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1. INTRODUCTION

With advances in both communication and multimedia technologies, there is a critical need to have

visual management systems or user-friendly tools to assist in information retrieval from digital

multimedia databases. Amongst the salient features that could be used to define visual content for

example, are pixel intensity, colour, texture, shape and motion. Of these, motion is the most obvious

and effective feature to provide global and local understanding as well as describing the dynamic

content within a video sequence. The extraction of motion parameters from video sequences has

therefore, been one of the key elements in a range of applications from computer vision through to

157

Fast Block-Based True Motion Estimation Using Distance

Dependent Thresholds

Golam Sorwar

School of Multimedia and Information Technology

Southern Cross University

Coffs Harbour, NSW 2457, Australia

Email: gsorwar@scu.edu.au

Fax: +61-2-6659-3612

Manzur Murshed and Laurence Dooley

Gippsland School of Computing and Information Technology

Monash University

Churchill, Vic 3842, Australia

Email: {Manzur.Murshed,Laurence.Dooley}@infotech.monash.edu.au

Fax: +61-3-9902-6879

A fast motion estimation algorithm, called distance-dependent thresholding search

(DTS), is presented for block-based true motion estimation applications, and

introduces the novel concept of variable distance dependent thresholds. The

performance of the DTS algorithm is analysed and quantitatively compared with

both the traditional and exhaustive full-search (FS) technique, and the compu-

tationally faster, non-exhaustive three-step-search (TSS) algorithm. Experimental

results show that by applying an appropriate threshold function, the DTS algorithm

not only matches the speed of the TSS algorithm, but both retains a block distortion

error comparable to the global minimum produced by the FS algorithm, and avoids

the problem of identifying a large number of spurious motion vectors in the search

process.

ACM Classification: I.4 (Image processing and computer vision)

Manuscript received: 3 June 2003

Communicating Editor: Robyn Owens

Copyright© 2004, Australian Computer Society Inc. General permission to republish, but not for profit, all or part of this

material is granted, provided that the JRPIT copyright notice is given and that reference is made to the publication, to its

date of issue, and to the fact that reprinting privileges were granted by permission of the Australian Computer Society Inc.

Journal of Research and Practice in Information Technology, Vol. 36, No. 3, August 2004

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popular video compression standards such as the Motion Picture Expert Group (MPEG-1/2/4)

family.

Motion in video sequences may generally be categorised by: camera movement, the movement

of objects within a frame, and movement of both camera and objects. Many different motion

estimation algorithms have been proposed, including pel-recursive (Robbins and Netravali, 1983;

Walker and Rao, 1984), block-matching (Jain and Jain, 1981), and the optical flow-based method

(Horn and Schunck, 1981; Lucas and Kanade, 1981). The block-matching algorithm (BMA) has

proved to be very popular because of its simplicity, robustness, and ease of implementation. The

algorithm, which estimates motion on a block-by-block basis, has been widely exploited in video

coding standards such as MPEG-1/2 and H.261/263. One important feature (Dufaux and Moscheni,

1995) of the BMA is that it exhibits superior performance for larger-sized pixel block

displacements.

The exhaustive BMA, known as the full search (FS) algorithm, searches each candidate block

for the closest match within the entire search region to minimise the block-distortion measure

(BDM). The BDM of image blocks may be measured using various criteria such as, the mean

absolute error (MAE), the mean square error (MSE), and the matching pel-count (MPC).

Since the FS algorithm exhaustively searches for a global minimum block-difference error for

each candidate block, it generally provides the lowest possible distortion error of any BMA. The

algorithm however, suffers two major drawbacks. Its exhaustive nature inevitably means it is very

computationally expensive and in addition, the algorithm tends to capture many false motion

vectors even when there is no object motion within the search region. This is due to the fact that the

distortion of an object in a video frame is relates to its velocity as well as the zoom factor of the

camera and therefore, as the length of a motion vector grows so does the block difference distortion

error. Although this observation has very little impact when the algorithm is used for video coding,

severe artifacts can arise when the algorithm is applied to estimate the true motion vectors, where

both object and/or camera motion is present.

A number of fast non-exhaustive block matching approaches have been proposed including the

three-step search algorithm (TSS) by Koga et al (1981), the new three-step search algorithm

(NTSS) by Li et al (1994), the 2D-logarithmic search algorithm (2DLOG) by Jain and Jain (1981),

the four-step search algorithm (4SS) by Po and Ma (1996), and the cross-search algorithm by

Ghanbari (1990). Of these, TSS has been recommended by both the Reference Model 8 (RM8) of

CCITT and Simulation Model 3 (SM3) of MPEG, because of its simplicity, regularity and

performance (Po and Ma, 1996; Kim and Choi, 1998). It is still today considered one of the best

algorithms against which to compare the performance of new fast algorithms (Zhou and Chen,

2001; Lai and Wong, 2002; Nam et al, 2000).

All the aforementioned fast algorithms have been based upon the assumption that the BDM

increases as the checking points move away from the global minima. According to Chow and Liou

(1993) however, this assumption does not hold true for real world video sequences. Any directional

search algorithm can, therefore, be ambiguous and converge to one of the local minima. Moreover,

none of the above fast algorithms address the key issue of avoiding the capture of significant numbers

of spurious motion vectors in the search process (Dufaux and Moscheni, 1995).

This paper directly addresses these issues by introducing a new distance dependent thresholding

search algorithm (DTS) which not only avoid picking a large number of false motion vectors, but

also simultaneously exhibits the characteristics of a fast search and low BDM. It is our assumption

that true motion, caused by moving objects, will produce an error surface that would stretch the

search even with thresholding.

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The paper is structured as follows. Section 2 explains the FS and the TSS algorithms, while the

novel distance dependent threshold search (DTS) algorithm using both linear and exponential

thresholding functions, is described in Section 3. Experimental results to verify the performance of

the DTS algorithm in terms of both its search speed and corresponding BDM error measure are

presented in Section 4, which also discusses the selection of the threshold function and related

parameters, as well as explaining how the DTS algorithm avoids a large number of spurious motion

vectors in the search process. Conclusions are provided in Section 5.

2. BLOCK MATCHING ALGORITHMS

Block-based motion estimation algorithm assumes that objects are rigid, move in a translational

movement for at least a few frames and occlusion of one object by another, and uncovered

background, are neglected. In a block-matching algorithm, the current frame is divided into equi-

sized non-overlapping small rectangular blocks, of M × N pixels, as shown in Figure 1. Throughout

the paper, the pixels in a frame are numbered using the Cartesian coordinate system with the origin

being in the upper-left corner. Bn(k,l) denotes the M × N sized block containing all the pixels px,y of

frame number n, where k ≤ x < k + N and l ≤ y < l+M.

For each block of the current frame n, a motion vector is obtained by finding a suitably matched

block, within the search window, of the next frame n+1. For example, in Figure 1, block Bn+1(k + u,

l + v) of the next frame is suitably matched with the block Bn(k,l) of the current frame, so that the

motion vector for the block Bn(k,l) is computed as (u, v).

2.1 The full search (FS) algorithm

In selecting a suitably matched block, the FS algorithm searches the entire search region for a block

such that the BDM is a global minimum. If more than one block generates a minimum BDM, the

FS algorithm selects the block whose motion vector has the smallest magnitude, in order to exploit

the centre-biased motion-vector distribution characteristics of a real-world video sequence (Li et al,

1994; Po and Ma, 1996). To achieve this, checking points are used in a spiral trajectory starting at

the centre of the search region. If the maximum displacement of a motion vector in both the

horizontal and vertical directions is ± d pixels, the total number of search points used to locate the

motion vector for each block can be as high as (2d + 1)2. The spiral trajectory of the checking points

used by the FS algorithm with the maximum displacement, d = 7, is shown in Figure 2.

Figure 1: Frame-block coordinate system

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2.2 The three step search (TSS) algorithm

The TSS algorithm is based on a coarse-to-fine approach with logarithmically decreasing step sizes

as shown in the example of Figure 3, which has a maximum displacement d = 7.

The initial step size is d/2, where d is the maximum motion displacement. At each step, nine

checking points are matched and the point with the minimum BDM is chosen as the starting centre

of the next step. It is straightforward to prove that the total number of checking points used with

maximum motion d is 1+ 8log2(d + 1).

3. THE DISTANCE DEPENDENT THRESHOLDING SEARCH (DTS) ALGORITHM

In the FS algorithm, the suitability of a block match is measured based on the optimal (minimum)

BDM. FS works well when there is no distortion, but as alluded in Section 1, the level of distortion

in any video frame increases with the velocity of the moving objects and/or the zoom factor used

Figure 2: The spiral trajectory of the checking points in the FS algorithm

Figure 3: Three step search path

• First step

■ Second step

♦Third step

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by the camera. Locating a block with the minimum difference, but with a motion vector of high

magnitude, is both ineffectual in the prevailing distorted search space, and may also lead to many

false motion vectors being erroneously selected. The exhaustive FS algorithm therefore, becomes

increasingly inefficient as the spiral trajectory (search pattern) expands.

The basis for the solution proposed in this paper is that the suitability measure of the FS

algorithm is relaxed from the optimal criterion as the spiral search trajectory moves from the centre,

and becomes distance-dependent based thereby exploiting the aforementioned observation, i.e. a

Distance-dependent Thresholding Search (DTS) algorithm.

Definition 1: Search Squares SSiThe search space with maximum displacement d, centred at

pixel pcx,cy, can be divided into d+1 mutually exclusive concentric search squares SSi, for all 0 ≤ i

≤ d, such that a checking point at pixel px,yis ∈ SSkif and only if max(|x–cx|,|y–cy|)=k, for all –d+cx

≤ x ≤ d+cx and –d+cy ≤ y ≤ d+cy.

The checking points used in the first three search squares SS0, SS1and SS2are clearly shown in

Figure 4. From this figure it can be easily identified that

(1)

• Checking points in SS0

■ Checking points in SS1

♦Checking points in SS2

3.1 The Formal DTS Algorithm

Like all block-base motion estimation search techniques, the DTS algorithm starts at the centre of

the search space. The search then progresses outwards by using search squares, SSi, in order while

monitoring the current minimum MAE. Aparametric thresholding function, Threshold(i), is used to

determine the various thresholds to be used in the search involving each SSi. After searching each

SSi, the current minimum MAE is compared against the threshold value of that specific search

square and the search is terminated if this MAE value is not higher than the threshold value. The

DTS algorithm is formally presented in Figure 5.

Figure 4: DTS search squares

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Threshold(i) in the DTS algorithm is a monotonically increasing function with respect to i,

which can have a linear, exponential, or any other complex analytic form. The following two

variable distance dependent threshold functions are applied in this paper.

3.2 Linear thresholding (LT)

Let the centre of the search region be at pixel pcx,cy, which also defines the starting point of the

search. In LT, the search will terminate at search square SSiwhen:

(2)

Assuming b-bit gray level intensity, the maximum value of the MAE will be 2b– 1, since the

pixel intensity is measured using 2blevels with values 0,1,…,2b– 1. As (d,d) is the longest possible

motion vector within the search region, an upper bound may be set for constant CLsuch that:

(3)

3.3 Exponential thresholding (ET)

In ET, the search terminates at search square SSiwhen

(4)

Using a similar argument to that in Section 3.1, an upper limit can be set for the constant CE:

(5)

• Precondition: Pixel pcx,cyis the centre of the search space with maximum displacement d.

• Initialisation:

MinMAE = MAE(cx,cy)(0,0)

MV = (0,0)

• Body:

If MinMAE > 0 Then

For i = 1, 2, …, d

For each checking point px,yin SSi

e = MAE(cx,cy)(x-cx,y-cy)

If e < MinMAE Then

MinMAE = e

MV = (x-cx,y-cy)

If MinMAE ≤ Threshold(i) Then Stop

• Postcondition: MV contains the motion vector and MinMAE contains the distortion error of the

respective block.

Figure 5: The DTS algorithm

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It is interesting to observe that by setting either CL= 0 or CE= 0 in (2) or (4) respectively, it

transforms the DTS algorithm into the exhaustive FS algorithm. It is also clear that the search time

for the DTS algorithm decreases as the value of the constant (CLor CE), used in the respective

threshold function is increased.

4. EXPERIMENTAL RESULTS

The performance of the DTS, TSS, and FS algorithms was evaluated using the luminance (Y-

component) signal of a large number of standard and non-standard video sequences such as:

Football (320×240 pixels), Flower Garden (352×240 pixels), Miss America (176×144 pixels),

Table Tennis (352×240 pixels), Foreman (176×144 pixels), Rocket (176×144 pixels), Ballet

(352×240 pixels), and Son (360×288 pixels). The Table Tennis, Football, Rocket, Ballet, Foreman,

and Son sequences comprise various kinds of motions, including translation, zooming, and panning,

the Flower Garden sequence mainly consists of high portions of fast panning motion, while Miss

America is a very low motion video conferencing sequence. All sequences are uniformly quantized

to an 8-bit gray level intensity. In the experiments, the block size dimensions were M = N = 16 and

d = ±7, i.e., each frame was divided into 16×16 pixel blocks and within each frame, a maximum of

(2d+1)2= 225 checking points were used.

Both linear and exponential threshold functions were used to assess the performance of the DTS

algorithm. In the following results, the linear threshold function with constant CLis denoted as

LT(CL) and the exponential threshold function with constant CEis denoted as ET(CE).

To quantitatively evaluate the performance of the DTS algorithm for both the LT and ET

functions, the following three specific measures were identified:

•

The average MSE between the reconstructed and the corresponding original frames.

•

The average number of search points.

•

The average percentage of true object motion vector captured.

4.1 MSE results

The performance of the DTS algorithm using both the LT and ET functions in terms of the average

MSE between the estimated and original frames is shown in Table 1 and Table 2 for the first 80 frames

of the Table Tennis, Flower Garden, Miss America and Football sequences. It can be observed that all

DTS algorithm variants compared very favorably with the FS algorithm for all test video sequences

except Football, even when the search points was comparable with the TSS algorithm, as for example

in the Tennis LT(8) and Miss America LT(2) cases. It can be also observed that for the Miss America

sequence, with LT(4), the speed improvement factor was almost 20 times faster whereas the average

MSE was very similar (within 0.24%) to the optimal average MSE of the FS algorithm. In contrast, the

performance of the TSS algorithm was significantly inferior, especially in respect of the motion

involved in the Tennis video sequence, as being a directional search algorithm, TSS tends to converge

to one of the local minima as explained in the introduction. Table 2 illustrates that the error performance

of the DTS algorithm was not so satisfactory for the complex motion video sequence, Football. In

Figure 6, we plotted the MSE performances of the DTS algorithm against the FS and TSS algorithms

for Flower Garden and Table Tennis sequences. For the sake of clarity in plotting, we only considered

the threshold function for the DTS algorithm that uses search points comparable to the TSS algorithm.

4.2 Search points results

The performance of the FS, TSS, and DTS algorithms in terms of the average search points to

estimate motion vectors is presented in Table 1 and Table 2. Again it is clear that in the Tennis case,

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DTS with LT(16) is more than 15 times faster than the FS algorithm while the MSE is comparable

to the TSS algorithm (9 times faster). For all values beyond LT(6) in Table 2, for the Miss America

sequence, while the search speed increased, the quality performance in terms of average MSE

remained constant, indicating that although the speed-up factor was high compared to TSS, it still

provided better prediction quality. For the Football sequence however, the search speed of the DTS

algorithm was not so satisfactory compared to TSS algorithm.

The results also proved that by choosing a suitable constant for the selected threshold function, the

average search points required by the DTS algorithm could be considerably less, while concomitantly

having a significantly lower average MSE. In Figure 7, we plotted the search point performances of

the DTS algorithm against the FS and TSS algorithms. For the clarity in plotting, we only considered

the threshold function for the DTS algorithm that generates MSE comparable to the TSS algorithm.

BMA

Flower Garden

MSE(avg) Search points(avg)

270.46

270.97

275.80

283.98

293.61

318.73

353.03

275.96

270.49

270.47

270.47

322.88

BMA

Tennis

MSE(avg) Search points(avg)

126.34

127.25

131.64

138.26

147.59

166.71

183.65

135.22

126.5

126.35

126.35

190.81

FS(±7)

LT(2)

LT(4)

LT(6)

LT(8)

LT(12)

LT(16)

ET(1)

ET(2)

ET(4)

ET(8)

TSS

Table 1: Average MSE and average search points per motion vector for Flower Garden and Tennis

sequences (1–80 frames)

199.76

155.02

73.48

45.93

33.59

23.05

18.60

70.16

155.02

175.65

180.65

23.22

FS(±7)

LT(2)

LT(4)

LT(6)

LT(8)

LT(12)

LT(16)

ET(1)

ET(2)

ET(4)

ET(8)

TSS

196.98

75.68

38.14

26.03

20.35

14.65

12.36

49.22

120.80

171.16

182.36

22.75

BMA

Miss America

MSE(avg) Search points(avg)

5.386

5.395

5.399

5.408

5.408

5.408

5.408

5.400

5.398

5.397

5.397

5.511

BMA

Football

MSE(avg) Search points(avg)

335.70

335.96

340.67

356.53

380.03

430.26

471.12

360.90

335.73

335.70

335.70

370.32

FS(±7)

LT(2)

LT(4)

LT(6)

LT(8)

LT(12)

LT(16)

ET(1)

ET(2)

ET(4)

ET(8)

TSS

Table 2: Average MSE and average search points per motion vector for Miss America and Football

sequences (1-80 frames)

168.21

15.14

14.60

9.01

7.90

7.25

7.22

12.81

26.61

48.20

64.31

19.67

FS(±7)

LT(2)

LT(4)

LT(6)

LT(8)

LT(12)

LT(16)

ET(1)

ET(2)

ET(4)

ET(8)

TSS

202.05

123.71

82.57

57.10

41.75

26.88

20.51

74.89

154.95

191.31

197.71

23.11

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Another finding from the results in Table 1 and Table 2 was that the LT function consistently

provided a better performance in comparison with the ET function for a wide range of different

video sequences. This was not surprising due to the fact that the distortion of an object in any frame

was linearly proportional to its velocity as well as the zoom factor of the camera.

4.3 True motion result

The performance of the DTS algorithm was also evaluated in terms of how effectively it could

capture true object motion. As the block-based technique captures both object and camera motion,

to remove camera motion when capturing true object motion vectors, a well known four parameter

(pan and zoom) global motion estimation model and Iterative-Least-Square Estimation technique

(Rath and Makur, 1999) have been used to estimate the global motion parameters. Having

compensated for global motion, true object motion vectors should usually be clustered in the blocks

Figure 7: Comparison of average search points required per motion vector for the

(a) Flower Garden; (b) Tennis sequences

(a)(b)

Figure 6: MSE Comparison: (a) Flower Garden; (b) Tennis video sequences

(a)(b)

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containing one or more objects. However, as block motion estimation cannot be performed with full

accuracy due to the limitations of block-based estimation techniques, false motion vectors appear

as noise, together with the true object motion vectors. To retain only the true object motion vectors,

these false motion vectors are removed.

A simple strategy is to define a false motion vector elimination threshold T, with the decision

based on the value of T (Kim and Ro, 1999). This approach is flawed however, since thresholding

only performs well if the true and false motion vectors have different magnitudes (lengths). In the

case where the lengths are similar, the technique will not separate true from false motion vectors. An

alternative strategy for eliminating false vectors is to gradually increase the length of the true motion

vectors by a larger amount compared with false motion vectors, so that the true motion vector lengths

can be separated by thresholding. To achieve this goal, the Mean Accumulated Threshold (MAT)

filter design proposed by (Sorwar, Murshded and Dooley, 2001) has been applied. This was

implemented as a two-stage combination of accumulation of the mean vector length, in addition to

the original vector length, and thresholding. The performance of the MAT filter proved to

Figure 9: Average number of true object motion vector captured by different algorithms

Figure 8: Comparison of LT, ET, FS and TSS in terms of the percentage of true motion vectors captured

with different noise tolerance thresholds

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significantly increase the length of true object motion vectors compared with all other vectors, within

a relatively small number of iterations (for certain sequences this can be as low as 2).

The above process was applied to six different standard video sequences (Table Tennis, Foreman,

Salesman, Rocket, Son and Ballet) from Berkeley MPEG library (Mpeg-lib, 1997) and the average

values are plotted in Figure 8 and Figure 9. Figure 9 shows the highest percentage of true motion

vectors over two iterations, obtained after filtering all the vectors using the MAT filter and manually

selecting using a priori knowledge concerning the moving objects in the frame, captured by different

search algorithms. From this plot it can be seen that DTS with the LT function captures approximately

75% of the true motion vectors, where as the FS and TSS algorithms capture only around 40% of true

motion vectors. This clearly confirms the superiority of the DTS algorithm, for both LT and ET

functions in capturing the true object motion vectors, for all noise tolerance threshold levels

considered. The graphs also reaffirm the earlier judgment that LT is a better thresholding function for

the DTS algorithm.

Figure 10 shows the motion vectors captured by all three algorithms for the pair of frames 32

and 33 from the Tennis sequence. Besides low camera motion (zoom out), the only moving objects

appearing in these frames are the ball, the bat, and a portion of the hand holding the bat. The figure

Figure 10: The motion vectors obtained from all four search algorithms applied to the frame pair 32 and 33

of the Tennis sequence

(c) ET(1)(d) TSS

(a) FS (b) LT(8)

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reveals that the FS and TSS algorithms perform far worse compared to the DTS algorithm, by

capturing a large number of spurious true motion vectors. The variable distance threshold of the

DTS algorithm eliminates many of the false vectors so ensuring an overall superior performance.

5. CONCLUSIONS

This paper has presented a novel Distance-dependent Thresholding Search (DTS) algorithm for

block-based motion estimation in video coding and true object motion estimation for object motion

based video analysis. An important feature of DTS is that the FS as well as other fast searching modes

are encompassed, with different threshold settings, enabling differing quality-of-service levels. A

unique characteristic of the DTS algorithm is that its flexibility in being able to trade predicted picture

quality (MSE) for search speed in different video sequences. This flexibility has considerable

potential for exploitation in a wide range of applications ranging from low-bit rate video con-

ferencing, through to adaptive high-quality video coding. The performance of DTS was examined

and shown, in comparison to both the full-search (FS) and the fast three-step-search (TSS) algorithms

for all test sequences. With the exception of the very high motion Football sequence, it provided

comparable speed performance, while retaining a distortion error comparable to the optimum value

produced by the FS algorithm. Both linear and exponential thresholding functions were examined

with the former consistently providing better performance. The variable thresholding feature of DTS

also avoided identifying large numbers of spurious motion vectors in the search process.

6. ACKNOWLEDGEMENT

The authors would like to formally acknowledge both anonymous reviewers for their insightful

comments, suggestions and criticisms, which considerably improved the quality of this paper.

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BIOGRAPHICAL NOTES

Golam Sorwar received his B.Sc (Hons.) in Electrical and Electronic

Engineering in 1994 from Bangladesh University of Engineering and

Technology (BUET), M.Sc. in Electrical, Electronic and Systems Eng. in 1998

from the National University of Malaysia, and Ph.D. in IT from Monash

University, Australia in 2003. He is currently a lecturer at the School of

Multimedia and Information Technology at Southern Cross University,

Australia, where his major research interests are in the fields of image/video

coding, indexing and retrieval, motion estimation, shot detection, multimedia

communication and artificial intelligence. Dr. Sorwar is a member of ACS,

IEEE, and Institute of Engineers of Bangladesh (IEB).

Manzur Murshed received his B.Sc.Engg. (Hons.) in Computer Science

and Engineering from Bangladesh University of Engineering and Technology

(BUET) in 1994 and Ph.D. in Computer Science from the Australian National

University in 1999. He is currently the Director of Research and a Senior

Lecturer at Gippsland School of Computing and Information Technology,

Monash University, Australia, where his major research interests are in the

fields of multimedia signal processing and communications, parallel and

distributed computing, algorithms, and multilingual systems development. He

has published more than 40 journal and peer-reviewed research publications.

Dr. Murshed is a member of the IEEE.

Laurence S. Dooley received his B.Sc.(Hons), M.Sc. and Ph.D. degrees in

Electrical Engineering from the University of Wales, Swansea in 1981, 1983

and 1987 respectively. He is currently Professor of Multimedia Technology at

the Gippsland School of Computing & IT, Monash University, Australia,

where his major research interests are in the fields of multimedia signal

processing, mobile multimedia communications and video technology. He has

published more than 80-international scientific peer-reviewed journal, book

chapters and conference papers. He is also Executive Director of the Monash

Regional Centre for ICT (MRCICT). Professor Dooley is a Senior Member of

the IEEE, a Chartered Engineer (C.Eng).

Golam Sorwar

Manzur Murshed

Laurence Dooley