A fast full-search motion-estimation algorithm using representative pixels and adaptive matching scan

1040 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 10, NO. 7, OCTOBER 2000

A Fast Full-Search Motion-EstimationAlgorithm Using Representative Pixels and

Adaptive Matching ScanJong-Nam Kim and Tae-Sun Choi, Senior Member, IEEE

Abstract—A full-search based block-matching algorithmfor motion estimation has a major problem of significant com-putational load. To solve this problem, extensive research infast-motion estimation algorithms have been carried out. How-ever, most of them have some degradation in the predictedimage from the reduced computation. To decrease the amount ofsignificant computation of the full-search algorithm, we proposea fast block-matching algorithm based on an adaptive matchingscan and representative pixels without any degradation of thepredicted image. By using Taylor series expansion, we obtain therepresentative pixels and show that the block-matching errorsfrom the reference block and candidate blocks are proportionalto the block complexity. With the derived result, we propose afast full-search algorithm with adaptive scan direction in blockmatching. Experimentally, our proposed algorithm is very efficientin terms of computational speedup, and is the fastest among allthe conventional full-search algorithms. Therefore, our algorithmis useful in VLSI implementation of video encoders for real-timeencoding.

Index Terms—Adaptive matching scan, block-matching algo-rithm, full search, motion estimation, representative pixels.

I. INTRODUCTION

M OTION estimation is defined as searching the best mo-tion vector, which is the coordinate of the best similar

block in previous frame for the block in current frame. Of var-ious approaches for motion estimation, the block-matching al-gorithm (BMA) is very popular in the framework of genericcoding [1], [2]. Block-based matching algorithms find the op-timal motion vectors which minimize the matching differencebetween reference block and candidate blocks. Therefore, thesame motion vector is used for all pixels within a block, unlikepel-recursive methods [3]. In two types of block-based motionmodels, a simple 2-D translational motion model assumes thatan image is composed of objects with transnational motion. Themodel is popular because a complex motion can be analyzedas translational motions, and it shows reasonable performancecompared with other complex motion models. Of course, morecomplex motion models can describe more accurate motion atthe sacrifice of increased computational complexity. However,they have two important defects. At first, the computational

Manuscript received July 1999; revised April 2000. This work was supportedby the Brain Korea 21, Ministry of Education, Korea. This paper was recom-mended by Guest Editor Y.-Q. Zhang.

The authors are with the Signal and Image Processing Laboratory, Depart-ment of Mechatronics, KwangJu Institute of Science and Technology (K-JIST),KwangJu, Korea (e-mail: [email protected]; [email protected].).

Publisher Item Identifier S 1051-8215(00)08204-5.

complexity and computing time to perform motion estimationis drastically increased. Second, more complex motion modelsrequire more overhead information. If the gain due to more ac-curate motion vectors cannot surpass this additional side infor-mation, then these models may actually result in lower perfor-mance. Therefore, the popularity of motion estimation based onthe simple 2-D translational model originates from less com-puting time, less overhead data to represent the motion field,and easy VLSI implementation with simple structure [2], [3].

Full search in the BMA based on translational motion modelfinds the location with the minimum value of matching errorsof all candidate displacements within a given search range. Ithas been popularly used in video-coding applications becauseof its simplicity and easy hardware implementation. However,its heavy computational load for a large search range can bea significant problem in real-time video-coding applications.Many fast motion-estimation algorithms to reduce the compu-tation of the full search have been studied in recent decades.We can classify these fast motion-estimation methods into twogroups. One is lossy motion-estimation algorithm, which hassome degradation of predicted images, and the other is losslessone without any degradation of predicted images compared withthe conventional FS algorithm. The former, lossy algorithm,includes following subgroups: unimodal error search assump-tion (UESA) techniques [5]–[13], multiresolution techniques[14]–[19], variable search range techniques with spatial/tem-poral correlation of the motion vectors [20]–[28], half-stop tech-niques using threshold of matching distortion [9], [16], [17],[29], integral projection technique of matching block [30]–[34],lower bit-resolution techniques [35]–[39], subsampling tech-niques of matching block [40]–[43], and so on. The latter, lossyalgorithm, contains following several algorithms: vertical, hor-izontal and massive projection techniques for reference blockand candidate blocks [44], fast 2-D FIR filtering based algo-rithm [45], candidate elimination algorithms using sum of ref-erence block, candidate blocks, minimum sum of absolute dif-ference (SAD), and its modified algorithms [46]–[49], partialmatching distortion elimination method [50]–[52], and so on.

In this paper, a fast-matching algorithm using adaptivematching scan from representative pixels is proposed to reducecomputational complexity of the full-search algorithm, whichis contained in the group of lossless motion estimation in theabove classification. The proposed algorithm is motivated fromthe idea of partial distortion elimination (PDE) [50]–[52] asa fast-matching technique. The speedup problem in the PDEalgorithm depends on how fast computation of matching error

1051–8215/00$10.00 © 2000 IEEE

KIM AND CHOI: A FAST FULL-SEARCH MOTION-ESTIMATION ALGORITHM USING REPRESENTATIVE PIXELS AND ADAPTIVE MATCHING SCAN 1041

is stopped according to the partial sum of matching error.Therefore, we want to stop computing the matching error fasterby applying the adaptive matching scan from representativepixels of the reference block. To justify our intention reason-ably, we mathematically derive the relationship between spatialcomplexity of the reference block and matching distortion. Inthe derivation, we show that the matching distortion betweenthe reference block and candidate block is proportional to theimage complexity of the reference block which is based onthe concept of representative pixels. That is, we first computethe matching error with the representative pixels to obtainlarger matching error with less computation. In this context, wesuggest a new and adaptive matching-scan algorithm for fastmotion estimation with the concept of the representative pixels.

This paper is organized as follows. In Section II, convention-ally fast full-search algorithms are described and then, the moti-vation of the proposed algorithm is explained based on the pre-vious works. We describe the proposed algorithm in Section III,which is adaptive matching-scan algorithm for fast motion esti-mation with the representative pixel. In Section IV, experimentalresults for various sequences and discussions of the results aregiven. Finally, the conclusion is followed in Section V.

II. CONVENTIONAL FAST FULL-SEARCH ALGORITHMS

Most of the algorithms for fast motion estimation have degra-dation of quality in predicted images because of partial searchin the search range or partial matching. In limited bit-rate appli-cations, wrong motion vectors from these fast techniques cancause serious problems because of increased error data fromsub-optimal prediction. For many hardware implementations ofmotion estimation, full search has been used due to its accu-racy of the prediction and simple search rule. The following fastsearching methods with lossless predicted images are related tothe fast full-search algorithm.

Y. C. Lin and S. C. Tai [44] proposed another fast-matchingalgorithm of full search using fast-matching criteria, which arethe sum of squared vertical projections , sum of squaredhorizontal projections , and sum of squared massiveprojection . They used the fact that the three termsshould be less than mean square error (MSE), and global min-imum MSE should be less than MSE of acandidate block in given search range. They used following fourinequalities. MSE is calculated when at least one of followingfour inequalities is violated. In (1), means matching blocksize

(1)

By using (1), we can remove many useless computationswithout any degradation of predicted images. But, this ap-proach is inappropriate for VLSI implementation because ofmultiplication of in the MSE computation. Naito, Miyazaki,and Kuroda proposed fast-matching algorithm of full searchfor a programmable processors with a multiplier-accumulator

[45]. In the method, MSE was used as a matching criterion.They decomposed the MSE into the power of the referenceblock, cross term of reference block and candidate blocks,and the power of the candidate blocks. Main idea for speedupis motivated from cross term of reference block and candi-date blocks. They obtained the speedup by using a fast 2-Dfinite-impulse response (FIR) filtering algorithm for the crossterm and reducing the computation of the overlapped area ofthe power in the reference block. But, it has been reportedthat the matching criterion, MSE, is not appropriate for VLSIimplementations because of multiplication.

Another technique for fast full search is to eliminate candi-date-checking points using boundary equation from the sum ofreference block, sum of candidate block, and minimum SADat that time. The main idea for the algorithm, which is calledsuccessive elimination algorithm (SEA), is as follows. At first,one fast computes sum norms of the reference block and candi-date blocks by reducing overlapped part of computing blocks.After calculating the initial matching error of determined searchorigin, one removes impossible candidate motion vectors bycomparing with (3). The algorithm starts from (2) and then fi-nally (3) is produced. In (3), the second term on the left sidemeans the minimum matching error at that time. The centralterm in (3) represents the sum norm of the reference block inthe current frame, and the first term represents the sum normsof candidate blocks with motion vector in the previousframe. With (3), one can efficiently avoid useless computationfrom impossible candidates without any degradation of the pre-dicted image [46]

(2)

(3)

A few algorithms of modified versions based on SEA havebeen reported. Speedup performance of the SEA depends onthe initial matching error. De Oliverira and Alcaim proposedthe modified algorithm with less initial matching distortionfrom adjacent motion vectors [47]. Lu, Wu, and Lin reducedmore of the candidates by using the hierarchical structure ofMinkowski’s inequality with pyramid of five levels [48]. Cobanand Mersureau used the concept of (3) to determine motionvector with optimized rate distortion [49]. So, they extendedthe (3) by adding the weighted rate term to avoid enormouscomputation.

Besides the above algorithms, another algorithm to reducethe computational complexity efficiently is the PDE method


[50]–[52]. It uses the partial sum of matching distortion toeliminate impossible candidates before complete calculationof matching distortion in a matching block. That is, if anintermediate sum of matching error is larger than the minimumvalue of matching error at that time, the remaining computationfor matching error is abandoned. In the PDE, theth partialSAD to check during the matching is as follows:

(4)represents matching block size in (4). Ifis smaller than

from the partial SAD and exceeds the current SADmin, then wecan quit the remaining summation of the matching-error cal-culation and kick out the impossible candidate motion vector

. The PDE technique has been widely used to reduce thecomputational load in the full-search algorithm.

The reduction of calculation in obtaining motion vector withthe PDE algorithm depends on how fast global minimum ofmatching distortion is detected. If we find the global minimumof distortion in calculation of matching error faster, completecomputation of matching error in a block is avoided more andin the (4) is determined faster. We can improve the speedup if weemploy properly adjacent motion vectors of spatial or temporaldomain as [23]–[29] for initial motion vector. In fast full-searchalgorithms with SAD as the matching criterion, an importantthing has been neglected: that the fast PDE algorithm can be ob-tained from fast matching, as well as fast searching. Here, fastmatching means a fast algorithm for calculating the matchingerror on a candidate, and fast searching denotes the fast one forfinding the global minimum error point in a given search range.The fast matching is related to the other matching scan insteadof the conventional top-to-bottom matching scan. We proposenew fast-matching algorithm for fast full search with SAD asthe matching criterion in Section III. We show that we can fur-ther reduce the computational complexity in full search by usingthe proposed fast-matching algorithm.

III. PROPOSEDALGORITHM

Lossy fast algorithms with degradation of predicted imagemight have serious problems for some applications. Due to theproblem, the full-search algorithm is still a good candidate dueto its good error performance and simple search rule. Two kindsof fast full-search algorithms using SAD as matching criterionhave been proposed as shown in Section II. One is SEA [46]and its modified algorithms [47]–[49], the other is the PDE al-gorithm [50] and its modified algorithms [51]–[52]. The modi-fied versions of SEA and PDE with fast searching methods wereproposed to reject more impossible candidates. SEA’s modi-fied algorithms use correlation of adjacent motion vector andMinkowski’s inequality [47]–[49]. Meanwhile, PDE’s modi-fied algorithms employed the spiral search instead of top-to-bottom search in the search range and other matching techniques[51]–[52].

An important thing in the PDE algorithm is that how fast im-possible candidates are detected by removing unnecessary com-putation. We use the relationship between block-matching error

and image complexity of reference block using representativepixels. We first show that the block-matching error is propor-tional to image complexity of reference block. By using therelationship, we propose new block-matching-scan algorithmswith representative pixels of reference block to kick out the im-possible candidates faster. For this purpose in the proposing al-gorithm, the adaptive block-matching-scan instead of the con-ventional top-to-bottom matching scan is carried out based onthe direction from the representative pixels of reference block.Therefore, we can check impossible candidates faster, resultingin much reduced computations compared with the conventionalPDE and its modified algorithms.

A. Representative Pixels of Reference Block and its Extraction

At first, we mathematically describe the relationship betweenthe block-matching error and image complexity of referenceblock. In developing the relationship, a Taylor series expansionis introduced. Finally, it is shown that matching distortion is pro-portional to the image complexity of the reference block. In thiscontext, complex image area is regarded as representative pixelsin the block and it is applied to our adaptive matching-scan al-gorithm. That is, by examining the representative pixels earlierthan other pixels, we can detect impossible candidates faster andkick out them. Therefore, we can obtain the reduction of com-putation in the block-matching algorithm without any degrada-tion of predicted image compared with conventional PDE algo-rithms. Mean, gradient magnitude, variance, and so on can beused to measure the image complexity. We will use the gradientmagnitude due to performance and computational complexity.

In general, the gradient of some functionindicates the direction of the maximum rate of increase of it, andgradient magnitude represents the maximum rate of increase of

per unit distance in the direction . The defi-nition and approximation of the gradient magnitudeis shown in (5) as follows:

(5)

Taylor series expansion provides a formulation for predictinga function value at some point in terms of the functionvalue and its derivatives at a nearby point. We use the seriesexpansion to show the relationship between matching error andgradient magnitude of reference block. General Taylor seriesexpansion is expressed as follows:

(6)

where


Fig. 1. Proposed adaptive matching scans. (a) Horizontal matching scan (top-to-bottom). (b) Horizontal matching scan (top-to-bottom). (c) Vertical matchingscan (left-to-right). (d) Vertical matching scan (right-to-left).

Fig. 2. Proposed first algorithm: adaptive-matching scan based on representative pixels. (a) Sub-block division for block complexity with(i)+(ii), (iii)+(iv),(i) + (iii), and(ii) + (iv). (b) Horizontal matching scan (top-to-bottom) when(i) + (ii) is maximum. (c) Horizontal matching scan (bottom-to-top) when(iii) + (iv) is maximum. (d) Vertical matching scan (left-to-right) when(i) + (iii) is maximum, (e) Vertical matching scan (right-to-left) when(ii) + (iv) ismaximum.

Fig. 3. Proposed second algorithm: adaptive-matching scan by sorted rows/columns based on representative pixels. (a) Sub-block division for blockcomplexitywith (i) + (ii), (iii) + (iv), (i) + (iii), and(ii) + (iv). (b) Horizontal matching scan by sorted rows when(i) + (ii) or (iii) + (iv) is maximum value. (c)Vertical matching scan by sorted columns when(i) + (iii) or (ii) + (iv) is maximum value.

Let the image intensity at the position of the thframe (reference block) be , , and the motionvector of position be . So, we can approx-imately describe the relationship between the current frame andprevious frame

(7)

The equation starts from the definition of absolute differencefor matching error. In the first and third approximation of (7),the relationship between reference block of current frame andcandidate block with optimal motion vector of previous frameis used. The modified form of Taylor series expansion is used inthe second approximation of (7). By using a modified form ofthe series expansion, we can express the matching distortion in

terms of gradient magnitude of the reference block as (7). Here,means a candidate motion vector corre-

sponding to matching distortion. From (7), we find an importantfact: that the matching distortion at a positionis proportional tothe gradient magnitude of reference block in the current frame.

B. Adaptive Matching-Scan Algorithms Using RepresentativePixels of Reference Block

We propose new adaptive matching-scan algorithm with theresult derived in the previous subsection. Before describing ouralgorithms, we will summarize the conventional PDE algorithm.As shown in Fig. 1(b), simple PDE algorithm means top-to-bottom matching scan based on (7) with top-to-bottom searchin a given search range. Ability to reject impossible candidatesin the PDE algorithm depends on the search strategy which al-lows minimum matching error to be detected faster. For this pur-pose, the spiral search method is very efficient. So, the combinedPDE algorithm uses (4) and spiral search. As shown in the ex-


Fig. 4. Average checked rows for each frame with “foreman” sequence.

Fig. 5. Average checked rows for each frame with “claire” sequence.

perimental results, the combined PDE algorithm rejects morethe impossible candidates than simple PDE. Therefore, we em-ploy the spiral search in the matching-scan algorithms to be pro-posed.

With the computed gradient magnitude, we calculate block-matching distortion from a new matching-scan direction insteadof the conventional top-to-bottom scan. The ultimate purposeof our proposed algorithm is to find a motion vector as fast aspossible by rejecting impossible candidates. As shown in (7),block-matching error is proportional to the gradient magnitudeof reference block. By first calculating block-matching errorwith larger gradient magnitude, we can detect the impossiblecandidates faster. It is possible from the new adaptive matchingscan shown in Fig. 1 instead of the conventional top-to-bottommatching scan.

We carry out the adaptive matching scan based on the com-puted gradient magnitude. In the first proposed algorithm, wefirst calculate the gradient magnitude for divided sub-block ofby matching block as shown in Fig. 2(a) and then make a sumof gradient magnitudes in sub blocks as shown in Fig. 2(b)–(e).In the results of four cases which are , ,

and , we find the maximum value. Finallywe take appropriate matching scan in the order of maximumsum of gradient magnitudes. If of four terms is max-imum value, we take top-to-bottom matching scan as shown inFig. 2(b). Similarly, when is maximum value in thefour terms, we select a right-to-bottom matching scan, as shownin Fig. 2(e). As shown in experimental results later, we rejectimpossible candidate faster than the conventional top-to-bottommatching-scan algorithm.


Fig. 6. Average checked rows for each frame with “trevor” sequence.

Fig. 7. Average checked rows for each frame with “grandmother” sequence.

We can extend the concept of our proposed algorithm bydividing the reference block minutely in the order of gradientmagnitude. By doing that, we can first compute the matchingerror for the area with more representative pixels. Therefore,another approach to detect impossible candidates faster isto sort the gradient magnitude of rows or columns in thematching block and then to perform the block matching inthe order of sorted results. In the second proposed algorithm,we compute the gradient magnitude for a divided sub-blockof by matching blocks, as shown in Fig. 3(a), and thenmake a sum of gradient magnitudes for the sub blocks, asshown in Fig. 2(b)–(e). In the results of four cases which are

, , , and , we findthe maximum value. Unlike the first proposed algorithm, the

second proposed algorithm only determines row-matching orcolumn-matching. Then, for the determined matching direc-tion of row or column, the reference block is sorted withthe selected matching direction. Therefore, if or

is the maximum value, we perform ra ow-matchingscan. The next step is to sort reference blocks for the rowfield. Finally we compute the matching error according tothe result of the previous steps, as shown in Fig. 3(b). Sim-ilarly, if or has maximum value, acolumn-matching scan with the result of sorting the refer-ence block in a column field is carried out as shown inFig. 3(c). We will show in the experimental results that thesecond proposed algorithm reduces the computation for mo-tion estimation more than the first one proposed.


TABLE IEXPERIMENTAL RESULTS FORAVERAGE CHECKED ROWS OFSEVERAL ALGORITHMS

TABLE IIEXPERIMENTAL RESULTS FORCOMPUTATIONAL REDUCTION RATION OF SEVERAL ALGORITHMS

TABLE IIIEXPERIMENTAL RESULTS FORPSNROF FULL-SEARCH ALGORITHM

IV. EXPERIMENTAL RESULTS AND DISCUSSION

To compare the performance of the proposed algorithmwith the conventional algorithms, we use 100 frames of“foreman,” “car phone,” “trevor,” “claire,” “akio,” and “grand-mother” image sequences. In these sequences, “foreman”and “car phone” have large motions compared with otherimage sequences, while “claire,” “akio,” and “grandmother”are almost inactive sequences compared with first three se-quences. “trevor” sequence has intermediate motions. Theproposed algorithms are compared with the SEA [46], PDEwith conventional top-to-bottom search (nonspiral PDE) [50],and PDE with spiral search (spiral PDE) [51]. The nonspiralPDE algorithm performs partial distortion elimination withtop-left-to-bottom-right search in a given search range, whilethespiral PDE algorithm does partial distortion elimination withspiral search. We exclude the algorithms [44], [45] usingMSE criterion for fast full-search algorithms because they areinappropriate for VLSI implementation. The block size is 16

16 pixels and the search range is 7 pixels. Image formatis QCIF (176 144) for each sequence, and only forwardprediction is used. SAD is employed as an error criterion forblock matching. The simulation results are shown with averagenumber of checking rows, and a computational reduction ratiowith reference to that of the conventional full search withoutany fast operation. Average number of checking rows is usedas a measure of reduced computation, because comparison for

partial distortion and minimum distortion at that time is per-formed row by row or column by column, as shown in (6). Weconvert the computational complexity resulted from SEA intocomputed rows. Tables I and II summarize the computationalcomplexity resulting from each algorithm.

From the experimental results in Tables I and II, we can seethat the proposed algorithm has more computational reductionthan the conventional fast full-search algorithms. In the tables,we can see that simple PDE (nonsprial) algorithm has the mostcomputation and SEA has almost same computational load asPDE (spiral) algorithm. Our proposed algorithms, which useadaptive matching scan according to the gradient magnitude ofreference block, require much less computation than SEA, non-spiral PDE, and spiral PDE algorithms. As shown in Table III,all algorithms obtain the same PSNRs in predicted images. Wecan see in Table III that our proposed algorithm requires only9%–20% in the computation of the conventional full-search al-gorithm. It is noted that we further reduce the computationalcomplexity by using combined scheme with SEA and our pro-posed algorithm because SEA and our algorithm are indepen-dent to each other. Figs. 4–7 show checked average rows tomeasure the reduced computation for each frame of all the se-quences. In Fig. 6, experimental results in about the 60th frameare strange because of scene change about the frame. From thesefigures, we find the that difference of checking rows between theconventional spiral algorithm and our first proposed algorithm isfairly large, as compared with the second proposed algorithm.


With the experimental results, we can conclude that adaptivematching-scan algorithm based on gradient magnitude of refer-ence block is effective for all kinds of sequences, which includeactive motions or inactive ones.

V. CONCLUSION

In this paper, we mathematically showed the relationshipbetween block-matching error and representative pixels of areference block. To measure the representative pixels, we useda gradient magnitude which has reasonable performance inconsidering computational complexity. We could find that theblock-matching error is proportional to the gradient magnitudeof the reference block. Then, the representative pixel-basedadaptive matching-scan algorithm using the obtained re-lationship was proposed. It rejects impossible candidatemotion vectors faster than the conventional top-to-bottommatching scan without any degradation of predicted image.Our proposing matching-scan algorithms are composed ofadaptive matching direction and sorting the reference blockaccording to the determined direction. The former includesfour matching-scan directions which are the top-to-bottomhorizontal, bottom-to-top horizontal, left-to-right vertical,and right-to-left vertical scan. The latter sorts the referenceblocks for low fields or column fields according to the obtaineddirection. From the above experimental results, we can seethat our algorithm saves the amount of computation by about80%–91%, as compared with the full-search algorithm withoutany degradation of PSNR in the predicted image. Therefore,the proposed algorithm is very useful, especially in a real-timevideo encoder with VLSI implementation.

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Jong-Nam Kim received the M.S. degree ininformation and communications engineering fromKwangJu Institute of Science and Technology,KwangJu, Korea, in 1997, where he is currentlyworking toward the Ph.D. degree in the Departmentof Mechatronics.

His research interests include image processing,scalable coding, fast motion estimation, post-videoprocessing, software-based video codec, video-dataindexing/retrieval, object extracting/tracking, andVLSI design for video coding.

Tae-Sun Choi (S’88–M’93–SM’99) received theB.S. degree in electrical engineering from SeoulNational University, Seoul, Korea, in 1976, theM.S. degree in electrical engineering from KoreaAdvanced Institute of Science and Technology,Seoul, Korea, in 1979, and the Ph.D. degree inelectrical engineering from the State University ofNew York at Stony Brook in 1993.

He is currently an Assistant Professor in the De-partment of Mechatronics, KwangJu Institute of Sci-ence and Technology, KwangJu, Korea. His research

interests include image processing, machine/robot vision, and visual communi-cations.

Documents

A fast full-search motion-estimation algorithm using representative pixels and adaptive matching scan