Multipath Flatted-Hexagon Search for Block Motion Estimation

(1)

Ubiquitous International Volume 1, Number 2, April 2010

Multipath Flatted-Hexagon Search for Block Motion

Estimation

Chao-Ho Chen

Department of Electronic Engineering National Kaohsiung University of Applied Sciences 415, Chien Kung Rd., Kaohsiung 807, Taiwan (R.O.C.)

thouho@cc.kuas.edu.tw

Tsong-Yi Chen

Department of Electronic Engineering National Kaohsiung University of Applied Sciences 415, StreetChien Kung Rd., Kaohsiung 807, Taiwan (R.O.C.)

chentso@cc.kuas.edu.tw

Da-Jinn Wang

Department of Information Management National Kaohsiung Marine University

No.142, Haijhuan Rd., Nanzih District, Kaohsiung City 81143, Taiwan (R.O.C.) wangdaj@mail.nkmu.edu.tw

Yi-Fan Li

Department of Electronic Engineering National Kaohsiung University of Applied Sciences 415, StreetChien Kung Rd., Kaohsiung 807, Taiwan (R.O.C.)

Received August 2009; revised March 2010

Abstract. This paper proposes a novel and simple multipath search with atted-hexagon or diamond pattern for block motion estimation to achieve adjustable speed/accuracy in block-matching algorithm (BMA). To improve the accuracy of the fast BMA near to that of full search (FS), the inherent problem of being trapped at the local minimum block distortion measure (BDM) should be overcome substantially. In the proposed method, a threshold of BDM is introduced to determine the possible-optimal search directions in order to escape from being trapped into a local minimum BDM, followed by a atted-hexagon or diamond search performed in these directions with a BDM below a threshold. Then, the estimated motion vector will be re

ned at each search step until the searching process is stopped. The BDM threshold will be adjustable for the purpose of adjusting the search speed and search accuracy speci

ed in the certain applications. Experimental results show that the proposed multipath search algorithm can achieve an average matching probability up to 98% near to that of FS and about 10 times of checking points faster than FS in most of real-world sequences. Keywords: Motion Estimation, Block-matching Algorithm, Multipath Search, Flatted-hexagon Search

1. Introduction. Motion estimation can make the interframe coding to achieve a very high compression ratio, when compared to the intraframe coding, by exploiting the heavy temporary redundancy between successive frames. Among various motion estimation techniques, the block-matching algorithm (BMA) is the most attractive method for

(2)

the current international video compression standards including H.261, H.263, MPEG-1, MPEG-2 and MPEG-4 [1]-[6], because of its effectiveness and simplicity for implemen-tations [7]. However, the matching process of finding the optimal still involves a large amount of calculations, e.g. the full search (FS) method (i.e., the most accurate approach), in which all candidate blocks require to be evaluated. To reduce the intensive computa-tional complexity with a tolerable distortion, many fast block-matching algorithms were developed [8]-[21].

Among the above suboptimal methods, both the search patterns attributes and initial searching range always directs the developmental processes of these algorithms. By taking advantage of the characteristics of the center-biased motion vector distribution existed in most real-world image sequences, the new three-step search (NTSS) [9], four-step search (4SS) [10] and block-based gradient descent search (BBGDS) [11] perform better than the three-step search (3SS) [8], where these four search patterns are square-shaped. Based on a practical compact-shaped pattern with fewer candidate search points per block, a diamond-search (DS) algorithm [12][13] can not only improve the searching speed but also reduce the chances of being trapped in local minimum block distortion measure (BDM) points, when compared to those four algorithms. To improve the local-minimum trapping problem in the 3SS algorithm for the estimation of small motions, an efficient three-step search (E3SS) algorithm [14] employs a small diamond pattern in the first step and the unrestricted search step is used to search the center area. It performs better than DS in terms of MSE with fewer or comparable number of search points for the sequences that contain medium to large motion, but is inferior in speed performance to DS when searching small motion vectors. The hexagon-based search (HEXBS) algorithm [15] utilized a hexagon-shaped pattern with only 7 checking points in the initial search and 3 checking points in the following searches to achieve substantial speed improvement over the DS algorithm with similar distortion performance for most high-resolution (e.g. 720 × 480) image sequences. Nevertheless, the matching-probability (i.e., the probability of finding the true motion vector) will degenerate with the decreasing resolution of the video format. By introducing a fast inner search into the interior of hexagonal pattern, an enhanced hexagonal search algorithm [16] is proposed to improve HEXBS in search accuracy. The introduction of flatted-hexagon search (FHS) pattern will make the FHS algorithm [17] to provide a better speed-probability product than the above fast BMAs, when both speed performance and matching probability need to be considered. The basic idea behind the FHS algorithm is that the covering range of a search pattern should be enlarged as horizontal as possible to find the optimal motion vector quickly because the occurrence probability of horizontal-biased motions is larger than that of vertical-biased motions in most of real-world image sequences. To obtain a faster searching speed than the DS algorithm while maintaining similar search quality, the cross-diamond search (CDS) algorithm [18] and cross-diamond-hexagonal search (CDHS) algorithm [19] employed a cross-shaped pattern at the initial step to exploit the characteristics of the center-biased motion vector distribution very efficient, followed by the halfway-stop technique, and the large/small diamond or hexagon search patterns in the subsequent steps. Based on inter-block correlations, an adaptive rood pattern search (ARPS) [20] dynamically determines the size of the search pattern in the initial search stage in order to find a good starting point for each macroblock. In addition, zero-motion prejudgment is incorporated to further speed up the search, particularly beneficial to the sequences containing small motions. By vector quantization technologies [22][23], a new approach of using predictive fine granularity successive elimination for fast optimal block matching motion estimation is proposed in [21]. Nevertheless, various search patterns and/or extra processes at searching steps will make those algorithms [18]-[21] to be complicated in realization, especially

(3)

112 C.-H. Chen, T.-Y. Chen, D.-J. Wang, Y.-F. Li

for VLSI implementation, because of considering the regularity [24]. Without loss of generality, a regular searching algorithm using a single search-pattern is always more interesting in realization cost than the search algorithm using the complicated search process or multiple various search-patterns.

Generally speaking, the common drawback of fast BMAs is that they cant almost approach FS in search accuracy for the real-world sequences, so these algorithms are also called suboptimal BMAs. In fact, the local-minimum trapping problem will be major factor and may occur when there are multiple local minima existed in the search window, especially for large motion blocks, in the real-world sequences. However, most of the previous fast BMAs are based on the assumption that the BDM increases monotonically as the search pattern moves away from the global minimum BDM point. Owing to using such a monotonous searching path, those BMAs frequently suffer the local-minimum trapping problem and hence cant have a matching probability near to FS. In theory, to cope with the local-minimum trapping problem, the multipath search approach will be the better method, especially for the case of multiple minimum BDM points existed. Besides, those algorithms cant also provide an adjustable search speed and picture quality for some specific applications. To reduce the local-minimum trapping problem, this paper develops a multipath search algorithm that uses the dynamic BDM threshold to derive possible directions of leading to the global minimum BDM point. The proposed search method is dedicated to achieving high search accuracy near to FS, i.e., people cant visually discriminate the difference of motion-compensated results using motion vectors estimated by the both search algorithms. In the proposed multipath search scheme, many well-known search patterns can be employed. In this paper, we propose two multipath search algorithms: multipath flatted-hexagon search (MFHS) and multipath diamond search (MDS), for low-resolution (e.g. CIF, 352x288 or SIF, 352x240) and high-resolution (e.g. CCIR601, 720x480)) image sequences, respectively. The searching scheme employs the flatted hexagonal pattern or diamond pattern to search for each possible optimal path and is further designed for adjusting the search speed and matching probability. It also points out that the flatted-hexagon pattern is more effective than others in the image sequences mainly containing horizontal-biased motions for low-resolution image sequences. For brevity, only the MFHS algorithm is discussed since MDS has the same search process as MFHS except that the search pattern used is different from that of MFHS. The following section describes the proposed multipath search algorithm including the analysis of search strategy, selection of search pattern, and the search process of MFHS. Section III discusses the simulation results of FHS, MFHS and MDS and comparisons with several reported fast BMAs, and conclusions are made in the final section.

2. Multipath Search Algorithm.

2.1. Analysis of Search Strategy. Most conventional block motion estimation algo-rithms are explicitly or implicitly based on the assumption: BDM increases monotonically as the checking point moves away from the global minimum. Obviously, this assumption essentially requires that the error surface is unimodal over the search windows. Unfor-tunately, this is usually not true due to many reasons such as the aperture problem, the textured (periodical) local image content, the inconsistent block segmentation of moving object and background, the luminance change between frames, noises, and etc. As a consequence, this may make the search easy to be trapped into a local minimum.

Recently, some pre-existing fast BMAs [14][18]-[21] employed a cross-shape search pat-tern in the first step to possibly avoid being trapped at a local minimum BDM point. In those methods, even all fast BMAs, the search direction for the next step is oriented by

(4)

someone search point that has the least BDM value among points checked in the current step. However, it may be not always true for the assumption that the search direction oriented by the minimal BDM point at each step will be toward the final position of the global minimum error. This may be explained by the fact that there is one local minimum BDM point existed in the neighborhood of the point with the least BDM value and this will lead the search to be trapped into that local minimum. Basically, the direction of the global minimum is always oriented by the search points of low BDM value. Hence, it implies that such low-BDM points should be considered to settle the searching direction for the next step in order to escape from being trapped into a local minimum. In other words, those low-BDM points will be the candidates of searching in the direction of the global minimum. As an example, Figure1 describes a case of misleading the search direc-tion for the next step in the DS algorithm and thus it will be likely to be trapping into one of local minima around the point of BDM value 67, where the grayish point of BDM value 4 indicates the global minimum. In the figure, there are two smaller BDM points of values 67 and 73 among checking points searched in the current step. Obviously, to avoid misleading the search direction for the next step, these two points of BDM-value 67 and 73 seem to be required for being oriented as the search directions in the following search path to find the global minimum point. Based on the above discussions, it reveals that the multipath search in the direction of certain low-BDM points for the following step will be more effective to cope with the local-minimum trapping problem than the single-path search used in those famous fast BMAs.

Figure 1. An example of false searching direction for DS.

2.2. Selection of Search Pattern. An in-depth examination of the previous researches [8]-[20] reveals that both shape and size of a search pattern can influence the searching speed and quality significantly. In respect to shape, the main merit of compactness is to consider all possible searching directions for tracking the optimal motion vector that has the least matching error. The hexagon is more compact than the diamond, as shown in Figure 2(a) and (b), which in turn is better than the square. The patterns size will affect the probability of the best match and also the moving speed of the search pattern. The moving speed of a search pattern within the searching window is directly proportional to the size of that pattern. The faster moving of a large search pattern will increase the speed

(5)

114114 C.-H. Chen, T.-Y. Chen, D.-J. Wang, Y.-F. LiC.-H. Chen, T.-Y. Chen, D.-J. Wang, Y.-F. Li

of finding the large motion vector. As a result, a large search pattern is more suitable for the video with large motion contents than a small pattern. Small-size pattern usually causes the searching to be trapped into a local minimal-error point, especially for those image sequences with large motion contents which may also implies the high-resolution format. On the other hand, a large search pattern is most likely to result in misleading of the searching direction that may frequently either delay the searching time or even miss the optimal one, especially for the video with small-motion contents or low-resolution format. Besides, the quantity of checking points required at each step will also have the similar influence on the search speed and quality as the patterns shape and size. Basically speaking, fewer checking points needed in every step can speed up the search but suffer a larger distortion, and oppositely more checking points will reduce the search speed but can provide a better quality performance of block-matching. The matching rate of a search pattern at each step is mainly dependent on the quantity of the checked points within all candidate search points covered by that pattern. In other words, the matching probability will be inversely proportional to the hollowness degree, which is defined as the ratio c/n where c is the number of unchecked points and n is the number of total points within the search pattern, i.e., all candidate search points.

⃝: checking point; : unchecked point

Figure 2. Shapes of various search patterns: (a) diamond pattern; (b) hexagon pattern; (c) 5-point cross pattern; (d) ﬂatted-hexagon pattern.

Among fast BMAs with the center-biased search, the diamond-shaped search algorithm [12, 13] performs better than those square-shaped methods [8-11], because its medium-size compact-shape pattern with 9 checking points can find any-size motion vectors under a certain search speed and quality. Besides, the unrestricted search process minimizes the distortion caused by the local-optimal trapping problem. The hexagon pattern adopted in [15] has a more compact (i.e., circle-approximated) shape with larger size and less checking points (7 checking points) than the diamond pattern. By using such a search pattern, the HEXBS algorithm has a speed-up improvement over the DS algorithm mainly owing to the contribution of less checking points. But, the combination of fewer checking points and larger size for the search pattern will make HEXBS to suffer degradation on the probability of finding true motion vectors. Thus, the HEXBS algorithm can maintain a matching probability similar to that of the DS algorithm for most high-resolution image sequences (e.g. CCIR601) or some certain low-resolution image sequences (e.g. SIF or CIF) with a highly center-biased motion vector distribution. Basically speaking, HEXBS has a significant degradation of matching-probability for most low-resolution image sequences in comparison with DS. The best explanation of low matching-probability for HEXBS is its high degree of hollowness, 10/17, existed in the search pattern, while the diamond pattern used in DS has a lower hollowness degree of 4/13. Both DS and HEXBS adopt a cross-pattern of five points, as shown in Figure 2(c), to recheck whether the zero motion vector obtained by the initial search is the final solution. An initial search by using 5-point

(6)

cross pattern will provide a very high search speed and matching probability for block motion estimation in an image sequence containing massive quasi-zero motion vectors. For an image sequence containing massive zero motion vectors, the HEXBS algorithm will have a similar matching-probability but a faster search speed compared to the DS algorithm because HEXBS can save 2 checking points than DS on the initial search.

Based on an advanced analysis on the distributions of motion vectors in the most real-world image sequences, it is clear that the occurrence possibility of horizontal-biased motions is signiﬁcantly greater than that of vertical-biased motions. Table 1 lists the probability distributions of horizontal-biased and vertical-biased motions in seven well-known image sequences with various motion contents for a search window ±7. In the table, the horizontal-biased and vertical-biased motion vectors are deﬁned as a vector in which the angle between the motion vector and the horizontal and vertical axis, re-spectively, is equal or small than 30X. For the video-conferencing sequence, the Salesman sequence bears a very high center-biased motion vector distribution, i.e., containing a large quantity of small motions, with a low H/V (horizontal/vertical) probability ratio of 17.94/14.17. Belonging to the medium-motion sequence, Foreman has a medium H/V ra-dio of 30.17/22.62, but the Coastguard sequence has a very high H/V rara-dio of 81.85/3.53. Involving complicated large-motion contents, the Football sequence and Tennis sequence have medium H/V ratios of 27.14/17.05 and 26.07/20.50, respectively, but the Garden sequence captured by panning the camera with translation has an extremely high H/V ratio of 92.78/2.12.

The above analysis reveals that the covering range of a search pattern may need to be flatted horizontally in order to find the optimal motion vector quickly. This implies that both speed and probability performances in block-matching process will be improved for the most of real-world sequences if the shape of a search pattern is flatted horizon-tally. A hexagon will be the most attractive search-pattern to be flatted, since it has a more compact form than other search patterns reported previously. Based on both hor-izontallyVflatted and hexagonal characteristics, a flatted-hexagon search pattern used in the block-matching algorithm for motion-vector estimation is proposed [17]. The flatted-hexagon pattern can be viewed as that a flatted-hexagon pattern is flatted horizontally or that both top and bottom checking points of a diamond pattern are removed. Besides, similar to the hexagon search pattern, the flatted-hexagon search pattern is composed of seven checking points with the center surrounded by six endpoints of the flatted hexagon, as described in Figure 2(d). Because of its small shape, the flatted hexagon pattern has a lower hollowness degree of 4/11 than that of the hexagon pattern used in the HEXBS algorithm. Both features of low hollowness and horizontal-biased shape will significantly improve the matching probability over HEXBS, and a quantity of only seven checking points required in the pattern will provide a faster search speed than DS.

On the other hand, pre-determining an initial search point through evaluating cer-tain highly reliable predictor sets can improve the searching eﬃciency substantially. The

(7)

Table 1. Probability Distributions of Horizontal- And Vertical-Biased Motions. Sequence Format Horizontal Probability(%) Vertical Probability(%)

Salesman CIF,80 frames 17.94 14.17

Foreman CIF,300 frames 30.17 22.62

Coastguard CIF,300 frames 81.85 3.53

Garden CIF,115 frames 92.78 2.12

Tennis CIF,67 frames 26.07 20.50

Football CIF,125 frames 27.14 17.05

*Horizontal-biased and vertical-biased motion vectors are deﬁned as the vectors with θv ≤ 30◦and θh ≤ 30◦ , respectively.

search using various search pattern in diﬀerent search steps [16][18][19] will also improve the search speed and matching probability. However, in point of fact, those methods cant completely solve the local-optimal trapping problem, especially for the situation of multiple local-optimal points existed. Besides, using a single search pattern with a simple monotonous searching strategy is more suitable for being employed into the multipath search than the complicated or multi-pattern search because they will largely complicate the realization when they are used in the multipath searching process.

Theoretically, a multi-path search can increase the matching probability by escaping being trapped into a local minimal point, but the speed performance will be substantially reduced owing to searching multiple paths, compared to the single-path search. So, the search pattern used in the multi-path search should be designed with less checking points at each step to avoid reduction in speed performance. The ﬂatted hexagonal pattern has only seven checking points and performs better than the above well-known search patterns when both search speed and matching probability need to be considered concurrently. Therefore, the ﬂatted hexagonal search pattern will be the most suitable for the proposed multipath search approach.

2.3. MFHS Algorithm. The basic search strategy of the flatted hexagon search pattern is to keep advancing with the center moving to any of the six endpoints and whichever endpoint the center of the search pattern moves to. Thus, there are always three new endpoints introduced and the other three endpoints and the original center point are overlapped, as shown in Figure 3. A 5-point cross pattern, as plotted in Fig. 3 (b) that is also used in those famous BMAs, is finally used in the focused inner search. Firstly, a minimum block distortion measure is obtained by calculating the 7 search-points of the flatted-hexagon pattern which is located at the center of the search window, as shown in Figure 3 (a). If the minimum BDM is found at the central checking point, the search will switch to use the 5-point cross pattern which introduces new 4 search points around that center for ending the search, as depicted in Figure 3 (b). Then, one with minimum BDM among these 5 checking points will be selected as the optimal solution for motion vector estimation. Otherwise, the flatted-hexagon pattern moves toward one endpoint with a minimum BDM and then the search continues with the same flatted-hexagon pattern centered at that minimum BDM point in two normal forms of Figure. 3 (c).

In essence, each search path of MFHS adopts the search process of FHS, exclusive of determining the next search-paths. To judge which paths are required for approaching the optimal solution, a dynamic threshold is introduced to determine the local minimum points that may be in the direction of the global minimum. The block matching error is based on the measurement of SAD (sum of absolute diﬀerences) and SADmin denotes the minimum SAD value among all checking points in a search step. For every search step, if

(8)

the absolute diﬀerence between SAD value of someone point and SADmin is smaller than or equal to a threshold T, such a point will be regarded as a local minimum. That is,

if _|SADp− SADmin| 5 T, p is a local minimum (1)

Then, the center of a new FHS needs to be moved to the local minimum point. The local-minimum decision rule (1) is used to find the next local minimum point from those checking points of multiple new FHSs searching patterns. Such a process will be continued until there is no new FHS excited. Thus, the motion vector is estimated at the location of the latest SADmin. On the other hand, if the local minimum is located at the center of FHS, a 5-point cross search is executed for ending this search-path. But, in the first step, a 5-point cross pattern will end the MFHS process if there is only one local-minimum point located at (0, 0). The above discussion of the proposed MFHS algorithm is summarized in Figure 4. In Figure 5, we illustrate a search process with T = 25 for finding a motion vector (4, -1) by using 24 checking points. In the step 1, three local-minimum points with SAD = 50, 70, and 75 are firstly derived by the local-minimum decision rule (1) and then the SADmin is set to 50. Thus, the following step performs three search paths based on those three local-minimum points, in which there are two new searches of FHS centered at points of SAD = 50 and 70 and one new 5-point cross search centered at the point of SAD = 75. Then, the value of SADmin is updated by 20. In the step 3, only one local-minimum point of SAD = 40 is found, so the search process is reduced to one search-path and SADmin remains as 20. Because the local-minimum of SAD = 40 is located at the center of an FHS, a 5-point cross search is executed for ending this search-path, as described in the step 4. Then, the value of SADmin is updated by 10 and such a point of SADmin is used to estimate a motion vector as (4, -1) with 24 ( = 7+10+3+4 ) checking points.

Figure 3. Various forms of the ﬂatted-hexagon search pattern: (a) start-ing search-points; (b) endstart-ing search-points; (c) search points of two normal searches. ( _{• : the required checking point.)}

In the proposed algorithm, a ﬁxed T may result in diﬀerent searching results for image sequences of various contents. Therefore, an adjustable scheme is introduced to provide an appropriate T for various image sequences, as shown in the following equation (2).

T = SADmin× β (2)

In the equation, β is a parameter of local-minimum decision and its value ranges from 0 to 1 for most of the real world sequences, and the required number of checking points is

(9)

Figure 4. The MFHS algorithm

likely linearly proportional to β. If β = 0, T will reduce to zero and this means that only one local-minimum point is regarded as being in the direction of the global minimum at each step, i.e., MFHS will return to FHS. If β = 1, the matching probability will be near to 100%, i.e., the quality performance of MFHS will approach that of FS. Generally, we cant visually distinguish the motion-compensated result using motion vectors estimated by MFHS from that of FS when β is above 0.5, so the value of β is usually set below 0.5. It is pointed out that the noise interference and certain motion contents will aﬀect the matching probability because these factors will result in more local minimum points to be veriﬁed. For the sequence containing complicated motions or zooming-captured motions, it needs a larger β to provide a better performance in search accuracy. Thus, by introduction of β, the value of T will be adjustable in order to make both search speed and matching probability to be adjustable.

(10)

3.4. Discussions. From the above experimental results, the proposed multipath search algorithm can achieve an average matching probability up to 98and about 10 times of checking points faster than FS in most of real-world sequences. Besides, the BDM thresh-old will be adjustable for the purpose of adjusting the search speed and search accuracy specified in the certain applications. However, the proposed multipath search algorithm will spend more search time when meeting a low-contrast image sequence, in which there are more local minimum BDM points needed to be checked. In a low-contrast image sequence, it will generate many quasi-zero motion vectors because the pixel difference is very slight. To cope with this problem, a zero-motion prejudgment [20] may be employed to initially find zero motion vectors to avoid further searching for the optimal point. This is because most video compression standards only require the motion vector that is acceptable, not the optimal.

4. Conclusions. In this paper, we have proposed a novel and simple speed/accuracy-adjustable block-matching algorithm based on multipath search scheme. By the multipath search strategy, it can substantially reduce the local-minimum trapping problem to achieve a high matching probability near to FS but still obtain about ten times of search speed faster than FS. It also provides adjustability in search speed/accuracy by a local-minimum decision parameter. Besides, the implementation is not complex because the number of search paths required is determined by a simple decision rule of BDM and each path is searched by use of the identical search pattern. Furthermore, in theory any search pattern can be also used in the proposed multipath search method for various-purpose applica-tions. The experimental results imply that the multipath flatted-hexagon search (MFHS) algorithm and multipath diamond search (MDS) algorithm are suitable for low-resolution (e.g. CIF, 352x288 or SIF, 352x240) and high-resolution (e.g. CCIR601, 720x480)) image sequences, respectively. When the search accuracy (i.e., picture quality) is considered for approaching that of FS, the proposed multipath search algorithm will be more attractive than other suboptimal BMAs.

Acknowledgement. This work is supported by National Science Council under Grant NSC94-2213-E-151-008, Taiwan, R.O.C.. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

REFERENCES

[1] Information Technology-Coding of Moving Pictures and Associated Audio for Digital Storage Media at up to About 1.5 Mbit/s-Part 2: Video, ISO/IEC 11 172-2 (MPEG-1 Video), 1993.

[2] Information Technology-Generic Coding of Moving Pictures and Associated Audio Information: Video, ISO/IEC 13 818-2 (MPEG-2 Video), 2000.

[3] Information Technology-Coding of Audio Visual Objects - Part 2: Visual, ISO/IEC 14 469-2 (MPEG-4 Visual), 1998.

[4] Video Codec for Audiovisual Services at p × 64 kbits/s, ITU-T Recommendation H.261, Mar. 1993. [5] Video Coding for Low Bit Rate Communication, ITU-T Recommendation H.263, Feb. 1998. [6] Advanced Video Coding, ITU-T Recommendation H.264/ISO/IEC 14496-10, Final Committee

Draft, Document JVC-E022, September 2002.

[7] Hui Wang, Joyce Liang and C.-C. Jay Kuo, Overview of robust video streaming with network coding, Journal of Information Hiding and Multimedia Signal Processing, vo1. 1, no. 1, pp. 36-50, Jan. 2010. [8] T. Koga, K. Iinuma, A. Hirano, Y. Iijima, and T. Ishiguro, Motion compensated interframe coding for video conferencing, Proc. of National Telecommunications Conf., pp. G5.3.1- G5.3.5, New Orleans, LA, Nov. 1981.

[9] R. Li, B. Zeng, and M. L. Liou, A new three-step search algorithm for block motion estimation, IEEE Trans. Circuits Syst. Video Technol., vol. 4, pp. 438-443, Aug. 1994.

(11)

Multipath Flatted-Hexagon Search for Block Motion Estimation 131

[9] R. Li, B. Zeng, and M. L. Liou, A new three-step search algorithm for block motion estimation, IEEE Trans. Circuits Syst. Video Technol., vol. 4, pp. 438-443, Aug. 1994.

[10] L. M. Po and W. C. Ma, A novel four-step search algorithm for fast block motion estimation, IEEE Trans. Circuits Syst. Video Technol., vol. 6, pp. 313-317, June. 1996.

[11] L. K. Liu and E. Feig, A block-based gradient descent search algorithm for block motion estimation in video coding, IEEE Trans. Circuits Syst. Video Technol., vol. 6, pp. 419-423, Aug. 1996.

[12] J. Y. Tham, S. Ranganath, M. Ranganath, and A. A. Kassim, A novel unrestricted center-biased diamond search algorithm for block motion estimation, IEEE Trans. Circuits Syst. Video Technol., vol. 8, pp. 369-377, Aug. 1998.

[13] S. Zhu and K. K. Ma, A new diamond search algorithm for fast block-matching motion estimation, IEEE Trans. Image Processing, vol. 9, pp. 287-290, Feb. 2000.

[14] X. Jing and L. P. Chau, An efficient three-step search algorithm for block motion estimation, IEEE Trans. Multimedia, vol. 6, no. 3, pp. 435-438, June 2004.

[15] C. Zhu, X. Lin, and L. P. Chau, Hexagon-based search pattern for fast block motion estimation, IEEE Trans. Circuits Syst. Video Technol., vol. 12, no. 5, pp. 349-355, May 2002.

[16] C. Zhu, X. Lin, L. P. Chau, and L. M. Po, Enhanced hexagonal search for fast block motion estima-tion, IEEE Trans. Circuits Syst. Video Technol., vol. 14, no. 10, pp. 1210-1214, Oct. 2004.

[17] T. H. Chen and Y. F. Li, A novel flatted hexagon search pattern for fast block motion estimation, Proc. of IEEE 2004 International Conference on Image Processing (ICIP), Singapore, pp. 1477-1480, Oct. 2004.

[18] C. H. Cheung and L. M. Po, A novel cross-diamond search algorithm for fast block motion estimation, IEEE Trans. Circuits Syst. Video Technol., vol. 12, no. 12, pp. 1168-1177, Dec. 2002.

[19] C. H. Cheung and L. M. Po, A novel cross-diamond-hexagonal search algorithm for fast block motion estimation, IEEE Trans. Multimedia, vol. 7, no. 1, pp.16-22, Feb. 2005.

[20] Y. Nie and K. K. Ma, Adaptive rood pattern search for fast block-matching motion estimation, IEEE Trans. Image Processing, vol. 11, no. 12, pp. 1442-1449, Dec. 2002.

[21] C. Zhu, W. Qi, and W. Ser, Predictive fine granularity successive elimination for fast optimal block matching motion estimation, IEEE Trans. Image Processing, vol. 14, no. 2, pp. 213-221, Feb. 2005. [22] C. Zhu and L. M. Po, Minimax partial distortion competitive learning for optimal codebook design,

IEEE Trans. Image Processing, vol. 7, no. 10, pp. 1400-1409, Oct. 1998.

[23] C. Zhu, A new subsampling-based predictive vector quantization for image coding, Proc. of Signal Processing: Image Communication (EURASIP), vol. 17, no. 6, pp. 477-484, July 2002.

[24] T. H. Chen, A cost-effective 3-step hierarchical search block-matching chip for motion estimation, IEEE Journal of Solid-State Circuits, vol. 33, no. 8, pp. 1253-1258, Aug. 1998.