 Research
 Open Access
A novel search method based on artificial bee colony algorithm for block motion estimation
 Weiyu Yu^{1}Email author,
 Dan Hu^{1},
 Na Tian^{1} and
 Zhili Zhou^{2}
https://doi.org/10.1186/s1364001702141
© The Author(s). 2017
 Received: 9 April 2017
 Accepted: 4 September 2017
 Published: 19 September 2017
Abstract
The large amount of bandwidth that is required for the transmission or storage of digital videos is the main incentive for researchers to develop algorithms that aim at compressing video data while keeping their quality as high as possible. Block matching has been extensively utilized in compression algorithms for motion estimation as they reduce the memory requirements of any video file. A novel method by using modified artificial bee colony algorithm (MABCA) is proposed, which is the combination of basic ABCA and several techniques—initialization based on temporalspatial correlation, duplicate searching avoidance technique, adaptive search criteria for iteration, and early termination of block matching. Experimental results show that the proposed method has achieved significant improvement over the existing popular blockmatching methods in terms of estimation accuracy and computational complexity, especially when dealing with sequences with violent motion. This method can also adaptively adjust the average search point number according to the motion intensity of the different sequences in order to get the best search result at the lowest possible cost.
Keywords
 Artificial bee colony algorithm
 Motion estimation
 Fast blockmatching method
1 Introduction
Motion compensation has been adopted by all of the existing videocoding standards, such as the MPEG1, MPEG2, and MPEG4 and ITUT H.261, H.264, and H.265, owing to its high compression efficiency. Video redundancy is mainly from spatial (intraframe) and temporal (interframe) correlations. Motion estimation and compensation are used to remove the data redundancy and the unimportant visual details. It is apparent that the changes in a scene are due to object motion. Even minute movement can still lead to a great difference between successive frames, especially when movement is near the edge of the moving object. However, prediction residual can be reduced by using a region with a certain displacement in the previous frame to predict the current region in the current frame. Such method taking advantage of the motion vector of the offset to predict the new scene is called motion compensation (MC) [1]. And the process for the encoder to search for the best motion vector is called motion estimation (ME) [2]. There are generally two kinds of motion estimation: blockmatching algorithm (BMA) and pixelbased algorithm (PBA). BMA is simple and efficient. A large number of researchers employed and improved BMA in their lossless video compression schemes. The motion estimation prediction difference is encoded by a method called motion compensation prediction residual coding (MCPRC). Temporal redundancy between successive frames allows the ME and MC techniques to play an active role in video compression coding [3, 4]. Motion estimation is the process of determining motion vectors that describe the transformation from one image to another, while motion compensation [5] describes a picture in terms of the transformation of a reference frame to the current frame. Therefore, the more accurate the motion vectors are yielded by ME, the less forecast error there will be. And finally, the amount of transmission information will be largely reduced. For the foregoing reasons, motion estimation has been a critical technique in promoting the video compression ratio.
There are three basic types of motion estimation: the BMA, the pelrecursive method, and the modelbased method [6]. Among them, the blockmatching approach is more widely employed in motion estimation, because it is more practical and adaptable. The purpose of a BMA is to find the displacements of the blocks in the current frame according to the reference frame [7, 8]. It can be used to remove temporal redundancy in the video sequence, increasing the video compression effectiveness.
In the whole process, several criteria are used to determine whether a given block in current frame matches the search block in reference frame, such as mean absolute error (MAE), mean square error (MSE), and sum absolute difference (SAD).
The computational complexity of a motion estimation technique can be determined by three factors: (1.) search algorithm, (2.) cost function, and (3.) search range parameter p. Actually, we can reduce the complexity of the motion estimation algorithms by reducing the complexity of the applied search algorithm and/or the complexity of the selected cost function.
For the past decade, many fast BMA motion estimation methods have been proposed, such as full search (FS) [9], threestep search (TSS) [10], new threestep search (NTSS) [11], simple and efficient search (SES) [12], fourstep search (FSS) [13], diamond search (DS) [14], dynamic search window adjustment and interlaced search (DSWA/IS) algorithm [15], and nearest neighbors search algorithm [16]. The main concepts of fast algorithms can be classified into six categories: reduction in search positions, simplification of matching criterion, bit width reduction, predictive search, hierarchical search, and fast full search. Full search method can guarantee the best motion vector and be implemented in hardware easily. However, the full search method just simply searches all the possible points within a search window, which also makes it not very practical for its enormous computational complexity. The other methods can achieve adequate reconstructed image quality with less average search point number for most of the images with smooth motion. The TSS is the most popular algorithm. While the FSA requires, for a standard window size of ±7 pixels, 225 comparisons to find the best match, the TSS algorithm requires only 25 comparisons. The TSS algorithm, however, uses a uniformly allocated checking point pattern, making it inefficient for searching small motion video sequences. The NTSS algorithm is an altered version of the existing TSS algorithm. While the TSS algorithm requires predefined checking point pattern, the NTSS algorithm uses centerbiased checking point pattern, by making the search adaptive to the motion vector distribution. In NTSS, a halfwaystop technique is used to reduce the computation cost. SES aims at further reducing the computational complexity to speed up the TSS by a factor of two and maintain its regularity and good performance comparable with the TSS. The FSS produces better performance than the TSS and has similar performance as compared with the NTSS, while reducing the worstcase computational search point number from 33 to 27 and the average search point number from 21 to 19 as compared with NTSS. The DS algorithm can deal with both small and large motion image sequences with smaller motion estimation error and search point number than other fast search algorithms like TSS, NTSS, SES, and FSS which might only work well for the image sequences with certain degree of motion. The DSWA algorithm adaptively adjusts the size of the search window based on the best match position, while in the IS algorithm, only five positions are alternatively tested. The DSWA/IS algorithm presents a more intelligent logarithmic step search with variable patterns. The nearest neighbors search algorithm [16] presents a new motion estimation algorithm for low bit rate video coding, where each motion vector is predicted from its neighboring (already coded) motion vectors. It uses the (+) cross as a search pattern. The algorithm terminates only when the best match is found at the center or when the window boundary is reached. A modified oneatatime search algorithm [17] modifies the existing oneatatime search algorithm [18]. The modification is based on using the interblock matching between the motion vectors and the adjacent blocks. The algorithm improves the quality and reduces the number of comparisons required to obtain the best match. A Polynomial Approximation Motion Estimation Model for motioncompensated frame interpolation is proposed [19, 20]. Adaptive lowcomplexity motion estimation algorithm for high efficiency video coding encoder is presented [21] in order to speed up integer ME in high efficiency video coding. This study presents a fast center search algorithm (FCSA) and an adaptive search window algorithm (ASWA) for integer pixel ME. In addition, center adaptive search algorithm, a combination of the two proposed algorithms FCSA and ASWA, is proposed in order to achieve the best performance. Nevertheless, all these fast search methods typically suffer from different degrees of loss in the image quality. This can be attributed to the demand for less time complexity which prelimits the candidate points to be only a very small fraction of the points in the search window, consequently leaving the search with a great possibility of being trapped in local optima when processing violent motion. Motion estimation is facing a dilemma of reducing the computational complexity at the cost of worsening the estimation accuracy. Therefore, it is very necessary to find a balance between the accuracy and computational complexity.
In recent years, optimization algorithms such as the genetic algorithm (GA) and the particle swarm optimization (PSO) have been successfully applied to motion estimation [22–24]. However, these algorithms still suffer from the problem of local optima sticking. Meanwhile, artificial bee colony algorithm (ABCA) has emerged in the field of swarm intelligence [25–27], with the ability to effectively avoid falling into local optimum. It has already been applied to various problem domains, such as image segmentation [28–30], data clustering [31], and digital filters [32] and has made significant performances. Hence, in this paper, a new blockmatching algorithm for motion estimation using modified ABCA is proposed. The modified ABCA is the combination of basic ABCA and several techniques—initialization based on temporalspatial correlation, duplicate searching avoidance technique, adaptive search criteria for iteration, and early termination of block matching. Compared with other six motion estimation algorithms on 10 different video sequences, experimental results show that the proposed method could achieve significant improvements over existing fast block search methods in estimation accuracy and computational complexity.

First, a new multiple objective fitness function is proposed in this paper with the incorporation of a new motion estimation. The spatial neighborhood information of frame is critical to image quality. However, such spatial information is neglected in conventional ABCbased motion estimation approaches. In view of this, a new measure is incorporated into the cost function of the proposed approach.

Second, a parametric motion estimation method is utilized in the proposed approach, rather than searching for optimal pixel values in the whole image space. A novel method by using modified artificial bee colony algorithm (MABCA) is proposed, which is the combination of basic ABCA and several techniques—initialization based on temporalspatial correlation, duplicate searching avoidance technique, adaptive search criteria for iteration, and early termination of block matching.
The remainder of the paper is organized as follows: Section 2 mainly introduces the basic ABCA. In Section 3, the blockmatching algorithm for motion estimation using basic ABCA is firstly discussed and then the modified ABCA (MABCA) based on several improvement techniques is proposed. Section 4 gives the parameter setting and experimental results, and the conclusion is drawn in Section 5.
2 Artificial bee colony algorithm
Artificial bee colony algorithm [33–35] is a populationbased minimal bee foraging model, consisting of three groups of bees: employed bees, onlookers, and scouts. The search space represents the solution, within which all the points are considered as food sources the bees can exploit. The quality of the food source is measured by the function to be optimized [15, 36].
where j(j ≤ D) and k(k ≤ FN ∩ k ≠ i) are chosen randomly.
However, if the fitness value has not been improved by the new fitness after the preordained maximum iterations (limit), the associated employed bee will abandon this food source and will become a scout to randomly search another food source in the search window. After the new locations of the employed bees (or the food sources) are determined, a next iteration will be started until the termination condition is satisfied.
3 Method
In blockmatching algorithm using ABCA, a swarm of bees will exploit within a search window which range from − p to p in the reference frame. Each food source in the search window represents the central pixel of a candidate block, which indicates that parameters \( {x}_1^i,{x}_2^i,\dots, {x}_D^i \) of the food source \( {\mathrm{FS}}_i=\left({x}_1^i,{x}_2^i,\dots, {x}_D^i\right) \) record the location of the central pixel of the candidate block. So, in this paper, we choose the dimension D = 2 and use \( {x}_1^i,{x}_2^i \) to describe the vertical and horizontal coordinates of the central pixel of the twodimensional block. In the following, we firstly proposed a blockmatching algorithm based on ABCA. Since the result is not good enough, we then proposed a novel blockmatching algorithm based on MABCA with several techniques to improve the quality of the reconstructed image and the computational speed.
3.1 Motion estimation using ABCA
3.2 Improvement techniques

Firstly, it fails to consider the temporalspatial correlation of the motion vectors. In motion estimation, the vectors of the neighbor blocks and previous frame block are interrelated [3, 6]. We can make use of the regularity to estimate the current motion vector and improve the search result.

Secondly, one candidate food source can be searched for several times due to the fact that the new food sources are chosen randomly in the basic ABCA. The computational complexity will decrease a lot, if choosing the point previously searched is avoided.

In addition, the flexibility of stop condition is poor. The computational complexity will be reduced if the stop condition is appropriately adjusted when dealing with smooth motion sequences because it is easier to find the optimal solution for these sequences.

Lastly, the judgment on stationary block is not enough. The basic ABCA is still running to find the motion vector even when dealing with stationary block, which will greatly increase the time cost. In fact, there is no necessity to run ABCA for each block of the sequence, since most of the blocks from the small motion sequences are stationary.
In view of the above observations, a modified ABCA (MABCA) model is proposed. Below is the further explanation of the improvement process.
3.2.1 Food source initialization
The motion estimation using basic ABCA lacks prejudgment of the initial location of the food sources. In fact, in motion estimation, the distribution of the motion vectors has two main characters: enterbias property and temporalspatial correlation. Hence, we can make use of these characters and choose several points as the fixed initial points. However, if all the initial points are fixed, there will be a possibility for the algorithm to lose the randomness for severe motion videos. Therefore, we adopt a new technique of fixed points and random points combined to improve the search result.
3.2.2 Duplicate searching avoidance technique
During the process of employed bees and onlookers improving the current food source, since random numbers are involved in the rule of selecting new neighborhood, shown in Eq. (7), there is a large possibility of researching the same point, especially when the search window is restricted in a small range. Accordingly, the computation complexity will increase unnecessarily as the same point is researched again and again.
To solve this problem, we proposed a duplicate searching avoidance technique with a twodimensional history flag matrix recording all the previous research points. Each element in the matrix represents a candidate point in the search window. The initial value of the matrix is zero at the beginning of the algorithm for each block. If a point is visited during the search, then the value of the matrix’s element corresponding to that point is set to “1.” Before calculating any point within the block, the value of the element corresponding to that point is checked. If the value is zero, the calculating operation is permitted or the operation is forbidden, and the algorithm has to produce a new candidate point to check.
3.2.3 Adaptive search criteria for iteration

Stop searching the current block when the total number of iterations reaches a predetermined number (maxCycle).

Stop searching the current block even if the current iteration number does not reach maxCycle when the result of each iteration remains the same value for N times of iteration.
The estimation accuracy and computational complexity are both proportional to the maxCycle and N. So, in this paper, we select maxCycle to be 10 and N to be 7 to provide a good tradeoff between the image quality and time cost.
3.2.4 Early termination of block matching
If the values of SAD_{0} is below a preset threshold SAD_{ T }, the current block is considered to be a stationary block, its corresponding motion vector is recorded as zero, and the blockmatching algorithm will start searching the next block of the current image. Based on a series of test value of SAD_{ T }, we find that SAD_{ T } = 128SAD_{ T } gives a good performance in balancing the estimation accuracy and computational cost. Hence, in this paper, we choose SAD_{ T } to be 128.
3.3 Blockmatching algorithm for motion estimation using MABCA
4 Experimental results and discussions
4.1 Experimental setup
Parameters of blockmatching algorithm
Parameter  Explanation  Value 

mbsize  Search block size  8 
p  Maximum displacement  7 
Since the MABCA is based on a certain degree of randomness, the result of each test video sequence is averaged over the 45 tested frames, and the MSE result of each frame is in addition averaged over a mass of blocks. For example, for a CIf sequence “Bus,” there are in total \( 1584\left(=\frac{288\times 352}{8^2}\right) \) blocks for each frame. And the final result of each video sequence is further averaged over multiple times of running the MABCA until the averaged results of the same video sequence become to yield very little changes.
4.2 MABCA parameter setup
For the MABCA, the swarm size NP is chosen to be NP = 16, including 8 onlookers waiting in the colony and the other 8 employed bees respectively assigned to the fixed and random points.
For the FoodNumber, as discussed in Section 2, FoodNumber is equal to the number of employed bees, and since the initial number of employed bees is 8, we have FoodNumber = 8.
For the limit and maxCycle, small values of limit and maxCycle can lead to a fast search progress, while big values help in gaining better reconstructed image accuracy. In order to get a balance between the speed and accuracy, we finally choose limit = 10 and maxCycle = 10.
As discussed in Sections 3.2.3 and 3.2.4, for the adaptive search criteria for iteration (N) and early termination criterion SAD_{ T }, we choose N = 7, SAD_{ T }=128.
Parameters of ABC algorithm
Parameter  Explanation  Value 

D  Dimension of the algorithm  2 
NP  Swarm size  16 
FoodNumber (FN)  The total number of the food source  8 
maxCycle  The maximum number of cycles for foraging  10 
Limit  The maximum number of trials  10 
N  Adaptive search criteria for iteration  7 
SAD_{ T }  Early termination criterion  128 
4.3 Experimental results
Motion intensity of the five CIF and five QCIF sequences (the means and standard deviations of the magnitude of the motion vectors)
Sequence  Mean  Standard deviation 

CIF  
Bus  4.9924  2.0486 
Stefan  2.2919  2.7147 
Hall_motion  1.7279  2.4868 
Bridge_close  1.3882  3.2778 
News  0.7015  1.8178 
QCIF  
Highway  1.5741  2.3646 
Hall_motion  0.4588  1.2365 
Silent  0.3217  1.1873 
News  0.1044  0.5914 
Salesman  0.0776  0.3802 
4.3.1 PSNR
The average PSNR values of the five CIF sequences using the seven methods
CIF sequence  FS  TSS  SES  NTSS  FSS  DS  MABCA  

Bus  PSNR  25.6952  22.9695  21.2909  22.816  21.722  21.6976  25.5943 
Δ  0  − 2.7258  − 4.4043  − 2.8792  − 3.9732  − 3.9976  − 0.1010  
Stefan  PSNR  26.7676  24.6908  24.3372  24.7661  24.5414  24.3416  26.6243 
Δ  0  − 2.0767  − 2.4304  − 2.0015  − 2.2262  − 2.4260  − 0.1433  
Hall  PSNR  35.9483  35.5824  35.2018  35.6083  35.5667  35.5654  35.8232 
Δ  0  − 0.3659  − 0.7465  − 0.3401  − 0.3817  − 0.3830  − 0.1252  
Bridge  PSNR  35.0582  35.0542  35.0534  35.0546  35.0545  35.05443  35.0563 
Δ  0  − 0.0040  − 0.0048  − 0.0036  − 0.0037  − 0.0038  − 0.0020  
News  PSNR  37.2027  36.6369  36.0007  36.7163  36.3581  36.3203  38.94554 
Δ  0  − 0.5658  − 1.2019  − 0.4864  − 0.8445  − 0.8824  − 0.2075 
The average PSNR values of the five QCIF sequences using the seven methods
QCIF sequence  FS  TSS  SES  NTSS  FSS  DS  MABCA  

Highway  PSNR  37.4059  36.2228  35.6754  36.3604  36.3254  36.3353  36.8790 
Δ  0  − 1.1831  − 1.7305  − 1.0455  − 1.0805  − 1.0706  − 0.5270  
Hall  PSNR  36.0298  35.7070  35.4881  35.9241  35.8282  35.8998  35.9385 
Δ  0  − 0.3228  − 0.5417  − 0.1057  − 0.2016  − 0.1300  − 0.0913  
Silent  PSNR  37.1058  36.6899  36.2318  36.7073  36.5686  36.5434  36.9554 
Δ  0  − 0.4159  − 0.8739  − 0.3985  − 0.5372  − 0.5624  − 0.1504  
News  PSNR  37.7176  37.4014  37.2655  37.5466  37.4927  37.5625  37.6087 
Δ  0  − 0.3162  − 0.4521  − 0.1710  − 0.2249  − 0.1551  − 0.1090  
Salesman  PSNR  39.2987  39.0400  38.8450  39.2411  39.0850  39.2029  39.2376 
Δ  0  − 0.2586  − 0.4537  − 0.0576  − 0.2137  − 0.0958  − 0.0611 
Further observation of the comparison of the seven blockmatching estimation methods (Fig. 3) tells that the superiority of MABCA is increasingly apparently reflected as the motion intensity increases. For sequences with smooth motion, “News,” “Bridge_close,” and “Hall_motion,” the PSNR values of the seven methods are very close to each other and yield very small Δ values. The reason is that the motion vectors of the sequences with unimodal error surface and smooth motion are mostly in the vicinity of the origin, which makes it more easy to find the global optimum. While for the sequences with violent motion, “Bus” and “Stefan,” the gaps of the difference Δ values between MABCA and the other five fast search methods increase sharply, and MABCA starts to be distinctly superior to the other five fast search methods. This is because the motion vector of the sequences with violent motion is far from the origin, and the number of extreme points increases, which indicates that the unimodal error surface assumption is not satisfied. In this case, the conventional fast search methods are easily trapped in local optimum. However, the MABCA, different from the conventional fast search methods, which does not rely on the unimodal error surface assumption, can jump out of local optimum and find the global optimum. So, in this way, the result of MABCA is always very close to FS.
The above analysis is also tenable when judging from the 45 frames of one single sequence. Take the sequence “Stefan” as an example; the PSNR values of the 45 frames of “Stefan” are shown in Fig. 6. The PSNR values of the first 20 frames of the sequence “Stefan” are generally lower than the later frames because we can see from the luminance images that the first 20 images mainly record the scene of the ball flying to the tennis ball player and a series of the player’s swing which are the vigorous exercise part of the sequence with violent motion vector. The estimation accuracy of these motion vectors are reasonably lower than the motion vectors of the later frames that record the scene after hitting the ball. Consequently, the PSNR values of the first 20 frames are generally lower than the later 25 frames. Besides, for the first 20 frames, the unimodal error surface assumption is not satisfied, and the number of extreme point increases. Therefore, we can see from Fig. 6 that for the first 20 frames, the PSNR values of the MABCA are obviously better than the other five fast search methods.
4.3.2 Average search point number
For the searching process, the whole searching time is mostly cost by the process of calculating the MSE value between the reference block and the new candidate block. Therefore, we have good reason to believe that, under the condition of the same sequence frames, the same search range, and the same search block, the average search point number can represent the computational complexity.
The average search point numbers of the 10 video sequences using the seven methods
Sequence  FS  TSS  SES  NTSS  FSS  DS  MABCA 

CIF  
Bus  214.5176  24.3574  16.2369  28.0036  21.701  20.9074  48.2545 
Stefan  214.5176  24.1371  16.7680  21.2419  18.5633  16.1671  37.0971 
Hall_motion  214.5177  24.1346  17.0952  19.2263  17.6345  14.4339  33.9602 
Bridge_close  214.5176  24.1191  16.8881  17.1419  17.6922  15.1559  46.4251 
News  214.5176  24.1000  17.2851  17.8282  17.0949  13.7218  6.6690 
QCIF  
Highway  204.2828  23.3167  16.6563  18.1492  17.2760  14.4792  21.4177 
Hall_motion  204.2828  23.2501  16.9569  16.6065  16.1936  12.7627  9.9697 
Silent  204.2828  23.2149  16.9587  16.5957  16.1836  12.8024  10.5074 
News  204.2828  23.2129  17.0460  16.0354  15.8814  12.3547  6.2020 
Salesman  204.2828  23.2141  17.0595  16.0131  15.8884  12.3349  8.1457 
The total block, average stationary block, and percentage parameters of the five QCIF sequences
Sequence  Total block  Average stationary block  Percentage (%) 

Highway  396  251.0227  63.39 
Hall_motion  396  335.1778  84.64 
Silent  396  332.4889  83.96 
News  396  361.2222  91.22 
Salesman  396  346.5333  87.51 
Total block is the total block number of one frame. Average stationary block is the number of stationary block (SAD_{0} < SAD_{ T }), averaged over 45 frames. Percentage represents the proportion of the stationary blocks.
From the experimental result, for the sequences with large motion, the average search point number of MABCA is correspondingly higher than the other five methods but is lower than FS. Take the most violent sequence “Bus.cif” as an example; the proposed MABCA has a speedup ratio about 4.4 (=214.5176/48.2545) over the FS method. For the sequences with slight motion, the average search point number of MABCA is also the lowest than all the other methods. See the example of “News.cif”; MABCA has a speedup ratio of 32(=214.5176/6.6690) and 3.6(=24.1000/6.6690) over the FS and TSS. And for both of the two kinds of sequences, violent and smooth, the estimation accuracy of the MABCA is always the best for most of them.
5 Conclusions
Blockmatching algorithm is widely used in motion estimation and has made a great contribution to improve the transmission efficiency. In this paper, a combination of artificial bee colony algorithm and a series of improved approaches—the modified ABCA (MABCA)—is proposed and applied to blockmatching algorithm for motion estimation. The experiment results show that the proposed method can effectively improve the estimation accuracy and avoid local optima problem. It can improve the estimation accuracy of violent motion sequences with a little sacrifice of computational complexity, while reducing the computational cost greatly when dealing with smooth sequences at the premise of high estimation accuracy.
Though the proposed MABCA has achieved significant performances, the work can be extended by using dynamic search window adjustment, switching search patterns, and block classification to further improve the estimation accuracy for sequences with smooth motion and reduce the computational complexity for the sequences with violent motion.
Declarations
Acknowledgements
Not applicable.
Funding
This work is partially supported by the National Natural Science Foundation of China (No.61302120), National Engineering Center for Mobile Ultrasonic Detection (No.2013FU125X02), and the supports of the Priority Academic Program Development of Jiangsu Higher Education Institutions, Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology (No.KJR16237).
Availability of data and materials
Not applicable.
Authors’ contributions
Yu is the first and corresponding author. The other authors made the algorithm and experiments. All authors read and approved the final manuscript.
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
 S. Kappagantula, K.R. Rao, Motion compensated interframe image prediction. IEEE Trans. Commun. COM33, 1011–1015 (1985)View ArticleGoogle Scholar
 C. STILLER, Estimating motion in image sequences: a tutorial on modeling and computation of 2d motion. IEEE Signal Process. Mag. 16(4), 70–91 (1999)View ArticleGoogle Scholar
 D.W. Kim, J.H. Choi, Y.S. Choi, C.H. Jeon, N.Y. Ko, in 1996 IEEE TENCONdigital signal processing applications. Block motion estimation based on spatiotemporal correlation 2, 955–960 (1996)Google Scholar
 Y.J. Koh, S.B. Yang, An adaptive search algorithm for finding motion vectors, in Proceedings of the IEEE region 10 conference on TENCON99. 1, 186–189 (1999)Google Scholar
 T. Koga, K. Iinuma, A. Hirano, Y. Iijima, T. Ishiguro, in Proceedings of NTC8. Motion compensated interframe image coding for video conference (1981)Google Scholar
 L. Hsieh, W.S. Chen, C.H. Liu, Motion estimation using twostage predictive search algorithms based on joint spatiotemporal correlation information. Expert Syst. Appl. 38, 11608–11623 (2011)View ArticleGoogle Scholar
 M.C. Chang, J.S. Chein, in Proc. IEEE Int. Symp. Circuits Syst. (ISCAS’06). An adaptive search algorithm based on block classification for fast block motion estimation, 3982–3985 (2006)Google Scholar
 F. Yu, M. Hui, W. Han, P. Wang, L.q. Dong, Y.j. Zhao, The application of improved blockmatching method and block search method for the image motion estimation. Opt. Commun. 283, 4619–4625 (2010)View ArticleGoogle Scholar
 T.G. Ahn, Y.H. Moon, J.H. Kim, Fast fullsearch motion estimation based on multilevel successive elimination algorithm. IEEE Transactions on Circuits and Systems for Video Technology 14(11), 1265–1269 (2004)View ArticleGoogle Scholar
 J.N. Kim, T.S. Choi, A fast threestep search algorithm with minimum checking points using unimodal error surface assumption. IEEE Trans. Consum. Electron. 44(3), 638–648 (1998)View ArticleGoogle Scholar
 R. Li, B. Zeng, M.L. Liou, A new threestep search algorithm for block motion estimation. IEEE Trans.on Circ. Syst. Video Technol 4(4), 438–442 (1994)Google Scholar
 J. Lu, M.L. Liou, A simple and efficent search algorithm for block matching motion estimation. IEEE Trans.on Circ. Syst. Video Technol 7(2), 429–433 (1997)Google Scholar
 L.M. Po, W.C. Ma, A novel fourstep search algorithm for fast block motion estimation. IEEE Trans. Image Processing. 9(2), 287–290 (2000)Google Scholar
 S. Zhu, K.K. Ma, A new diamond search algorithm for fast blockmatching motion estimation. IEEE Trans. Image Processing. 9(2), 287–290 (2000)Google Scholar
 Karaboga D. An idea based on honey bee swarm for numerical optimization[R]. [S. l.]: Erciyes University, Technical Report: TR06, (2005)Google Scholar
 L.W. Lee, J.F. Wang, J.Y. Lee, J.D. Shie, Dynamic searchwindow adjustment and interlaced search for blockmatching algorithm. IEEE Trans. Circ. Syst. Video Technol. 3(1), 85–87 (1993)View ArticleGoogle Scholar
 M. Gallant, F. Kossentini, An efficient computationconstrained blockbased motion estimation algorithm for low bit rate video coding. IEEE Trans. Image Process. 8, 1816–1823 (1998)View ArticleGoogle Scholar
 A. Mohammad, L. George, in World Comput. Int. Conf. on IPCV. Fast predictive coding method based on an enhanced blocks motion estimation. 472–476 (2008) Google Scholar
 R. Srinivasan, K.R. Rao, Predictive coding based on efficient motion estimation. IEEE Trans. Commun. COM 33(8), 888–896 (1985)View ArticleGoogle Scholar
 Y.B. Zhang, L. Xu, X.Y. Ji, Q. Dai, Polynomial approximation motion estimation model for motioncompensated frame interpolation IEEE trans. ON Circuits and systemsfor video technology 26(8), 1421–1432 (2016)View ArticleGoogle Scholar
 A. Medhat, A. Shalaby, M.S. Sayed, M. Elsabrouty, F. Mehdipour, Adaptive lowcomplexity motion estimation algorithm for high efficiency video coding encoder. IET Image Process. 10(6), 438–447 (2016)View ArticleGoogle Scholar
 S. Li, W. Xu, N. Zheng, H. Wang, A novel fast motion estimation method based on genetic algorithm. Acta Electron. Sin. 28(6), 114–117 (2000)Google Scholar
 Z.H.A.N.G. Ping, W.E.I. Ping, Y.U. Hongyang, F.E.I. Chun, A novel search algorithm based on particle swarm optimization and simplex method for block motion estimation. International Journal of Digital Content Technology and its Applications 5(Number 1) (2011)Google Scholar
 R.C. Eberhart, Y. Shi, in Proceedings of the 7th Interna. Conference on Evolutionary Programming VII. Comparison between genetic algorithm and particle swarm optimization, vol 1447 (1998)Google Scholar
 D. Karaboga, B. Akay, A comparative study of artificial bee colony algorithm. Appl. Math. Comput. 214(1), 108–132 (2009)MathSciNetMATHGoogle Scholar
 Zhaoqing Pan, Yun Zhang, and Sam Kwong, "Efficient motion and disparity estimation optimization for low complexity multiview video coding," IEEE Trans. Broadcasting. 61(2), 166–176 (2015)Google Scholar
 Yu Xue, Jiongming Jiang, Binping Zhao and Tinghuai Ma, "A selfadaptive articial bee colony algorithm based on global best for global optimization", Soft Computing. (2017). doi:10.1007/s0050001725471
 Karaboga D. A New Design Method Based on Artificial Bee Colony Algorithm for Digital IIR Filters, Journal of the Franklin Institute, 346(4), 328–348 (2009)Google Scholar
 Y.f. Cao, W.y. Yu, Y.h. Xiao, et al., Image segmentation using artificial bee colony and fast FCM algorithms. Adv. Sci. Lett. 4, 400–407 (2011)View ArticleGoogle Scholar
 P.K. Sahooa, G. Arorab, A thresholding method based on 2D Renyi’s entropy. Pattern Recogn. 37, 1149–1161 (2004)View ArticleGoogle Scholar
 D. Karaboga, C. Ozturk, A novel clustering approach: artificial bee colony (ABC) algorithm. Appl. Soft Comput. 11, 652–657 (2011)View ArticleGoogle Scholar
 D. Karaboga, A new design method based on artificial bee colony algorithm for digital IIR filters. Journal of the Franklin Institute 346(4), 328–348 (2009)MathSciNetView ArticleMATHGoogle Scholar
 D. Karaboga, B. Basturk, On the performance of artificial bee colony (ABC) algorithm. Appl. Soft Comput. 8(1), 687–697 (2008)View ArticleGoogle Scholar
 A. Baykasoùlu, L. Özbakır, P. Tapkan, Artificial Bee Colony Algorithm and Its Application to Generalized Assignment Problem. Swarm Intelligence: Focus on Ant and Particle Swarm Optimization, Book edited by: Felix T. S. Chan and Manoj Kumar Tiwari, ISBN 9783902613097, 532, Itech Education and Publishing, Vienna, (2007)Google Scholar
 B. Akay, D. Karaboga, Parameter tuning for the artificial bee colony algorithm. In: Nguyen N, Kowalczyk R, Chen SM (eds) Proceedings of the ICCCI 2009, LNCS, vol 5796. Springer, Berlin/Heidelberg, 608619 (2009)Google Scholar
 D. Karaboga, B. Basturk, A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Glob. Optim. 39(3), 171–459 (2007)MathSciNetView ArticleMATHGoogle Scholar