An efficient fractional-pixel motion compensation based on Cubic convolution interpolation

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1 Journl of Electricl nd Electronic Engineering 2014; 2(3): Published online September 20, 2014 ( doi: /j.jeee ISSN: (Print); ISSN: (Online) An efficient frctionl-pixel motion compenstion bsed on Cubic convolution interpoltion Lung-Jen Wng *, Chi-Tzu Shu Dept. of Computer Science nd Informtion Engineering, Ntionl Pingtung University, Pingtung, Tiwn, R. O. C. Emil ddress: (Lung-Jen Wng) To cite this rticle: Lung-Jen Wng, Chi-Tzu Shu. An Efficient Frctionl-Pixel Motion Compenstion Bsed on Cubic Convolution Interpoltion. Journl of Electricl nd Electronic Engineering. Vol. 2, No. 3, 2014, pp doi: /j.jeee Abstrct: The frctionl-pixel motion compenstion is used in the H.264/AVC lgorithm, in order to improve the coding efficiency of frctionl-pixel displcement, n efficient cubic convolution interpoltion (CCI) with four coefficients is proposed. In this pper, the detiled derivtion of the CCI filter nd using CCI with frctionl-pixel displcement re presented. It is shown by computer simultion tht the presented method substntilly reduces the computtion complexity nd lso increses the precision of the motion compenstion. Keywords: H.264/AVC, Motion Compenstion, Frctionl-Pixel Displcement, Cubic Convolution Interpoltion 1. Introduction A video cn be viewed s time-ordered sequence of imges-frmes [1]. In generl, the volume of uncompressed video dt is so lrge tht the use of video compression is lmost mndtory. In High Definition TV (HDTV), if uncompressed, the bitrte could esily exceed 1Gbps. Therefore, video compression llows the video to be trnsmitted over the Internet in rel time. Also it reduces the requirements for video storge. The H.264/AVC lgorithm is one of the ltest interntionl stndrd for the video compression technique, which ws jointly implemented by ITU-T video coding experts group (VCEG) nd ISO/IEC motion picture experts group (MPEG) [2][3]. In order to improve the precision for motion compenstion prediction in the H.264/ AVC lgorithm [4]-[8], the frctionl-pixel displcement is clculted, which is used the interpoltion process to estimte the frctionl-pixel (1/2- nd 1/4-) positions between the existing positions. In the H.264/ AVC stndrd, there re two processing steps in the frctionl-pixel displcement. First, fixed 6-tp Wiener filter is clculted for the 1/2-pixel displcement, nd then the biliner interpoltion is used for the 1/4-pixel displcement. The disdvntge of the H.264/ AVC stndrd is tht the computtions required for 1/2-pixel displcement with 6-tp Wiener filter re substntilly incresed. The 6-tp Wiener filter requires not only huge computtionl cost, but lso its ccurcy is not gurnteed in the frctionl-pixel displcement [7]. Interpoltion is the process of estimting the intermedite vlues of continuous event from discrete smples. It is used extensively in imge processing to mgnify or reduce imges nd to correct sptil distortions. Becuse of the mount of imge dt, n efficient interpoltion lgorithm is essentil. Rigorously speing, the process of decresing the dt rte is clled decimtion nd incresing the dt smples is termed interpoltion [9]-[11][16]-[18]. It is well nown tht severl decimtion nd interpoltion functions such s liner interpoltion [10], cubic convolution interpoltion [11], cubic B-spline interpoltion [16], liner spline interpoltion [17], cubic spline interpoltion [9][18], etc. cn be used in the imge processing. The uthors proposed cubic convolution interpoltion (CCI) with four coefficients in [12], in order to reduce the computtion complexity of the frctionl-pixel displcement in the H.264/AVC stndrd. This pper proposes more detiled descriptions for the CCI nd the frctionl-pixel motion compenstion prediction for the H.264/ AVC lgorithm. Tht is, the detiled derivtion of CCI nd combintion with motion compenstion re presented in this pper. Finlly, experimentl results show tht the proposed CCI method is used to speed up the 6-tp Wiener filter in the H.264/AVC stndrd nd still obtin superior performnce for motion compenstion. The primry dvntge of the CCI method is tht it increses the precisions nd lso substntilly reduces the computtion complexity for the frctionl-pixel displcement.

2 Journl of Electricl nd Electronic Engineering 2014; 2(3): This pper is orgnized s follows. Section 2 describes the bcground of this wor for the interpoltion function, H.264/AVC lgorithm nd interpoltion in frctionl-pixel displcement. Then the proposed CCI filter with four coefficients (4-tp CCI) is presented in Section 3. In this section, the cubic convolution function nd 4-tp CCI re discussed in detil. In Section 4, the proposed CCI combined with motion compenstion is illustrted for the H.264/AVC lgorithm. The motion compenstion with CCI nd the CCI interpoltion computtion re lso described in detil. Finlly, experimentl results nd conclusions re discussed in Sections 5 nd 6, respectively. 2. Bcground of this Wor 2.1. Interpoltion Functions An interpoltion function is specil type of pproximting function. A fundmentl property of interpoltion functions is tht they must coincide with the smpled dt t the interpoltion nodes, or smple points. In other words, if f is smpled function, nd if fˆ is the corresponding interpoltion function, then f ˆ( x ) = f( ) x whenever x is n interpoltion node [11]. Thus, n interpoltion function cn be expressed in the following form. N f ˆ ( x) = c R ( x x ) (1) = 1 where c = f x ) re the coefficients to be determined ( from the input dt, R (x) is the chosen interpoltion bsis function, x nd x represent continuous nd discrete vlue, respectively, nd N is the number of given dt points. There re severl interpoltion functions, shown in Fig. 1, such s liner function, cubic B-spline function, sinc function, nd cubic convolution function [10][11]. R 1 (x) () Liner function (two squres convolved) R 3 (x) (c) Sinc function x x R 2 (x) (b) Cubic B-spline function (two liner convolved) R 4 (x) (d) Cubic Convolution function Figure 1. Severl interpoltion functions. x x The liner function provides the first-order liner smple interpoltion with tringle-shped interpoltion wveforms. This liner function my be considered to be the result of convolving squre function with itself. It requires only one ddition nd one shift in ech interpoltion. The convolution of the liner function with itself yields cubic B-spline function. The cubic B-spline function is prticulrly ttrctive cndidte for imge interpoltion becuse of its properties of continuity nd smoothness t the smple points [10]. The sinc convolution function uses mny smple points for ech interpoltion point. It provides n exct reconstruction, but it cnnot be physiclly generted by n incoherent opticl filtering system [10]. It is possible to pproximte the sinc function by truncting its tils. Tht is to sy if we only consider the sinc function with four smple intervl. The problem is tht the slope discontinuity t the ends of the sinc wveform will led to mplitude ripples in reconstructed function. In order to eliminte mplitude ripples in reconstructed function, the cubic convolution interpoltion is developed to force the slope of the ends of interpoltion to be zero [11] The H.264/AVC Algorithm The H.264/AVC stndrd is the ltest lgorithm of video compression technique [2][3]. The bloc digrm of the H.264/AVC encoder is shown in Fig. 2. In this figure, the input video frme is prtitioned into some blocs. For ech bloc of input video frme, the H.264/AVC encoder pplies either intr-frme prediction or inter-frme prediction to process the video signl. In the intr-frme prediction, ech bloc is converted by the DCT trnsform into the DCT coefficients. Next the quntiztion (Q) nd the entropy coding (ENC) re used for the DCT coefficients. In the inter-frme prediction, which is lso clled s the motion compensted prediction or temporl prediction, the motion estimtion uses the current frme bloc from reference frmes to predict the content of the current frme bloc [15]. Furthermore, the de-quntiztion (Q -1 ) nd the inverse DCT (IDCT) trnsform re used to obtin the reconstructed video frme Interpoltion in Frctionl-Pixel Displcement In the H.264/AVC lgorithm, the displcement vectors with frctionl-pixel resolution re pplied to perform the motion compensted prediction. In order to estimte nd compenste the frctionl-pixel displcement, the two-step interpoltion process is used in [7]. In H.264/AVC, the bloc digrm of the two-step interpoltion process is shown in Fig. 3. In the first step, the smpling rte of imge I is incresed by fctor of 2 nd filtered by the 6-tp Wiener filter with the six coefficients: [1,-5, 20, 20, -5, 1]/32 is used to interpolte the w 1/2-pixel positions in this step nd n imge I is generted fter the first step. In the second step, the smpling rte of the w resulting imge I is lso incresed by fctor of 2 nd filtered by simple 2-tp biliner interpoltion filter with the

3 49 Lung-Jen Wng nd Chi-Tzu Shu: An Efficient Frctionl-Pixel Motion Compenstion Bsed on Cubic Convolution Interpoltion two coefficients: [1, 1]/2 is used to interpolte the 1/4-pixel positions nd n imge I is generted fter the second step. In Fig. 4, the interpoltion reltionship between the full-pixel positions (blc), the 1/2-pixel positions (gry) nd the 1/4-pixel positions (white) re shown. In this figure, t first, the 1/2-pixel positions, bb, b, q, cc, dd, nd ee, ff, h, l, gg, hh re clculted, using horizontl or verticl 6-tp Wiener filter, respectively. For exmple, = (A1-5A2 + 20A3 + 20A4-5A5 + A6) / 32, nd ee = (A1 5B1 + 20C1 + 20D1 5E1 + F1) / 32, respectively. Using the sme Wiener filter pplied t 1/2-pixel positions, bb, b, q, cc, nd dd, the 1/2-pixel position j is obtined s: j = ( 5bb + 20b + 20q 5cc + dd) / 32. In the second step, the remining 1/4-pixel positions re computed using the biliner interpoltion filter bsed on the clculted 1/2-pixel positions nd existing full-pixel positions [8]. For exmple, = (C3 + b) / 2 nd d = (C3 + h) / 2 in horizontl nd verticl interpoltions, respectively. 3. Cubic Convolution Interpoltion 3.1. The Cubic Convolution Function The cubic convolution function ws given in [11], which is composed of piecewise cubic polynomils defined on the subintervls (-2, -1), (-1, 0), (0, 1), nd (1, 2). Outside the intervl (-2, 2), the function is zero. The function ernel must be symmetric. As consequence of this condition, the cubic convolution function is defined by 3 2 A1 t + B1 t + C1t + D1 3 2 R ( t) = A2 t + B2 t + C2 t + D2 0, 0 t < 1,1 t < 2, 2 t where R ( 0) = 1, R( ± 1) = R( ± 2) = 0 nd R(t) nd R (t) re continuous t t = 0, 1, 2 nd R ( ± 2) = 0. In (2), A 1, B1, C1, D1, A2, B2, C2 nd D 2 re eight unnown coefficients. To solve these coefficients, Keys in [11] supposes A 2 =, then the remining seven unnown coefficients cn be determined in terms of. Tht is, the cubic-convolution function in (2) cn be expressed in terms of s (2) Figure 2. Bloc digrm of the H.264/AVC encoder. 3 2 ( + 2) t ( + 3) t R ( t) = t 5t + 8t 4 0, 0,1 t < 2, 2 t < 1 t (3) W I Figure 3. Two-step interpoltion process used in H.264/AVC. A1 A2 A3 A4 A5 A6 B1 B2 B3 bb B4 B5 B6 C1 C2 C3 b c C4 C5 C6 Figure 5. The CCI function. d e f g ee ff h i j l gg hh m n o p Furthermore, Keys in [11] lso uses A 2 = = -1/2, finlly, the cubic convolution function, shown in Fig. 5, is given by D1 D2 D3 q D4 D5 D6 E1 E2 E3 cc E4 E5 E6 F1 F2 F3 dd F4 F5 F6 3 2 ( 3/2 ) t ( 5/ 2 ) t + 1, 0 t < R(t) = ( 1/ 2 ) t + ( 5/ 2 ) t 4 t + 2, 1 t < 2 0, 2 t For more detils on this discussion, see Keys [11]. (4) Figure 4. Interpoltion reltionship.

4 Journl of Electricl nd Electronic Engineering 2014; 2(3): Tp Cubic Convolution Interpoltion Let τ be fixed, positive integer. Also, let X (t) be the full-pixel smples in the current frme, where 0 t n 1, nd X0,, X n 1 be the n existing full-pixel smples in the reference frme. The shift function of the cubic convolution function cn be defined s ( t) = R( t τ) for 0 n 1. Then the frctionl-pixel displcement X ˆ( t ) in the reference frme by the cubic convolution interpoltion (CCI) s n 1 = 0 n 1 Xˆ ( t) = X R ( t) = X R( t τ ) (5) = 0 where R (t) is the cubic convolution function in (4). The frctionl-pixel function X ˆ( t ) in (5) is the CCI function of the full-pixel smples X0,, X n 1 in the reference frme. One cn be find the function X ˆ( t ) in (5) tht minimize the prediction error of X ˆ( t ) to X (t) is defined by n 1 t = 0 R e ( t) = X( t) Xˆ ( t) (6) Thus, the sequence of n frctionl-pixel vlues X ˆ( t ) in (5) cn be obtined by the CCI function nd used for the 1/2-pixel nd 1/4-pixel displcements, respectively, in the H.264/AVC motion compenstion. Furthermore, the frctionl-pixel displcement X ˆ( t ) between the two djcent existing full-pixel smples X nd X + 1 in the reference frme is illustrted in Fig. 6 nd given by the sum of the CCI function, Xˆ( t R 1 ) = X + X R ( t 1 1 R ) + X ( t X ˆ( t ) R ( t ) for t < t R X X Xˆ ( t 1 ) X + 1 R +1 X +2 ) + X < t R + 1 ( t R +2 t 3 t 2 t 1 t t t + 1 t +2 t + 3 t + 4 t ) (7) In (7) nd Fig. 6, let t = t +1 t nd t = t t, then the displcement from t to t 1, t+ 1nd t + 2 re t t 1 = t + t, t t +1 = t t, nd t = t 2 t, respectively. t +2 Tble 1. List of CCI coefficients for frctionl-pixel displcement frctionl-pixel displcement CCI coefficients 1/2-pixel displcement [-1, 9, 9, -1]/16 1/4-pixel displcement [-9, 111, 29, -3]/128 3/4-pixel displcement [-3, 29, 111, -9]/128 In order to clculte the frctionl-pixel displcement, if we set t = 1 nd t =1/ 2, then the 1/2-pixel displcement cn be given by 1 X ˆ( t) = ( X 1 + 9X + 9X+ 1 X+ 2 ) (8) 16 Moreover, if we set t = 1nd t =1/ 4, then the 1/4-pixel displcement cn be given by 1 X ˆ( t) = ( 9X X + 29X+ 1 3X+ 2) (9) 128 Tht is, if we set t = 1nd displcement cn be given by t =3/ 4, then the 3/4-pixel 1 X ˆ( t) = ( 3X X + 111X + 1 9X+ 2) (10) 128 In (8)-(10), the CCI filter with four coefficients (4-tp CCI) for the frctionl-pixel (1/2-, 1/4- nd 3/4-) displcements re summrized in Tble Using CCI in Motion Compenstion 4.1. Motion Compenstion with CCI In the frctionl-pixel motion compenstion, there re two processing steps in the H.264/AVC lgorithm, shown in Fig. 3. In the first processing step, fixed 6-tp Wiener filter is used for the 1/2-pixel displcement. The second processing step is to use the biliner interpoltion for the 1/4-pixel displcement. In this pper, the CCI filter with four coefficients (4-tp CCI) is proposed to reduce the computtionl complexity of the Wiener filter with six coefficients in the 1/2-pixel displcement. In Fig. 7, the first interpoltion step is filtered by the 4-tp CCI process for the 1/2-pixel displcement, nd the second interpoltion step is then filtered by the 2-tp biliner process for the 1/4-pixel displcement. This is lso our proposed method nd lbeled s CCI+Biliner. In Fig. 8, two processing steps re ll filtered by the 4-tp CCI interpoltion for both 1/2- nd 1/4-pixel displcements. This method is lso lbeled s CCI. t Figure 6. The frctionl-pixel interpoltion between smples.

5 51 Lung-Jen Wng nd Chi-Tzu Shu: An Efficient Frctionl-Pixel Motion Compenstion Bsed on Cubic Convolution Interpoltion W I Figure 7. The proposed CCI+Biliner process. W I Figure 8. The CCI process The CCI Interpoltion Computtion B2 B3 bb B4 B5 C2 C3 b C4 C5 Stndrd), which Wiener filter nd biliner filter re used for the frctionl-pixel displcement. These three lgorithms re bsed on the JM 18.0 [13]. For the simultion common conditions of the H.264/AVC lgorithm, the most importnt settings re summrized in Tble 2. The objective performnce is mesured by the pe signl to noise rtio (PSNR) nd given by Y PSNR = 10 log 10 (db), MSE Y (11) where MSE Y is the men-squre error between the originl Y imge nd reconstructed Y imge for the YUV formt. Some stndrd QCIF (Bridge(close), Crew, HrBour, Highwy), CIF (Bridge(close), Bridge(fr), Foremn) nd 4CIF (City, Crew, HrBour) frme sequences re selected nd shown in Fig. 12. Performnce comprisons re crried out on the bove these frme sequences. All the experimentl results (bit rtes nd PSNR performnce) re computed from the reconstructed Y imges. B2 B3 bb B4 B5 ff h j l gg D2 D3 q D4 D5 C2 C3 b c C4 C5 ff h i j l gg E2 E3 cc E4 E5 Figure 9. 1/2-pixel CCI opertions: full-pixel positions (blc); 1/2-pixel positions (gry). In Fig. 9, the 4-tp CCI interpoltion is used to interpolte the 1/2-pixel positions nd the 1/2-pixel CCI opertions re illustrted: full-pixel positions (blc); 1/2-pixel positions (gry). For exmple, b = (-C2 + 9C3 + 9C4 - C5) / 16. In Figs. 10 nd 11, the 4-tp CCI interpoltion is lso pplied to interpolte the 1/4-pixel nd 3/4-pixel positions in horizontl nd verticl interpoltions, respectively. Fig. 10 shows the 1/4-pixel nd 3/4-pixel CCI opertions in horizontl interpoltions: full-pixel (blc); 1/2-pixel (gry); 1/4-pixel (white); 3/4-pixel (blue). For exmple, = (-9C C3 + 29C4 3C5) / 128, nd c = (-3C2 + 29C C4 9C5) / 128, respectively. In ddition, Fig. 11 shows the 1/4-pixel nd 3/4-pixel CCI opertions in verticl interpoltions: full-pixel (blc); 1/2-pixel (gry); 1/4-pixel (white); 3/4-pixel (blue). For exmple, d = (-9B C3 + 29D3 3E3) / 128, nd m = (-3B3 + 29C D3 9E3) / 128, respectively. D2 D3 q D4 D5 E2 E3 cc E4 E5 Figure 10. 1/4-pixel nd 3/4-pixel CCI opertions in horizontl interpoltion: full-pixel (blc); 1/2-pixel (gry); 1/4-pixel (white); 3/4-pixel (blue). B2 B3 bb B4 B5 C2 C3 b c C4 C5 ff d e f g h i j m n o p D2 D3 q D4 D5 l gg 5. Experimentl Results The proposed CCI+Biliner nd CCI methods, which re described in Section 4 nd shown in Figs. 7 nd 8, respectively, re implemented in Microsoft visul C++ progrm nd compred with the H.264/AVC stndrd method (lbeled s E2 E3 cc E4 E5 Figure 11. 1/4-pixel nd 3/4-pixel CCI opertions in verticl interpoltion: full-pixel (blc); 1/2-pixel (gry); 1/4-pixel (white); 3/4-pixel (blue).

6 Journl of Electricl nd Electronic Engineering 2014; 2(3): method by , nd for QCIF sequence, by , nd for CIF sequence, nd by , nd for 4CIF sequence, respectively. Thus, the proposed CCI+Biliner method chieves superior performnce in the frctionl-pixel displcement thn the H.264/AVC stndrd method. Tble 3. Number of opertions for three methods. Figure 12. Some stndrd video test sequences. Tble 2. Most importnt H.264/AVC coder settings [14] Prmeter Settings Profile: High Number of reference imges: 4 Number of B coded frmes: 2 Sequence type: I-B-B-P-B-B-P Hierrchicl Coding: off Weighted prediction: on Rte-distortion optimiztion: on Serch rnge: 32 for QCIF nd CIF 64 for 720p nd 1080p YUV formt 4:2:0 Quntiztion prmeter (I/P/B): 22/23/24, 27/28/29, 32/33/34, 37/38/39 For the computtionl complexity of the frctionl-pixel displcement in the Stndrd (H.264/AVC), CCI+Biliner nd CCI methods, the number of ddition(+), multipliction(*), nd shift(>>) re estimted nd compred in Tble 3 nd Tble 4. Obviously, in Tble 3, the estimted opertion number of the proposed CCI+Biliner method is less thn those of both Stndrd nd CCI methods. Tht is, the proposed CCI with biliner (CCI+Biliner) method is more fst nd efficient thn those of the H.264/AVC stndrd (Stndrd) nd the CCI methods. In other words, for the number of opertions, CCI+Biliner < Stndrd < CCI. In Tble 4, in terms of the number of ddition(+), multipliction(*) nd shift(>>) opertions, the CCI+Biliner method is less thn the H.264/AVC stndrd (Stndrd) Methods Opertions QCIF CIF 4CIF Stndrd (H.264/AVC) * >> CCI+Biliner * >> CCI * >> Some experimentl results of the rte-distortion curves for the Stndrd (H.264/AVC), CCI+Biner nd CCI methods re compred nd shown in Figs. 13, 14 nd 15. As shown in these three figures, the proposed CCI+Biliner nd CCI methods obtin the better PSNR vlues of reconstructed Y imge thn the Stndrd (H.264/AVC) method. Tht is, for the sme bit rtes, the PSNR vlues of the Y imges, obtined by the CCI+Biliner nd CCI methods re higher thn the Stndrd (H.264/AVC) method by 0.05 db nd 0.02 db for QCIF sequence, by 0.04 db nd 0.02 db for CIF sequence, nd by 0.14 db nd 0.06 db for 4CIF sequence, respectively. Tble 4. Comprison of opertions for Stndrd nd CCI+Biliner. Methods Opertions QCIF CIF 4CIF Stndrd (H.264/AVC) * >> CCI+Biliner * >> Stndrd minus * CCI+Biliner >> Figure 13. Rte-distortion comprison for QCIF sequence Bridge(close).

7 53 Lung-Jen Wng nd Chi-Tzu Shu: An Efficient Frctionl-Pixel Motion Compenstion Bsed on Cubic Convolution Interpoltion Figure 14. Rte-distortion comprison for CIF sequence Bridge(close). Figure 15. Rte-distortion comprison for 4CIF sequence HrBour. 6. Conclusions The H.264/AVC lgorithm is the interntionl stndrd for video compression. In the H.264/AVC stndrd, the frctionl-pixel displcement is used in the motion compensted prediction. There re two processing steps in the frctionl-pixel motion compenstion. In the first step, fixed 6-tp Wiener filter is used for the 1/2-pixel displcement. The second step is to use the biliner interpoltion for the 1/4-pixel displcement. In this pper, the 4-tp CCI filter is proposed to reduce the computtionl complexity of the 1/4-pixel displcement nd lso increse ccurtely the motion compensted prediction. In ddition, the derivtion of CCI filter nd CCI combined with motion compenstion re discussed in detil. Finlly, some computer simultions show tht the proposed CCI lgorithm with the biliner interpoltion cn be used to speed up the H.264/AVC stndrd nd lso obtins superior performnce for motion compenstion. Acnowledgements This wor ws supported by the Ntionl Science Council, R.O.C., under Grnt NSC E References [1] Z. N. Li nd M. S. Drew, Fundmentls of Multimedi. Person Prentice Hll, [2] T. Wiegnd, G. J. Sullivn, G. Bjontegrd, nd A. Luthr, Overview of the H.264/AVC video coding stndrd, IEEE Trns. on Circuits nd Systems for Video Technology, vol. 13, no. 7, pp , July [3] T. Wiegnd nd G. J. Sullivn, The H.264/AVC video coding stndrd [Stndrds in Nutshell], IEEE Signl Processing Mgzine, vol.24, no.2, pp , Mrch [4] T. Wedi, Adptive interpoltion filter for motion compensted hybrid video coding, in Proc. Picture Coding Symposium (PCS), Seoul, Kore, Jn [5] T. Wedi, Adptive interpoltion filter for motion compensted prediction, in Proc. IEEE Interntionl Conference on Imge Processing (ICIP), Rochester, NY, pp , Sept

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