global motion parameters estimation using a fast and robust algorithm

4
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 7, NO. 5, OCTOBER 1997 823 each CV. In fact, the data dependency between the CV’s can also be exploited to achieve a higher throughput for higher quality video applications by using some extra circuits. VI. CONCLUSION In this paper, we have introduced a CV-based BMME algorithm based on the consideration of VLSI implementation. Compared to the widely used fast BMME algorithms such as the TSS and NTSS algo- rithms, the proposed BMME algorithm possesses better algorithmic performance. Although the proposed algorithm has higher computa- tional complexity than TSS/NTSS for software execution, however, using the state-of-the-art VLSI technology, it can be implemented cost-effectively with the proposed VLSI architecture. Furthermore, the proposed BMME algorithm and the VLSI architecture can be easily extended with different designs of CV pattern for different video applications. REFERENCES [1] J. R. Jain and A. K. Jain, “Displacement measurement and its application in interframe image coding,” IEEE Trans. Commun., vol. COM-29, pp. 1799–1808, Dec. 1981. [2] R. Li, B. Zeng, and M. L. Liou, “A new three-step search algorithm for fast block motion estimation,” IEEE Trans. Circuits Syst. Video Technol., vol. 4, pp. 438–442, Aug. 1994. [3] T. Koga, K. Iinuma, A. Hirano, Y. Iijima, and T. Ishiguro, “Motion compensated interframe coding for video conferencing,” in Proc. Nat. Telecommunications Conf., New Orleans, LA, Nov. 29, Dec. 1981, pp. G5.3.1–G5.3.5. [4] M. Ghanbari, “The cross-search algorithm for motion estimation,” IEEE Trans. Commun., vol. 38, pp. 950–953, July 1990. [5] R. Srinivasan and K. R. Rao, “Predictive coding based on efficient mo- tion estimation,” IEEE Trans. Commun., vol. COM-33, pp. 1011–1015, Sept. 1985. [6] L. G. Chen, W. T. Chen, Y. S. Jehng, and T. D. Chiueh, “An efficient parallel motion estimation algorithm for digital image processing,” IEEE Trans. Circuits Syst. Video Technol., vol. 1, pp. 407–416, Dec. 1991. [7] L.-M. Po and W.-C. Ma, “A novel four-step algorithm for fast block motion estimation,” IEEE Trans. Circuits Syst. Video Technol., vol. 6, pp. 313–317, June 1996. [8] S. Kappagantula and K. R. Rao, “Motion compensated interframe image prediction,” IEEE Trans. Commun., vol. COM-33, pp. 1011–1015, July 1985. [9] T. Komarek and P. Pirsch, “Array architecture for block matching algorithms,” IEEE Trans. Circuits Syst., vol. 36, no. 10, pp. 1301–1308, 1989. [10] Y. S. Jehng, L. G. Chen, and T. D. Chiueh, “An efficient and simple VLSI tree architecture for motion estimation algorithms,” IEEE Trans. Signal Processing, vol. 41, no. 2, pp. 889–900, 1993. [11] Y. S. Jehng, L. G. Chen, and T. D. Chiueh, “A motion estimator for low bit-rate video codec,” IEEE Trans. Consumer Electron., vol. 38, pp. 60–69, May 1992. [12] H. M. Jong, L. G. Chen, and T. D. Chiueh, “Parallel architectures for 3-Step hierarchical search block-matching algorithm,” IEEE Trans. Circuits Syst. Video Technol., vol. 4, pp. 407–416, Aug. 1994. [13] Z. He, M. L. Liou, P. C. H. Chan, and R. Li, “Efficient architectures for the new three-step search algorithm,” in Proc. 38th Midwest Symp. Circuits and Systems, Rio de Janeiro, Brazil, Aug. 1995, vol. 2, pp. 1228–1231. Global Motion Parameters Estimation Using a Fast and Robust Algorithm Demin Wang and Limin Wang Abstract—The main difficulty in global motion parameters estimation resides in the disturbance of independently moving objects. The algorithm presented in this letter exploits global motion information not only from stationary objects and the image background, but also from independently moving objects. Simulation results show that the new algorithm is com- putationally fast and robust to the disturbance caused by independently moving objects. Index Terms—Global motion, motion estimation, video analysis, video compression. I. INTRODUCTION Global motion caused by camera zooming, panning, and rotation is quite common in video sequences. It has been shown that in video compression, global motion can be modeled using a few parameters [1]–[3]. Global motion compensation can significantly reduce the residual of motion compensation and the entropy of local motion vector fields. The main difficulty in estimating global motion parameters resides in the existence of independently moving objects which introduce a bias to the estimated parameters. The algorithms presented in [2]–[5] use the least-square approximation (linear re- gression) to extract global motion parameters from the motion vector fields generated by a local motion estimation algorithm, such as block-matching. To reduce the disturbance of moving objects, a recursive procedure is used to gradually remove the motion vectors of moving objects from the least-square approximation by thresholding. However, thresholding will not be able to eliminate the influence of moving objects if the moving objects are relatively large. Moreover, these algorithms are computationally expensive. This letter presents a new algorithm for global motion parameters estimation, which also operates on motion vector fields obtained by a local motion estimation algorithm. However, this algorithm exploits global motion information not only from stationary objects and the image background, but also from independently moving objects. II. THE ALGORITHM The global motion caused by camera zooming, panning, as well as rotation can be modeled by [1], [5] (1) where ( ) is the position of a pixel in the previous frame, ( ) is the associated motion vector caused by the global motion over one frame period, is the global motion parameter related to camera zooming, represents camera rotating, and and are the panning parameters. From (1), we have the following relations: (2) Manuscript received March 10, 1997; revised June 26, 1997. This paper was recommended by Associate Editor Y. Wang. The authors are with the Communications Research Centre, Ottawa, ON K2H 8S2, Canada. Publisher Item Identifier S 1051-8215(97)07381-3. 1051–8215/97$10.00 1997 IEEE

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Page 1: Global motion parameters estimation using a fast and robust algorithm

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 7, NO. 5, OCTOBER 1997 823

each CV. In fact, the data dependency between the CV’s can alsobe exploited to achieve a higher throughput for higher quality videoapplications by using some extra circuits.

VI. CONCLUSION

In this paper, we have introduced a CV-based BMME algorithmbased on the consideration of VLSI implementation. Compared to thewidely used fast BMME algorithms such as the TSS and NTSS algo-rithms, the proposed BMME algorithm possesses better algorithmicperformance. Although the proposed algorithm has higher computa-tional complexity than TSS/NTSS for software execution, however,using the state-of-the-art VLSI technology, it can be implementedcost-effectively with the proposed VLSI architecture. Furthermore,the proposed BMME algorithm and the VLSI architecture can beeasily extended with different designs of CV pattern for differentvideo applications.

REFERENCES

[1] J. R. Jain and A. K. Jain, “Displacement measurement and its applicationin interframe image coding,”IEEE Trans. Commun.,vol. COM-29, pp.1799–1808, Dec. 1981.

[2] R. Li, B. Zeng, and M. L. Liou, “A new three-step search algorithm forfast block motion estimation,”IEEE Trans. Circuits Syst. Video Technol.,vol. 4, pp. 438–442, Aug. 1994.

[3] T. Koga, K. Iinuma, A. Hirano, Y. Iijima, and T. Ishiguro, “Motioncompensated interframe coding for video conferencing,” inProc. Nat.Telecommunications Conf.,New Orleans, LA, Nov. 29, Dec. 1981, pp.G5.3.1–G5.3.5.

[4] M. Ghanbari, “The cross-search algorithm for motion estimation,”IEEETrans. Commun.,vol. 38, pp. 950–953, July 1990.

[5] R. Srinivasan and K. R. Rao, “Predictive coding based on efficient mo-tion estimation,”IEEE Trans. Commun.,vol. COM-33, pp. 1011–1015,Sept. 1985.

[6] L. G. Chen, W. T. Chen, Y. S. Jehng, and T. D. Chiueh, “An efficientparallel motion estimation algorithm for digital image processing,”IEEETrans. Circuits Syst. Video Technol.,vol. 1, pp. 407–416, Dec. 1991.

[7] L.-M. Po and W.-C. Ma, “A novel four-step algorithm for fast blockmotion estimation,”IEEE Trans. Circuits Syst. Video Technol.,vol. 6,pp. 313–317, June 1996.

[8] S. Kappagantula and K. R. Rao, “Motion compensated interframe imageprediction,” IEEE Trans. Commun.,vol. COM-33, pp. 1011–1015, July1985.

[9] T. Komarek and P. Pirsch, “Array architecture for block matchingalgorithms,”IEEE Trans. Circuits Syst.,vol. 36, no. 10, pp. 1301–1308,1989.

[10] Y. S. Jehng, L. G. Chen, and T. D. Chiueh, “An efficient and simpleVLSI tree architecture for motion estimation algorithms,”IEEE Trans.Signal Processing,vol. 41, no. 2, pp. 889–900, 1993.

[11] Y. S. Jehng, L. G. Chen, and T. D. Chiueh, “A motion estimator forlow bit-rate video codec,”IEEE Trans. Consumer Electron.,vol. 38, pp.60–69, May 1992.

[12] H. M. Jong, L. G. Chen, and T. D. Chiueh, “Parallel architecturesfor 3-Step hierarchical search block-matching algorithm,”IEEE Trans.Circuits Syst. Video Technol.,vol. 4, pp. 407–416, Aug. 1994.

[13] Z. He, M. L. Liou, P. C. H. Chan, and R. Li, “Efficient architecturesfor the new three-step search algorithm,” inProc. 38th Midwest Symp.Circuits and Systems,Rio de Janeiro, Brazil, Aug. 1995, vol. 2, pp.1228–1231.

Global Motion Parameters EstimationUsing a Fast and Robust Algorithm

Demin Wang and Limin Wang

Abstract—The main difficulty in global motion parameters estimationresides in the disturbance of independently moving objects. The algorithmpresented in this letter exploits global motion information not only fromstationary objects and the image background, but also from independentlymoving objects. Simulation results show that the new algorithm is com-putationally fast and robust to the disturbance caused by independentlymoving objects.

Index Terms—Global motion, motion estimation, video analysis, videocompression.

I. INTRODUCTION

Global motion caused by camera zooming, panning, and rotationis quite common in video sequences. It has been shown that invideo compression, global motion can be modeled using a fewparameters [1]–[3]. Global motion compensation can significantlyreduce the residual of motion compensation and the entropy of localmotion vector fields. The main difficulty in estimating global motionparameters resides in the existence of independently moving objectswhich introduce a bias to the estimated parameters. The algorithmspresented in [2]–[5] use the least-square approximation (linear re-gression) to extract global motion parameters from the motion vectorfields generated by a local motion estimation algorithm, such asblock-matching. To reduce the disturbance of moving objects, arecursive procedure is used to gradually remove the motion vectors ofmoving objects from the least-square approximation by thresholding.However, thresholding will not be able to eliminate the influence ofmoving objects if the moving objects are relatively large. Moreover,these algorithms are computationally expensive.

This letter presents a new algorithm for global motion parametersestimation, which also operates on motion vector fields obtained by alocal motion estimation algorithm. However, this algorithm exploitsglobal motion information not only from stationary objects and theimage background, but also from independently moving objects.

II. THE ALGORITHM

The global motion caused by camera zooming, panning, as well asrotation can be modeled by [1], [5]

ug(x; y)vg(x; y)

=a1 �a2a2 a1

x

y+

a3a4

(1)

where (x; y) is the position of a pixel in the previous frame, (ug; vg)is the associated motion vector caused by the global motion over oneframe period,a1 is the global motion parameter related to camerazooming, a2 represents camera rotating, anda3 and a4 are thepanning parameters. From (1), we have the following relations:

@

@xug (x; y) =

@

@yvg (x; y) = a1

@

@xvg (x; y) =

@

@yug (x; y) = a2:

(2)

Manuscript received March 10, 1997; revised June 26, 1997. This paperwas recommended by Associate Editor Y. Wang.

The authors are with the Communications Research Centre, Ottawa, ONK2H 8S2, Canada.

Publisher Item Identifier S 1051-8215(97)07381-3.

1051–8215/97$10.00 1997 IEEE

Page 2: Global motion parameters estimation using a fast and robust algorithm

824 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 7, NO. 5, OCTOBER 1997

In other words, parametersa1 anda2 can be obtained by calculatingthe partial derivatives of the motion vector field.

In practice, however, there may be independently moving objectsin video sequences. A motion vector (u; v) within a real motion fieldcan be considered as the superposition of a global (camera) motioncomponent (ug; vg) and a local (object) motion component (ul; vl),i.e.,

u

v=

ug

vg+

ul

vl:

If an object undergoes translational motion,ul andvl are constantswithin the object. From (1) and (2) the partial derivatives ofu

and v within the object are still equal toa1 and a2, respectively.Therefore, global zooming and rotation information can be extractedfrom not only stationary objects and the image background, butalso translational objects. Based on this principle, we develop thefollowing algorithm.

Let (u; v) denote the estimate of the motion vector (u; v) which isobtained using the block-matching technique. The partial derivativesof the estimated motion field are calculated as follows:

�u; x (x; y) = u (x; y)� u (x� 1; y)

�v; y (x; y) = v (x; y)� v (x; y � 1)

�v; x (x; y) = v (x; y)� v (x� 1; y)

�u; y (x; y) = u (x; y)� u (x; y � 1):

(3)

Based upon the above discussion, the mean value of�u; x (x; y) and�v; y (x; y) could be a reliable estimate for the zooming parametera1.However, the�u; x (x; y) and�v; y (x; y) located on the boundariesof translational objects and within rotating objects may still introducebias to the estimate. In general, their values are significantly differentfrom the others, and, hence, can be eliminated by thresholding. Letm denote the mean value of�u; x (x; y) and �v; y (x; y) over themotion field

m =1

2M(x; y)

[�u; x (x; y) + �v; y (x; y)] (4)

whereM denotes the number of�u; x (x; y) [or �v; y (x; y)] con-tained in the motion vector field. Ifj�u; x (x; y)�mj is greater thana thresholdT , this �u; x (x; y) is considered to be located on theboundary of a translational object or within a rotating object andtherefore should not be used in the estimation. The mean value ofthe remaining�u; x (x; y) and�v; y (x; y) is taken as the estimate forthe zooming parametera1, i.e.,

a1 =1

M 0 +M 00

j� (x; y)�mj<T

�u; x (x; y) +

j� (x; y)�mj<T

�v; y (x; y)

(5)

where M 0 and M 00 denote the numbers of the�u; x (x; y) and�v; x (x; y) satisfyingj�u; x(x; y)�mj < T andj�v; y(x; y)�mj <

T , respectively. The thresholdT may vary for different motion vectorfields. Based on experimentation, the threshold is set as

T = 1 +1

2M(x; y)

[j�u; x (x; y)�mj+ j�v; y (x; y)�mj]: (6)

The same methodology is used to estimate the rotation parametera2 from �v; x (x; y) and�u; y (x; y). Through the partial derivatives,the estimates ofa1 anda2 have no direct relationship to the size oftranslational objects.

TABLE IESTIMATION ERRORS FOR THESYNTHETIC MOTION FIELDS WITHOUT NOISE

TABLE IIAVERAGE ABSOLUTE ERRORS OF THEESTIMATED

PARAMETERS FOR 50 NOISY MOTION FIELDS

Parametersa3 anda4 can be obtained by subtracting the motioncomponents caused by zooming and rotation from the estimatedmotion vector field. Let

tu (x; y) = u (x; y)� a1x+ a2y

tv (x; y) = v (x; y)� a2x� a1y:(7)

According to (1), tu(x; y) and tv(x; y) are constants in regionsof the image background and of stationary objects. Therefore, themean values oftu(x; y) and tv(x; y) over regions of the imagebackground and of stationary objects provide good estimates ofa3

anda4, respectively. These mean values are determined by a similarmethod used for estimatinga1 anda2. For example, in estimatinga3,the mean value oftu(x; y) and the average absolute error oftu(x; y)

with respect to the mean are calculated over the entire motion field.A threshold is set to the average absolute error plus one. Then, themean value of thetu(x; y) which has an absolute error smaller thanthe threshold is computed and taken as the estimated value ofa3.

III. COMPUTATIONAL COMPLEXITY

In the algorithm mentioned above, (3) is performed with fouradditions (subtraction) for each motion vector. The computationsof (4) and (6) require two additions and four additions plus twocomparisons per motion vector, respectively. The final step forestimatinga1 is to compute (5). This step requires two comparisonsand at most two additions per motion vector. Hence, the estimationof a1 and a2 requires eight comparisons and at most 20 additionsper motion vector. In estimatinga3 and a4, (7) can be computedby an iterative algorithm which does not involve multiplications.For example,tu(x; y) can be obtained using the following iterativerelations:

tu (x; y) = u (x; y)� w(x; y)

w(x; y) =w(x; y � 1) + a2: (8)

These relations involve only two additions. The estimation ofa3 fromtu(x; y) [a4 from tv(x; y)] requires two comparisons and at most

Page 3: Global motion parameters estimation using a fast and robust algorithm

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 7, NO. 5, OCTOBER 1997 825

TABLE IIIESTIMATION RESULTS FOR MOTION VECTOR FIELDS OF REAL VIDEO SEQUENCES

Fig. 1. Structure of the synthetic motion field.

four additions. Therefore, the total operations required by the newalgorithm are 12 comparisons and at most 32 additions. On the otherhand, the algorithms based on least-square approximation [2]–[5]require multiplications and are more computationally expensive thanthe new algorithm [6].

IV. SIMULATION RESULTS

The new algorithm for global motion parameter estimation wastested with one synthetic motion field and two natural video motionfields. The synthetic motion field consisting of 63� 63 motionvectors was generated from (1) when the global motion parametersa1; a2; a3, anda4 are equal to 0.2, 0.1, 3.0, and 4.0, respectively.In order to examine the impact of independently moving objects onthe estimation, two independently moving objects were added in thesynthetic motion field, as shown in Fig. 1. The local motion vectorsassociated with the two independently moving objects are (�2, �3)and (14, 13), respectively.

The simulation results shown that, for the synthetic motion field,the estimated parameters obtained by the new algorithm are accurate(no error) if the moving objects are smaller than 31� 31. Forcomparison purposes, the recursive least-square algorithm presentedin [2] was extended and used to estimate the four global motionparameters (see [6]). It was found that the estimated parameters areinaccurate when the moving objects become larger than 19� 19.Note that 19� 19 motion vectors occupy only 20.16% of the motionfield area. The errors of the estimated parameters increase with thesize of moving objects, as shown in Table I. Generally, the algorithmsbased on least-square approximation are more sensitive to the size ofmoving objects than the new algorithm.

Robustness to noise is another important characteristic of analgorithm for global motion parameters estimation. To evaluate therobustness of the new algorithm, we generated 50 noisy motion fieldsby corrupting the synthetic motion field with additive Gaussian noisewith a mean of zero and a standard deviation of 0.5, and we estimatedthe global motion parameters of these noisy motion fields with thenew algorithm and the recursive least-square algorithm. The averageabsolute errors of the estimated parameters for these noisy motionfields are shown in Table II as the measure of robustness. From thistable, the new algorithm produces smaller average absolute errors of

(a)

(b)

Fig. 2. Motion vector field of sequenceTable Tennisand global motioncompensation: (a) motion vector field obtained using block matching and(b) local motion vector field after global motion compensation.

a1; a3, and a4 than the recursive least-square algorithm when themoving objects are larger than 15� 15. For example, the averageabsolute errors ofa1; a3, anda4 produced by the new algorithm areabout 50% smaller than those produced by the recursive least-squarealgorithm when the size of moving objects are 20� 20. However,the new algorithm results in greater average absolute errors whenthe moving objects are smaller than 10� 10. This is because therecursive least-square algorithm is an optimal algorithm in terms ofnoise robustness if there is no moving object. Generally, the newalgorithm outperforms the recursive least-square algorithm in casescontaining large translational objects and low-level noise, a veryfrequently encountered situation.

Fig. 2(a) shows the motion field obtained from the video sequenceTable Tennisby using block matching. The zeroth-order entropy ofthe motion vectors in this motion field is equal to 7.10. The global

Page 4: Global motion parameters estimation using a fast and robust algorithm

826 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 7, NO. 5, OCTOBER 1997

motion parameters were estimated using the new algorithm on a Sparc2 Workstation. As shown in Table III, the new algorithm takes only0.0067 s of CPU time, which is about 63% of the time taken by therecursive least-square algorithm. The local motion field after globalmotion compensation is illustrated in Fig. 2(b). The correspondingzeroth-order entropy decreases to 5.17. The estimation for a motionvector field of sequenceMobile is also shown in Table III.

V. CONCLUSION

In existing algorithms for global motion estimation, the motionvectors of independently moving objects disturb the estimation ofglobal motion parameters. By using the partial derivatives of motionfields, the new algorithm exploits global motion information not onlyfrom stationary objects and the image background, but also fromindependently moving objects. The estimated values of zooming androtation parameters do not depend directly on the size of translationalobjects. The new algorithm does not involve multiplication, so it iscomputationally fast. This algorithm has been tested with a syntheticmotion field and two motion vector fields of real video sequences.Performance of the new algorithm was compared with a recursiveleast-square algorithm. The comparison results show that the newalgorithm is very robust to translational objects. It is computationallyfaster than the recursive least-square algorithm. It should be noted thatthe use of the partial derivatives of motion fields in the new algorithmdoes not increase the robustness to nontranslational objects. Thedisturbance of nontranslational objects is reduced by thresholding,as used in the recursive least-square algorithm.

ACKNOWLEDGMENT

The authors gratefully acknowledge A. Vincent, J. Tam, and A.Mainguy for their help in this work.

REFERENCES

[1] S. F. Wu and J. Kittler, “A differential method for simultaneous esti-mation of rotation, change of scale and translation,”Signal Processing:Image Commun.,vol. 2, pp. 69–80, 1990.

[2] Y. T. Tse and R. L. Baker, “Global zoom/pan estimation and com-pensation for video compression,” inProc. ICASSP’91,May 1991, pp.2725–2728.

[3] P. Migliorati and S. Tubaro, “Multistage motion estimation for imageinterpolation,”Signal Processing: Image Commun.,vol. 7, pp. 187–199,1995.

[4] P. Formenti, P. Migliorati, L. Sorcineli, and S. Tubaro, “Global-local motion estimation in multilayer video coding,”SPIE, VisualCommunications and Image Processing’92,vol. 1818, pp. 573–584.

[5] C.-S. Kim, J.-B. Lee, and S.-D. Kim, “A novel global motion estima-tion/compensation technique for motion compensated coding,” inInt.Picture Coding Symp.’96,Melbourne, Australia, 1996, pp. 595–598.

[6] D. Wang and L. Wang, “Fast and robust algorithm for global motionestimation,” SPIE, Visual Communications and Image Processing’97,vol. 3024, pp. 1144–1151.

A High Performance Fast Search Algorithmfor Block Matching Motion Estimation

Zhongli He and Ming L. Liou

Abstract—In this paper, we introduce a new fast search block matchingmotion estimation algorithm with high performance. Based on the center-biased characteristic for most of the video sequences, the proposedalgorithm can jointly minimize the error image and total number of bitsspent on the motion vectors with much reduced computational complex-ity. Simulation results show that the proposed algorithm can producehigh performance with high speed-up ratio, especially for stationary orquasi-stationary video sequences.

Index Terms—Motion estimation, video sequence analysis, video signalprocessing.

I. INTRODUCTION

The block matching motion estimation (BMME) technique hasbeen recommended for interframe video coding in all of the recentlyestablished international standards. Generally speaking, there are twokinds of BMME algorithms. One is full-search and the other is fast-search [1]–[8]. Full-search can deliver optimal solution while it iscomputation-intensive. Fast-search can speed up the computation,however, it may fall into local optimum.

The objective for most of the fast search algorithms as well asfor the full-search algorithm is to find the motion vector (MV) forminimizing the error image regardless of the number of bits neededto represent the MV or the length of MV which is defined as thesum of the absolute values of horizontal and vertical componentsof the motion vector. In this paper, we will propose a fast BMMEalgorithm which can not only speed up the computation, but alsoreduce the number of bits for the MV. Consequently, we have morebits available to code the error image. Especially for stationary orquasi-stationary video sequences, the proposed algorithm can achievevery high speed-up ratio and superior algorithmic performance. In thenext section, we will introduce the design motivation of the proposedalgorithm. The algorithm description and the simulation results willbe presented in Sections III and IV, respectively. Finally, we giveconclusion in Section V.

II. DESIGN MOTIVATION

Statistically, most of the video sequences are stationary or quasi-stationary. That means most of the motion vectors are center-biased[3]. This observation suggests that a BMME algorithm should have ahigher priority to search the motion vector within a small search areaaround the center of a search window. If the matching error in thissmall area is less than a preset threshold, the search stops. Otherwise,we extend the search area and continue the search process. Thisapproach has the following two advantages. First, it can speed up thecomputation by stopping the search in the middle of process. Second,it can produce a smaller motion vector which requires fewer number

Manuscript received March 13, 1997; revised June 15, 1997. This paperwas recommended by Associate Editor Y.-Q. Zhang. This work was supportedby the Hongkong Telecom Institute of Information Technology under GrantHKTIIT92/93.001.

The authors are with the Department of Electrical and Electronic Engineer-ing, The Hong Kong University of Science and Technology, Clear Water Bay,Kowloon, Hong Kong.

Publisher Item Identifier S 1051-8215(97)07380-1.

1051–8215/97$10.00 1997 IEEE