel
motion vector;
2. Check the eight 1/2-pel positions
I
-
VI11
around the best
integer pixel position
C
in order to find the best 1/2-pel
motion vector;
Check the eight 1/4-pel positions a
-
h around the best 1/2-
pel position
V
in order to find the best 1/4-pel motion
vector;
4. Check the eight 1/8-pel positions
1
-
8
around the best 1/4-
pel position
h
so
as to find the best 1/8-pel motion vector;
5. Select the motion vector and block-size pattern, which
produces the lowest rate-distortion cost.
To acquire the positions of these fractional pixels, a 6 tap filter
(I,-5,20,20,-5,1)/32 is used to produce the 1/2-pel positions;
linear interpolation is employed to produce the 1/4-pel positions,
and an 8-tap filters is used in providing a 1/8-pel accuracy
3.
prediction[
I
j.
DI
I
HI IV
VI
DI
VI D2
I1
111
abc
CdVeHz
123
f
g4h5
618
VI1 VI11
v2
D4
Capital letters(C,Hi,Hz
...)
:
integer pixel positions
Roma numbers(I,II,III
...)
:
1/2-pel positions
Lower case letters(a,b,c
...)
:
1/4-pel positions
Arabian numbers( 1,2,3
...)
:
1/8-pel positions
Fig.
1
Full Fractional Pixel Motion Estimation
Clearly, totally 24 fractional positions are checked to get a
1/8-
pel resolution motion vector.
3.
PPFPS
-
Paraboloid Prediction based Fractional
Pixel Search Strategy
Since fractional-pel motion estimation strategy is carriled out in a
way that 1/2-pel motion estimation is followed
by
higher
resolution fractional-pel refinement such as 1/4-pel or
1
/%pel,
estimation accuracy of lower resolution motion estimation will
definitively influence that of higher resolution estimation.
Therefore, a fast and accurate 1/2-pel motion estimation
algorithm should be adopted in the first place.
Mathematical prediction model has been proposed as a fast 1/2-
pel motion estimation algorithm[l1][12], but only gives out
prediction on the horizontal or vertical direction, without the
required accuracy. We proposed a paraboloid prediction based
half pixel search (PPHFS) algorithm in[5]which can estimate not
only both the horizontal and vertical directions, but also the
diagonal direction. Thus a more accurate estimation and a better
performance can be achieved with searched 1/2-pel positions
decreasing from
8
to
3.
Based on
our
earlier work[5], the PPFPS strategy is proposed in
this paper, which takes PPHPS as the 1/2-pel motion estimation
algorithm and a novel higher resolution fractional-pel prediction
refinement algorithm is proposed.
3.1
PPHPS for 1/2:-pel motion estimation
In H.26L,
SAD
(Sum of Absolute Difference) is still used as the
basic cost function described as:
F(P)
=
t:IL(P)
-
wl
(1)
where
p
is an integer pixel or a fractional pixel in the previous
reconstructed picture,
C
is the pixel in the current picture and
L(*)
represents the luma
of
the pixel. The summation in
(I)
is
executed on different block-size pattems
in
H.26L. It can be
proved that, due to the property of SAD,
F(p)
is a smooth
convex function in the sub-area around the optimal matching
position[5]. Therefore, a quadratic equation is used to model the
convex function as
$(p)
=
A(x
-
J:~)~
+
B(y
-
yo)*
+
D
(2)
where
A
,
B
,
xo
,
yo
and
D
are five unknown parameters.
Supposing the coordinates of integer pixels
C
,
H,
,
H2,
V,
,
V2
are
(0,O)
,
(-1,O)
,
(1,O)
,
(0,
-1)
and (0,l) and that
the five pixels’ cost functxon values are
F(C)
,
F(Hl)
,
F(H2)
,
F(V,)
and
F(V2)
respectively (see Fig.l), if all
these 5 values are available in the integer pixel motion
estimation (called
Constraint
I),
the
5
unknown
parameters in
(2) can be solved as follows
I11
-
10

ifB=O.
Then we can decide the best 1/2-pel position by checking the
minimum cost function among the three 1/2-pel positions instead
of eight. The three 1/2-pel positions are given in Table
I,
which
are predicted according to the values of
xo
and
yo,
refer to Fig. 1
for designations.
Table
I
Search
Points
XO
=o,yo
10
xo
10,yo
=o
xo
>o,y,
=o
xo
>O,YO
>o
I,
IV, VI
111, v, VI11
v, VII, VI11
11,
111,
v
IV, VI, VI1
I,
11,
IV
3.2
Prediction refinement in 1/4-pel and 1/8-pel cases
chosen to be checked, such as the positions 2,3and 5 in Fig.2 (b).
Then the best 1/4-pel motion vector is obtained from the three
1/4-pels, according to the minimum cost function rule. The 1/8-
pel motion vector can be decided in the same way as that of the
1/4-pel.
-
B
-
123
4
-
5
123
4
-
5
Fig.2 Two patterns in prediction refinement
The refinement algorithm can also be used to find the best 1/2-
pel motion vector. But it should be noted that the algorithm can
not estimate the diagonal direction if only
Constraint
Z
is
satisfied,
so
it is not
so
accurate as using PPHPS to find a 1/2-pel
motion vector.
In conclusion,
3
fractional-pel positions need to be checked in
1/4-pel and l/S-pel motion estimation cases respectively and
totally
9
positions should be searched in order
to
get the 1/8-peI
motion vector. Compared with the 24 positions needed in the
Full Fractional Pixel Search algorithm of H.26L, roughly a
62.5% computation reduction is achieved in fractional-pel
motion estimation, where additional calculation for the
paraboloid prediction can be neglected.
Algorithm
3.3 Constraints
on
Fast Integer Pixel Search
After 1/2-pel motion estimation using PPHPS, further prediction
is proposed to achieve higher resolution of motion compensation.
be satisfied in this case,
so
that the PPHPS algorithm cannot be
that the Cost function
F(p)
is a smooth convex function in the
As
discussed
in
[SI,
Constraint
I
should be satisfied when
applying
the
ppHps
algorithm.
However,
not
all
integer
pixel
pixel
search
algorithms,
the
search process
is
divided
into
non-center points. The algorithm first searches all positions in
While it should
be
pointed
Out
that
Constraint
cannot
motion search algorithms
can
satisfy
Constraint
1.
In fast integer
used directly
in
ll4-pe1 or 1/8-pe1
motion
estimation.
Assuming consecutive layers[ 131, each containing a center point and Some
prediction area, we propose a simple and efficient prediction
refinement algorithm to estimate the 1/4-pel and 1/8-pel motion
vectors.
As
mentioned in the last section, three 1/2-pel positions around
the best integer pixel position
C
are checked in the PPHPS
algorithm and the best 1/2-pel position is found. In our
prediction refinement scheme, besides the best 1/2-pel position,
a sub-optimal 1/2-pel position whose cost function value
is
the
second smallest
of
the four positions (three 1/2-pel positions
checked plus the original best integer pixel position) is also
selected.
In view of the relative location of the best 1/2-pel position and
the sub-optimal 1/2-pel position, two patterns are considered.
Let A be the best 1/2-pel position and
B
the sub-optimal 1/2-pel
position. In the first pattern, A and B are in the same horizontal
or vertical line, and three 1/4-pel positions between
A
and
B
are
chosen as the checking pixels for 1/4-pel motion vector. An
instance is shown in Fig.2 (a), where positions
3,5
and 8 are
chosen. In the second pattern, A and
B
are lined up in diagonal
direction, and three 1/4-pel positions between A and
B
are
the current layer, and then chooses one of the optimal positions
as the center of the next layer. When the termination criterion
is
satisfied in a layer, the search will terminate. Here the form of
the non-center points is called Search Pattern. It is obviously
that diamond search pattern can satisfy
Constraint
Z,
and some
existing fast integer search algorithms such as Diamond Search
(DS)[6][7], Nearest-Neighbors Search ("S)[8] and
Unrestricted Center-Biased Diamond Search (UCBDS)[9] are all
based on this pattern[ 131, and they also satisfy
Constraint
I.
4. Simulation Results
The proposed algorithm is evaluated in the framework of H.26L
TML8.0 encoder. Some widely used test sequences, such as
News, Car Phone, Stefan and Coast Guard, are used in the
experiments. The frame rate of the input/output sequences is
30f/s. The picture format is CIF (4:2:0) and 100 frames are
coded in each sequence, the first frame being
I
frame and all
others
P
frames. There are no rate control algorithms introduced
in TML8.0,
so
that all tests are carried out under fixed
111
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11

quantization parameters (QP). Because different QP generates
similar results, QP=IO is selected without
loss
of universality.
For simplicity, we set Inter block search model to 16x16 only
and reference frame number to one, CABAC (context-based
adaptive binary arithmetic coding) employs the entropy coding
method. These options will not affect the final results of our
algorithm.
We adopt full search as the integer pixel motion estimation
algorithm,
so
as to focus our efforts on the studies of fast
fractional pixel motion estimation. Note that the full search also
satisfies
Constraint
I.
Test results for PSNR and bit rate are listed in Table I1 and
Table 111. In simulation, 1/8-pel resolution motion vector are
adopted and the reference method is FFPS, representing Full
Fractional Pixel Search algorithm used in H.26L, which needs
totally 24 fractional-pel positions in this case.
The computation load reduction of fractional-pel motion
estimation is remarkable. Additional computation for paraboloid
prediction as well as sub-optimal position search can be
neglected compared with the calculation of SAD, and in any
case (1/2-pel, 1/4-pel and 1/8-pel) roughly a computational
reduction of 62.5% can be achieved.
Table
I1
Average PSNR of
P
frames
Sequence PSNRldB
Table
111
Average
Bit
Rate of
P
frames
Sequence
As can be seen from
Table
11,
PSNR difference is small for each
sequence, the worst case for PSNR degradation is 0.013dI3 and
the best shows an increase of 0.003dB in PSNR. The average
degradation is 0.006dB.
In Table
111,
Bitr-P represents the average bit rate of P frames. It
can be calculated that the maximal increase of Bitr-P is 3.0%,
the minimal
-0.8%,
and the average value increases by 0.82%. It
can be concluded that the proposed algorithm preserves both
PSNR
and bit rate of the encoded images.
5.
Conclusions
Based on the assumption that the cost function of motion
compensation is a smooth convex function in the sub-area
around the optimal matching position, a paraboloid prediction
based half pixel search algorithm together with a prediction
refinement algorithm for higher resolution fractional-pel motion
estimation (1/4-pel, 1/8-pel, etc.) is adopted in the proposed
Paraboloid Prediction based Fractional Pixel Search strategy.
In any case (1/2-pel, 1/4-pel or 1/8-pel) a computation reduction
of
about 62.5% can be achieved,
so
it can greatly speed up the
fractional pixel motion search. With a remarkable computational
reduction for fractional pixel search, the proposed algorithm has
relatively high prediction accuracy. The proposed algorithm has
negligible affect on image quality and bit rate with an average
0.006 dB PSNR degradation and 0.82% bit rate increase reported
from the simulation of the test sequences as compared to full
fractional pixel motion estima.tion. Moreover, this strategy can
also be applied in MPEG-4 in which 1/4-pel motion vector is
supported.
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