Technical Report number RUCS/2005/TR/01/002/A
Linear Algorithm Predicted Two-Pass Hexagonal
Algorithm for Video Compression
Yunsong Wu,
Graham Megson
Parallel, Emergent and Distributed Architecture Laboratory
School of Systems Engineering,
Reading University
Yunsong Wu, Graham Megson
A Novel Linear Predicted Two-Pass Hexagonal
Search Algorithm for Motion Estimation
ABSTRACT
This paper presents a novel two-pass algorithm constituted by Linear Hashtable Motion
Estimation Algorithm (LHMEA) and Hexagonal Search (HEXBS) for block base motion
compensation. On the basis of research from previous algorithms, especially an
on-the-edge motion estimation algorithm called hexagonal search (HEXBS), we propose
the LHMEA and the Two-Pass Algorithm (TPA). We introduced hashtable into video
compression. In this paper we employ LHMEA for the first-pass search in all the
Macroblocks (MB) in the picture. Motion Vectors (MV) are then generated from the
first-pass and are used as predictors for second-pass HEXBS motion estimation, which
only searches a small number of MBs. The evaluation of the algorithm considers the
three important metrics being time, compression rate and PSNR. The performance of the
algorithm is evaluated by using standard video sequences and the results are compared to
current algorithms. Experimental results show that the proposed algorithm can offer the
same compression rate as the Full Search. LHMEA with TPA has significant
improvement on HEXBS and shows a direction for improving other fast motion
estimation algorithms, for example Diamond Search.
Keywords
video compression, motion estimation, linear algorithm, hashtable, hexagonal search.
School of Systems Engineering, Reading University, Reading, UK, RG6 6AA
Correspondence to: Yunsong Wu, PEDAL Group, School of Systems Engineering,
The University of Reading, Reading RG6 6AY, United Kingdom.
E-Mail: sir02yw@rdg.ac.uk
1. INTRODUCTION
In this paper, we propose a Linear Hashtable Motion Estimation Algorithm (LHMEA) and a Two-Pass
Algorithm constituted by LHMEA and Hexagonal Search (HEXBS) to predict motion vectors for
inter-coding. The objective of our motion estimation scheme is to achieve good quality video with
very low computational complexity. There are a large number of motion prediction algorithms in the
literature. This paper is only concerned with on one class of such algorithms, the Block Matching
Algorithms (BMA), which is widely used in MPEG2, MPEG4, and H.263. In BMA, each block of the
current video frame is compared to blocks in reference frame in the vicinity of its corresponding
position. The one with the least Mean Square Error (MSE) is considered as a match, and the difference
of their positions is the motion vector of the block in the current frame to be saved in the
corresponding position on the motion map. Motion estimation is quite computationally intensive and
can consume up to 80% of the computational power of the encoder if the full search (FS) is used. It is
highly desired to speed up the process without introducing serious distortion.
In the last 20 years, many fast algorithms have been proposed to reduce the exhaustive checking of
candidate motion vectors (MV). Fast block-matching algorithms (BMA) use different block-matching
strategies and search patterns with various sizes and shapes. Such as Two Level Search (TS), Two
Dimensional Logarithmic Search (DLS) and Subsample Search (SS) [1], the Three-Step search (TSS),
Four-Step Search (4SS) [2], Block-Based Gradient Descent Search (BBGDS) [3], and Diamond
Search (DS) [[4], [5]] algorithms. A very interesting method called HEXBS has been proposed by Ce
Zhu, Xiao Lin, and Lap-Pui Chau [6]. There are some variant HEXBS method, such as Enhanced
Hexagonal method [7], Hexagonal method with Fast Inner Search [8] and Cross-Diamond-Hexagonal
Search Algorithms[9]. The fast BMA increases the search speed by taking the nature of most
real-world sequences into account while also maintain a prediction quality comparable to Full Search.
As shown in the table 1, most algorithms suffer from being easily trapped in a non-optimum solution.
Our LHMEA method attempts to predict the motion vectors using a linear algorithm and Hashtable
[10]. In this paper we propose the LHMEA and the TPA. In the first-pass coding, we employ LHMEA
to search all Macroblocks (MB) in picture. Motion Vectors (MV) generated from first pass will be
used as predictors for second-pass HEXBS motion estimation, which only searches a small number of
the MBs. Because LHMEA is based on a linear algorithm, which fully utilizes optimized computer’s
structure based on addition, its computation time is relatively small. Meanwhile HEXBS is one of best
motion estimation methods to date. The new method proposed in this paper achieves the best results
so far among all the algorithms investigated. A test with moments invariant shows how powerful the
hashtable method can be.
Contributions from this paper are:
(1) It achieves the best results among all investigated BMA algorithms.
(2)First time, hashtable concept is used in the search for motion vectors in video compression.
(3) Linear algorithm is used in video compression to improve speed and allow for future parallel
coding.
(4) The Two Pass Algorithm (TPA) is proposed. LHMEA is used for the first pass while HEXBS is
used for a second pass. MVs produced by the first pass will be used as predictors for the second pass
and this makes up for the drawback of the coarse search in the hexagonal search. This can also be used
and leave space for research of nearly all kinds of similar fast algorithms for example Diamond Search
etc.
(5) Invariant moments are added into hashtable to check how many coefficients work best for
hashtable. We also prove that the more information hashtable has, the better result the table will have.
(6) Spatially related MB information is used not only in coarse search but also inner fine search.
The rest of the paper is organized as follows. Section I continues with a brief introduction to HEXBS
and varieties. The proposed LHMEA, moments method and LAHSBTPA are discussed in Section II.
Experiments conducted based on the proposed algorithm are presented in Section III. We conclude in
Section VI with some remarks and discussions about the proposed scheme.
Table 1: Comparison of different fast search algorithms and their disadvantage
Fast
Search
Algorithms
Disadvantage
Three
Step PSNR is substantially lower, it can
(Two-dimensional be easily trapped in a non-optimum
logarithmic )Search solution. Inefficiency to estimate
small motions.
(TSS)
New Three Step Small motion compensation errors
and much more robust than TSS
Search
method
(NTSS)
Four Step Search Performance of FSS is maintained
for image sequence that contains
(FSS)
complex movement such as camera
zooming and fast motion. Easily
trapped in non-optimum solution
The algorithm might actually have
Block-Based
Gradient Descent significant problems when coding
Search (BBGDS) non center- biased sequences. Easily
trapped in non-optimum solution
The problem of propagating false
Hierarchical
Motion Estimation motion vectors
(HME)
New
Diamond Sensitive to motion vectors in
different directions. Easily trapped in
Search (DS)
non-optimum solution
Hexagonal Search Easily trapped
solution
( HEXBS)
in
non-optimum
1.1 Hexagonal Search Algorithm
The Hexagonal Search Method is an improved method based on the DS (Diamond Search). HEXBS
has shown significant improvement over other fast algorithms such as DS. In contrast with the DS that
uses a diamond search pattern, the HEXBS adopts a hexagonal search pattern to achieve faster
processing due to fewer search points being evaluated. The motion estimation process normally
comprises of two steps. First is a low-resolution coarse search to identify a small area where the best
motion vector is expected to lie, followed by fine-resolution inner search to select the best motion
vector in the located small region. The large central 5x5 search pattern used in HEXBS, can provide
fast searching speed. It gives consistently better motion estimates and directions due to larger size.
Another relief of reducing checking points is to have successive search patterns can be overlapped.
HEXBS requires only three extra points to be evaluated in each step. Most fast algorithms focus on
speeding up the coarse search by taking various smart ways to reduce the number of search points to
identify a small area for inner search. There are two main directions to improve the coarse search:
1. usage of predictors [[8], [11]]
2. early termination [11]
A new algorithm [11] was introduced on HEXBS, which is similar as Motion Vector Field Adaptive
Search Technique (MVFAST) based on DS. The algorithm has significantly improved the preexisting
HEXBS both in image quality and speed up by initially considering a small set of predictors as
possible motion vector predictor candidates. Then using a modified Hexagonal pattern used the best
motion vector predictor candidate as the center of search. Another prediction set is proposed in the
literature [[13], [14]]. In general, Search blocks correlated with the current one can be divided into
three categories as in Figure.1.:
Figure. 1.
Blocks correlated with the current one
(1) Spatially correlated blocks (A0, B0, C0, D0),
(2) Neighboring blocks in the previous frame (A1, B1, C1, D1, E1, F1, G1, H1)
(3) Co-located blocks in the previous two frames (X2 and X3), which provide the Acceleration motion
vector (MV).
Except for coarse search improvement, Inner search improvement includes:
1. 4 points [8]
2. 8 points [11]
3.
Inner group search [11].
Figure. 2.
Inner Search Method
2. TYPESET TEXT LINEAR ALGORITHM AND HEXAGONAL
SEARCH BASED TWO-PASS ALGORITHM (LAHSBTPA)
Most of the current Hexagonal search algorithms are predictive methods that focus on relations
between current frame and previous frames. They approach the global minimum on assumption that
local minimum is global minimum which may not always be the case. What we want to do is to find a
fast method which discovers the predictor from the current frame information by using spatially
related MB or pixel information. The method can avoid trapping in local minimum, fast, accurate and
independent on finding right predictors. So we have designed a vector hashtable lookup and block
matching algorithm. It is more efficient method to perform an exhaustive search. It uses global
information in the reference block. The block-matching algorithm calculates each block to set up a
hashtable. By definition hashtable is a dictionary in which keys are mapped to array positions by a
hash function.
We try to find as few as possible variables to represent the whole macroblock. Through some
preprocessing steps, “integral projections” are calculated for each macroblock. These projections are
different according to each algorithm. The aim of these algorithms is to find the best projection
function. The algorithms we present here have two projections, one of them is the massive projection,
which is a scalar denoting the sum of all pixels in the macroblock. It is also DC coefficient of
macroblock. Another is A of Y=Ax+B (y is luminance, x is the location.) Each of these projections is
mathematically related to the error metric. Under certain conditions, the value of the projection
indicates whether the candidate macroblock will do better than the best-so-far match. The major
algorithm we discuss here is linear algorithm.
2.1 Linear Hashtable Motion Estimation Algorithm (LHMEA)
In previous research methods, when people try to find a block that best matches a predefined block in
the current frame, matching was performed by SAD (calculating difference between current block and
reference block). In Linear Hashtable Motion Estimation Algorithm (LHMEA), we only need compare
two coefficients of two blocks. In the current existing methods, the MB moves inside a search window
centered on the position of the current block in the current frame. In LHMEA, the coefficients move
inside the hashtable to find the matched blocks. If coefficients are powerful enough to hold enough
information of the MB, motion estimators should be accurate. So LHMEA increases accuracy, reduces
computation time and may allow for a new era of video encoding. The Linear Algorithm is the easiest
and fastest way to calculate on a computer because the constructions of computer arithmetic units are
based on additions. So if most of calculations of video compression are done on linear algorithm, we
can save lots of time on compression. It is also very easy to put on parallel machines in the future,
which will benefit real time encoding. In the program, we try to use polynomial approximation to get
such result y=mx+c; y is luminance value of all pixels, x is the location of pixel in macroblocks. The
way of scan y is from left to right, from top to button. Coefficients m and c are what we are looking
for to put into hashtable.
N
m
i 0
N
i 0
i 0
(1)
1000
N
c
N
N *  ( xi * yi )   xi *  yi
N
 y * x
i
i 0
i 0
N
N
N
i 0
N
i 0
N
  xi *  xi * y i
2
i
(2)
N *  xi   xi *  xi
2
i 0
i 0
i 0
According to experience of our research in the encoder, we changed m to keep its value around
100-1000. This improved a lot on previous research result whose m is always zero in hashtable, in
which case there is only c in hashtable. In this way, we initially realized the way to calculate the
hashtable.
2.2 Moments Invariants
Except for the coefficients from the Linear Algorithm, we put moments invariant into the hashtable as
a test. The set of moments we are considering is invariant to translation, rotation, and scale change.
We consider moments represent a lot more information than the coefficients m and c that we proposed
in LHMEA. As we can see from the experimental result, moments have some improvement on
hashtable method. By performing experiments on moments, we attempt to understand how many
coefficients work best for the hashtable. Second we try to prove that the more information hashtable
has the better the hashtable is.
In this paper, moments of two-dimensional functions are as following [14]:
For a 2-D continuous function f(x,y) the central moments are defined as
 pq 
 ( x  x)
x
where x 
p
( y  y)q f ( x, y)
(3)
y
m10
m
and y  01
m00
m00
The normalized central moments, denoted  pq , are defined as
 pq 
 pq
  00
where  
pq
 1 for p+q=2,3,….
2
A set of seven invariant moments can be derived from the second and third moments.
1  20  02
2  (20  02 )2  4112
3  (30  312 ) 2  (321  03 ) 2
4  (30  12 )2  (21  03 )2
5  (30  312 )(30  12 )(30  12 ) 2  3( 21  03 ) 2 

 (3 21   03 )( 21  03 ) 3(30  12 ) 2  ( 21  03 ) 2
6  ( 20  02 )(30  12 )  ( 21  03 )
 411 (30  12 )( 21  03 )
2
2


 7  (3 21   03 )( 30  12 )( 30  12 ) 2  3( 21   03 ) 2 

 (312  30 )( 21  03 ) 3(30  12 ) 2  ( 21   03 ) 2

Table 2 shows experiment result using three different algorithms: LAHSBTPA without moments;
LAHSBTPA with 2 moments 1 and 2 in hashtable; and LAHSBTPA with 7 moments in hashtable.
The experiments result proves that invariant moments used in hashtable help increase compression
rate and PSNR on the cost of compression time. It means if we can find better coefficients in hashtable,
the experimental result can be further improved.
Table 2: Comparison of compression rate, time and PSNR among TPA with different number of moments in
hashtable (based on 150 frames of Table Tennis)
Data
Steam
Table
Tennis
Table Tennis
Table Tennis
Moment Test
No moments
With 2 Moments
With 7 Moments
compressi
on time(s)
compressi
on rate
average P
frame
PSNR
16
32
43
94
94
95
40.2
40.6
40.6
2.3 The Proposed Two-Pass Algorithm
In order to take advantages of the two different schemes of LHMEA and HEXBS, meanwhile, in order
to strike a compromise between efficiency of LHMEA and performance of HEXBS in the estimation,
we develop an efficient TPA [16] where HEXBS’s problem is solved by LHMEA. Within the TPA,
first-pass, LHMEA will generate a set of MVs. The second-pass, which is the HEXBS, will use MVs
from first-pass for coarsely search as predictors, thereby further improving the efficiency of HEXBS
while these predictors are different from all previous predictors. They are based on full search and
current frame only. Because LHMEA is linear algorithm, it is fast. Because the predictors generated
are accurate, it improves HEXBS without too much delay.
(a) Original
Figure. 3.
(b) By proposed method
Original HEXBS Coarse Search [6] (a) and proposed HEXBS Coarse Search (b)
The original HEXBS is moved step by step, maximum two pixels per step, but in our proposed
method, in second-pass, the LHMEA motion vectors are used to move hexagon pattern directly to the
area where near to the pixel whose MB distortion is smallest. This saved computation in the
low-resolution coarse search and improved accuracy.
In summary, the TPA is shown in Fig. 4.
First Filter: LHMEA
MVs generated as predictors
Second Filter: HEXBS
Final MVs
Figure. 4. Process of TPA
3. EXPERIMENTAL RESULTS
In the Fig.5 we compare our method to other method. The method listed are Full Search (FS),
Linear Hashtable Motion Estimation Algorithm (LHMEA), Subsample Search (SS), Two Level Search
(TLS), Logarithmic Search (LS), Hexagonal Search (HEXBS) and Linear Algorithm and Hexagonal
Search Based Two-Pass Algorithm (LAHSBTPA). LAHSBTPA used 6-side-based fast inner search [11]
and early termination criteria mentioned in this paper. The reason of choice of other algorithms is that
they are most famous algorithms in the field. The LAHSBTPA was found to be the fastest of all the
current algorithms tested when compression rate and PSNR remain a priority. In Fig.5, LAHSBTPA is
fastest algorithm when compression rate is best and PSNR is high being 23% faster than the
Logarithmic Search. In the tables of Football, LAHSBTPA is the fastest algorithm when compression
rate is near same as the Full Search while the PSNR is same and is 27% faster than the Logarithmic
Search. LAHSBTPA is better than HEXBS on compression rate, time and PSNR. If we can find better
coefficients in the hashtable to represent MB, the hashtable may show great promise.
38
40
35
30
25
20
15
10
5
0
38
38
38
38
32
HE
XB
S
LA
HS
BT
PA
VE
CT
OR
_H
AS
H
TW
OL
EV
EL
LO
GA
RI
TH
MI
C
SU
BS
AM
PL
E
30
EX
HA
US
TI
VE
Compression Rate
Compression Rate of Different Algorithms
Compression Time(s)
Compression Time of Different Algorithms
149
160
140
120
100
80
60
40
20
0
108
46
44
22
E
IC
IV
HM
ST
IT
AU
R
H
GA
EX
LO
17
EL
EV
OL
TW
E
PL
AM
BS
U
S
17
S
XB
HE
PA
BT
HS
LA
SH
HA
R_
O
CT
VE
Figures. 5. Comparison of compression rate and time among FS, LS, SS, TLS, LHMEA,
LAHSBTPA, HEXBS (based on 150 frames of Flower Garden)
50
48
46
44
42
40
38
36
48
48
47
48
47
46
HE
XB
S
LA
HS
BT
PA
TW
OL
EV
EL
VE
CT
OR
_H
AS
H
SU
BS
AM
PL
E
41
EX
HA
US
TI
VE
LO
GA
RI
TH
MI
C
Compression Rate
Compression Rate of Different Algorithms
158
180
160
140
120
100
80
60
40
20
0
110
48
41
LA
HS
BT
PA
VE
CT
OR
_H
AS
H
14
HE
XB
S
14
TW
OL
EV
EL
LO
GA
RI
TH
MI
C
SU
BS
AM
PL
E
19
EX
HA
US
TI
VE
Compression Time(s)
Compression Time of Different Algorithms
Figure. 6. Comparison of compression rate and time among FS, LS, SS, TLS, LHMEA,
LAHSBTPA, HEXBS (based on 125 frames of Football)
45.2
40.4 40.8
42.3
43.7 43.8
40.1
HE
XB
S
46
44
42
40
38
36
EX
HA
US
TI
LO
VE
GA
RI
TH
MI
C
SU
BS
AM
PL
E
TW
OL
EV
VE
EL
CT
OR
_H
AS
H
LA
HS
BT
PA
PSNR(db)
Average PSNR ( P frame)
Figure. 7. Comparison of PSNR among FS, LS, SS, TLS, LHMEA, LAHSBTPA, HEXBS (based
on 150 frames of Flower Garden)
The FS, HEXBS, LAHSBTPA are certain center biased algorithms. This is also basis of several other
algorithms. It means that most of MVs are equal to each other as demonstrated in the figures below.
As the center-biased global minimum motion vector distribution characteristics, more than 80% of the
blocks can be regarded as stationary or quasi-stationary blocks and most of the motion vectors are
enclosed in the central area (as depicted in Fig. 8). Based on the fact that for most sequences motion
vectors were concentrated in a small area around the center of the search, it suggests that, instead of
initially examining the (0,0) position, we could achieve better results if the LHMEA predictor is
examined first and given higher priority with the use of early termination threshold. It avoids to be
trapped in local optimum around the central point of the search window which is also the problem of
most fast algorithms as previously mentioned. It also avoids producing wrong motion vectors for the
blocks undergoing large motion.
In Fig, 7 the MVs’ data is analyzed. X and Y are derived from MV(X,Y). Z is the total number of
MV(X,Y) in video P frames only.
MVs distribution
800
700
600
500
400
300
200
100
0
21
14
21
0
7
-7
-21
-14
0
MV_Y
-21
MV_X
(a) Flower Garden
MV Distribution
1000
800
600
400
200
21
0
14
21
7
0
-7
-21
-14
0
MV_Y
-21
MV_X
(b) Football
MV MV
Distribution
Distribution
1000
4000
3500
800
3000
2500
400
2000
1500
200
1000
0
500
0
21
21
14 21
-21
21
7
7 14
MV_X
0
-21-14
0
-14 -7
-7 0
-21
600
MV_Y
0
MV_Y
-21
MV_X
(c) Table tennis
Figure.8. MVs distribution of different video steams over the search windows (  10 ): Flower
Garden (a), Football (b), Table tennis (c). (based on P frames)
In Fig. 9. we randomly picked frames from Flower Garden, Football and Table Tennis MPEG clips
generated by LAHSBTPA. We analyzed MB types and displayed value of MVs in the pictures. These
pictures show our method made excellent decision on MB types.
Figure.9. Motion vectors and MB analysis in frames from Table Tennis, Football and Flower
Garden by LAHSBTPA.
4. CONCLUSION
In the paper we proposed a new two-pass algorithm called Linear Algorithm and Hexagonal Search
Based Two-Pass Algorithm (LAHSBTPA) for video compression. In our algorithm, a preprocessing
pass used a linear algorithm to set up hashtable. The algorithm searched in the hashtable to find
motion estimator instead of by FS. Then the generated motion vector was sent to the second-pass
HEXBS, which is found to be the best motion estimation algorithm, as the predictor. So TPA is
obtained by applying motion estimation twice, which we call two-pass algorithm. The result of
LAHSBTPA is much better than LHMEA or HEXBS used alone in motion estimation and also best in
all the surveyed algorithms. We did experiments on moments to show that the more information
hashtable has, the better it is. No matter in coarse search or fine inner search, new method used spatial
related MB or pixels’ information. In this way, both quality and speed of the motion estimation is
improved. The key point in the method is to find suitable coefficients to represent whole MB. The
more information the coefficients in hashtable hold about pictures, the better result LAHSBTPA will
get. At the same time, this TVP will improve other similar fast motion estimations and this leaves
space for future developments.
4. ACKNOWLEDGMENTS
Thanks for Dr. Simon Sherratt’s help on final paper.
5. REFERENCES
[1].
[2].
[3].
[4].
[5].
[6].
[7].
[8].
[9].
[10].
[11].
[12].
[13].
[14].
Ze-Nian li Lecture Note of Computer Vision on personal website (2000)
L. M. Po and W. C. Ma: A novel four-step search algorithm for fast block motion estimation,” IEEE and systems
for video technology, vol. 6, pp. 313–317, (June 1996.)
L. K. Liu and E. Feig: A block-based gradient descent search algorithm for block motion estimation in video
coding,” IEEE Trans. Circuits Syst. Video Technol., vol. 6, pp. 419–423, (Aug. 1996.)
S. Zhu and K.-K. Ma: A new diamond search algorithm for fast blockmatching motion estimation: IEEE Trans.
Image Processing, vol. 9, pp. 287–290, (Feb. 2000.)
J. Y. Tham, S. Ranganath, M. Ranganath, and A. A. Kassim: A novel unrestricted center-biased diamond search
algorithm for block motion estimation: IEEE Trans. Circuits and systems for video technology, vol. 8, pp.
369–377, (Aug. 1998)
Ce Zhu, Xiao Lin, and Lap-Pui Chau: Hexagon-Based Search Pattern for Fast Block Motion Estimation: IEEE
Trans on circuits and systems for video technology, Vol. 12, No. 5, (May 2002)
Ce. Zhu, X. Lin and L.P. Chau: An Enhanced Hexagonal Search Algorithm for Block Motion Estimation: IEEE
International Symposium on Circuits and Systems, ISCAS2003, Bangkok, Thailand, (May 2003)
Ce Zhu, Senior Member, IEEE, Xiao Lin, Lappui Chau, and Lai-Man Po: Enhanced Hexagonal Search for Fast
Block Motion Estimation: IEEE Trans on circuits and systems for video technology, Vol. 14, No. 10, (Oct 2004)
Chun-Ho Cheung, Lai-Man Po:Novel Cross-Diamond-Hexagonal Search Algorithms for Fast Block Motion
Estimation:IEEE Trans on Multimedia, Vol. 7, No. 1, (Feb. 2005)
Graham Megson & F.N.Alavi Patent 0111627.6 -- for SALGEN Systems Ltd
Paolo De Pascalis, Luca Pezzoni, Gian Antonio Mian and Daniele Bagni: Fast Motion Estimation With
Size-Based Predictors Selection Hexagon Search In H.264/AVC encoding: EUSIPCO (2004)
Alexis M. Tourapis, Oscar C. Au, Ming L. Liou: Predictive Motion Vector Field Adaptive Search Technique
(PMVFAST) Enhancing Block Based Motion Estimation: proceedings of Visual Communications and Image
Processing, San Jose, CA, January (2001)
A. M. Tourapis, O. C. Au and M. L. Liou: Highly Efficient Predictive Zonal Algorithms for Fast Block. Matching
Motion Estimation: IEEE Transactions on Circuits and Systems for Video Technology, vol. 12, No.10, pp
934-947, (October 2002)
H-Y C. Tourapis, A. M. Tourapis: Fast Motion Estimation within the JVT codec: Joint Video Team (JVT) of
ISO/IEC MPEG and ITU-T VCEG 5th meeting, Geneva, Switzerland: (09-17 October 2002)
[15]. Rafael C. Gonzalez: Digital Image Processing second edition: Prentice Hall (2002)
[16]. Jie Wei and Ze-Nian Li: An Efficient Two-Pass MAP-MRF Algorithm for Motion Estimation Based on Mean
Field Theory: IEEE Transactions on Circuits and Systems for Video Technology, vol. 9, No. 6, (Sep. 1999)