PAPER Optimal Quantization Parameter Set for MPEG-4 Bit-Rate Control

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1 3338 PAPER Optimal Quantization Parameter Set for MPEG-4 Bit-Rate Control Dong-Wan SEO, Seong-Wook HAN, Yong-Goo KIM, and Yoonsik CHOE, Nonmembers SUMMARY In this paper, we propose an optimal bit rate control algorithm which is fully compatible with MPEG-4 or H The proposed algorithm is designed to identify the optimal quantizer set through Lagrangian optimization when used for optimal bit allocation. To find the optimal quantizer set, we make use of the Viterbi algorithm in order to solve the dependency between quantization parameters of each macroblock due to the unique characteristics of MPEG-4 or H We set the Lagrangian cost function as a cost function of the Viterbi algorithm. We implement the proposed algorithm in MPEG-4 coders and compare its performance to the VM8 and optimal bit rate control algorithm, using independent quantization parameters in the circumstance of a low bit rate. key words: rate control, MPEG-4, Viterbi algorithm, Lagrangian optimization 1. Introduction Video compression standards such as H.26x of ITU or MPEG of ISO basically use DCT, quantization for DCT coefficients, RLC (Run Length Coding) and VLC (Variable Length Coding). Bit rate control algorithms have to select quantization parameters suitable for each macroblock in order to minimize the coding distortion existing within target bit-rates since quantization parameters determine the total number of bits and the quality of the video. That is, the purpose of bit rate control algorithms is to seek the best quantization parameter set, which minimizes average distortion for a target average bit rate (or vice versa). Generally an optimal solution to the bit allocation problem is solved by studying the problem identifying quantizer set within a selected frame and the Lagrange multiplier (λ), which minimizes the Lagrangian cost function [1] [3]. The Lagrangian cost function consists of the total number of bits and distortion calculated by the quantizer for each macroblock. Past studies have focused on finding a solution by following two basic approaches. One is that the quantizer set of each macroblock is calculated by means of minimizing the Lagrangian cost function of a given bit-rate model and distortion model [2], [4], [5]. It is suitable for real-time applications because it uses the quantizer calculated by model and uses an additional approximation, but it is not optimal because the model is not equal to actual bit-rates or amounts Manuscript received November 17, Manuscript revised March 5, The authors are with the Department of Electrical and Electronics Engineering, Yonsei University, Seoul, , Korea. The authors are with multimedia laboratory, OnTimetek Co. Ltd., Seocho-dong, Seocho-gu, Seoul, , Korea. This work is partially supported by ITRC (Information Technology Research Center) in Korea. of distortion. The other approach is that the quantizer set of each macroblock is determined by using Lagrangian optimization [1], [3], [6] and Dynamic programming [6], [7]. In this approach, the total bit rate and total amounts of distortion for all combinations of quantizers in one frame are calculated and then the quantizer set of one frame is determined by means of minimizing the Lagrangian cost function. It is not suitable for real-time applications because it requires a coding process for all available quantizers, but it presents the optimal solution for bit rate control and provides the optimal R-D (Rate-Distortion) bound for the benchmark. In this paper, we propose an optimal bit rate control algorithm fully compatible with both MPEG-4 [8] and H.263+ [9] which codes the quantization parameter of a given macroblock as the difference of the previous macroblock s quantization parameter along with the current macroblock s quantization parameter. We find the optimal quantizer set by means of using a Lagrange optimization and solve the dependency problem of quantization parameters by using the Viterbi decoding algorithm. Section 2 introduces the optimal bit rate control method and the dependency problem concerning quantization parameters. In Sect. 3, we describe the Viterbi algorithm using a Lagrangian cost function to solve the optimal bit allocation problem and calculate the optimal quantizer set through this method. Section 4 presents experimental results that compare our algorithm with the optimal bit rate control algorithm by using an independent quantization parameter [4], the VM8 [1] which is one of the model-based bit rate control algorithm and the constant QP approach which gives generally minimum distortion. 2. Optimal Bit Allocation Problem The optimal bit allocation problem is described as the constrained problem of seeking the best quantizer set which minimizes the total distortion (D) subject to the constraint that the total number of bits must be equal to a given target bit rate (R T ). This problem can be converted into an equivalent unconstrained problem by merging rate and distortion through the Lagrange multiplier (λ) [4]. The unconstrained problem is defined as: Q 1, Q 2,, Q N = arg min Q 1,Q 2,,Q N (D i (Q i ) + λr i (Q i )) (1)

2 SEO et al.: OPTIMAL QUANTIZATION PARAMETER SET FOR MPEG-4 BIT-RATE CONTROL 3339 where Q i is the optimal quantizer of i-th macroblock, Q i is the quantizer of i-th macroblock, N is total number of macroblock, λ is the Lagrangian multiplier of the positive value, and D i (Q i )andr i (Q i ) is distortion and rate of i-th macroblock using the quantizer Q i. If the quantization parameter of a given macroblock is independent like in MPEG-2 coding method, to minimize total cost function is equal to minimizing each cost function of a given macroblock as presented in Eq. (2). Then the optimization problem as shown in Eq. (1) is solved by using the constant slope optimization [4], [5]. min {D i (Q i ) + λr i (Q i )} = min {D i (Q i ) + λr i (Q i )} (2) In the constant slope optimization, the constant slope value λ is set as a value used to minimize the total Lagrangian cost function. The optimal quantizer of each macroblock is a value set to minimize the Lagrangian cost function of each macroblock with the constant slope value λ. This algorithm is not suitable for the MPEG-4 or H.263+ coding standards which quantization parameters are not independent. The quantization parameter of MPEG-4 or H.263+ coding standards is coded as the difference value of the Dquant (2 bits) between the quantization parameter of the previous macroblock and that of the current macroblock. Dquant { 2, 1, 0, 1, 2} (3) The unconstrained problem as presented in Eq. (2) is converted as shown in Eq. (4) designed to be suitable for determining the Dquant. Q 1, DQ 2,, DQ N = arg min (D i (Q i ) + λr i (Q i )) (4) Q 1,DQ 2,,DQ N Q i = Q i 1 + DQ i (5) Instead of finding each quantization parameter (Mquant) that minimizes the Lagrangian cost function, we find the optimal quantizer set by identifying the quantization parameter of the first macroblock as well as the Dquant for each maroblock. In fact, the Mquant method chooses the optimal quatizer set. In the Mquant method, 5 bits are allocated for use in the quantization parameter while in Dquant method, if Dquant = 0 it allocates 0 bits and otherwise it allocates 2 bits for the quantization parameter. The bits derivedbythedifference in coding quantization parameters elevates coding efficiency as we can see in the experimental results explained in Sect. 4. To solve the dependency problem of a given quantization parameter presented in an unconstrained problem as Eq. (4), we employ the Viterbi algorithm and describe the method thoroughly in Sect Optimal Bit Rate Control by Using the Viterbi Algorithm We must calculate the optimal quantizer set in condition of the dependency problem of quantization parameter. After calculating an optimal Lagrange multiplier, we solve the dependency problem through the Viterbi algorithm which uses the Lagrangian cost function. We find the optimal quantizer set that minimizes the cumulative Lagrangian cost function by calculating from the first macroblock to the N-th macroblock. 3.1 Viterbi Algorithm with Lagrangian Cost Function The Lagrangian cost function is used as the cost function for the Viterbi algorithm. First, we find the optimal λ which minimizes the total Lagrangian cost function after calculating each macroblock s D i (Q i )andr i (Q i ) for all quantization parameters (1, 2,, 31). The Lagrangian cost function is calculated without regard to the macroblock coding mode (e.g. SKIP, INTRA, INTER) because we calculate the D i (Q i )andr i (Q i ) after encoding i-th macroblock. Then the Lagrangian cost function is set by the optimal λ as presented in Eq. (6). The expression J i (Q i ) is the Lagragian cost function obtained when the i-th macroblock is quantized by Q i. J i (Q i ) = D i (Q i ) + λr i (Q i ) (6) The Lagrangian cost function is calculated for all kinds of quantization parameters and then the cumulative Lagrangian cost function is calculated as shown in Fig. 1. In the first macroblock, the cumulative Lagrangian cost function is equal to the Lagrangian cost function of the first macroblock because the previous stage does not exist. Figure 1 describes the process that calculates the cumulative Lagrangian cost function when the quantization parameter of the i-th macroblock is equal to j. The optimal path to the quantization parameter j of the i-th macroblock is the quantization parameter of the (i 1)-th macroblock that has a minimum cumulative Lagrangian cost function of quantization parameter { j 2, j 1, j, j + 1, j + 2}. If i 1 ( j 1) Fig. 1 The cumulative Lagrangian cost function.

3 3340 Fig. 2 Viterbi algorithm with Lagrangian cost function. is minimum, then the cumulative Lagrangian cost function of i-th macroblock with quantization parameter j is represented by Eq. (7) and the node j of i-th macroblock has the node j 1of(i 1)-th macroblock as the previous node. i ( j) = i 1 ( j 1) + J i ( j) (7) After iterating the above process, the cumulative Lagrangian cost function at the N-th macroblock for all quantization parameters (1,2,,31) is calculated. The optimal quantizer set, satisfying the dependency of quantization parameter is the quantizer set that has the minimum cumulative Lagrangian cost function. Figure 2 describes the process that identifies the optimal quantizer set by using a Viterbi algorithm. If j + 2isthe quantization parameter that has minimum cumulative Lagrangian cost function of N-th macroblock, the node ( j + 2) of N-th macroblock has previous quantization parameter, which has the minimum (N 1)-th cumulative Lagrangian cost function. Therefore the optimal quantization parameter of the (N 1)-th macroblock is j + 1, that is, Q N = j + 2, Q N 1 = j + 1, Q N 2 = j 1, Q N 3 = j 2. We can choose the optimal quantizer set {Q 1, Q 2,, Q N } under the condition of Dquant by iterating this process from the N-th macroblock to the first macroblock. This is equal to quantifying {Q 1, DQ 2, DQ 3, DQ N }. Only this result is used to locate the optimal quantizer set for coded not Mquant (5 bits) but Dquant (2 bits). 3.2 Bit Rate Control by the Optimal Quantizer Set We describe the process to find the optimal quantizer set in an individual frame. The process is described by two operations. First, the flowchart of the optimal algorithm for a given operating slope λ will be detailed (). Second, the method to find the optimal value of λ is described (I). Step 1: Generate the rate and the distortion of all quantization parameter of all macroblocks in one frame Step 2: For the current λ, calculate the Lagrangian cost function J i ( j) Step 3: Calculate the cumulative Lagrangian cost function i ( j) Step 3.1: IfQP = j, findtheqp that has the minimum cumulative Lagrangian cost function calculated by the previous QP { j 2, j 1, j, j + 1, j + 2} Step 3.2: Update the cumulative Lagrangian cost function and save the QP of Step 3.1 Step 3.3: Ifi = N, move to Step 4, otherwisei = i + 1 and move to Step 3.1 Step 4: Find the optimal quantizer set that has minimum cumulative Lagrangian cost and i = N Step 4.1: SetQ N to the QP that has the minimum cumulative Lagrangian cost function and calculate i = i 1 Step 4.2: Set Q i to the QP saved while calculating i+1 ( j) Step 4.3: Ifi = 1, go to Step 4.4, otherwise set i = i 1 and move to Step 4.2 Step 4.4: Calculate the total distortion value as D(λ) = N D i(q i ) and the total rate value as R(λ) = N D i(q i ) The above process calculates the optimal quantization parameter set through the Viterbi algorithm and the Lagrangian optimization for a given constant slope λ and calculates the total distortion and rate. This process could be a subroutine called by I, described later in this section. The problem of picking the optimal slope value of λ for a given rate is solved through I. I calculates the optimal quantization parameter set for the bit allocation problem described in Sect. 2. I Step 1: Setλ to very small value and calculate the total distortion (D H )andrate(r H ) through Step 2 - Step 4 in Step 2: Setλ to very large value and calculate the total distortion (D L )andrate(r L ) through Step 2 - Step 4 in Step 3: Recalculate λ as λ = [D H D L ] / [R L R H ]If R(λ) > R T,thenD H = D(λ) andr H = R(λ). Otherwise, D L = D(λ)andR L = R(λ) calculated as Step 1. Until R(λ) = R T, iterate Step 3 Step 4: λ = λ calculate the optimal quantization parameter set through 4. Experiments and Results We implement our algorithm in MPEG-4 coders and compare its performance using R-D characteristics with the VM8, the Mquant method, and the constant QP approach. The VM8 is a model-based rate control algorithm. The Mquant method is a bit rate control incorporating the Lagrangian optimization with independent quantization parameters. The constant QP approach encodes all frames by one quantization parameter. Generally speaking, the constant QP approach gives minimum distortion and constant quality.

4 SEO et al.: OPTIMAL QUANTIZATION PARAMETER SET FOR MPEG-4 BIT-RATE CONTROL 3341 Fig. 3 R-D graph of optimal RC (Foreman.Qcif). Fig. 5 R-D graph of optimal RC (Carphone.Qcif). Fig. 4 R-D graph of optimal RC (Susie.Qcif). Fig. 6 R-D graph of optimal RC compared with constant QP (Foreman.Qcif). The proposed algorithm evaluated on the Foreman (360 frames), Susie (200 frames) and Carphone (200 frames) test sequences which are in the standard QCIF format. We encoded these sequences based on experimental conditions that the target frame rate was 10 and Intra update did not exist for various bitrates between kbps. We used QP = 5 for the first I frame, interceded the rest as P frames using rate control. In Figs. 3, 4, 5, we set the target rate of each frame as a constant value. In Fig. 6, we set the target rate of each frame as the actual rate generated by the constant QP approach in order to compare the other algorithms with the constant QP algorithm. Generally, we expect that the Mquant method has a more efficient quantizer set than the Dquant method. Since the Mquant method finds the optimal quantization parameter of each macroblock, which can have all kinds of quantization parameters and the Dquant method calculates the optimal quantization parameter of each macroblock, which exists under the dependency problem. The dependency problem means that the current macroblock s quantization parameter is coded as the difference ( 2 to +2 range) from the previous macroblock s. However, as we know from Figs. 3,4,5, the Dquant method has a more efficient performance maximally of 0.5 db and minimally of 0.2 db than the Mquant method. Since the Mquant method allo- cates 5 bits for its quantization parameter while the Dquant method allocates 2 bits or 0 bits and the residual bits is allocated to code the DCT-coefficients. For an example of the QCIF image size, the Dquant method saves a minimum of 297 bits (3 bits 99 blocks) and a maximum of 495 bits (5 bits 99 blocks), allocated to the quantization parameter than the Mquant method. In fact, the Dquant method saves 300 bits in one frame on average and the saved bits create the added coding efficiency. In the experimental results, the Dquant method improves coding efficiency more in a low bit rate application than in a high bit rate application. Table 1 shows actual rate and distortion (PSNR) for the target bit rate. As presented in Table 1, the actual bits of the Dquant method are more near to the target bits than that of the Mquant. In Fig. 6, we compared the proposed algorithm with constant QP approach. The Dquant method has the same picture quality as the constant QP approach, while the Mquant method can t catch up with the constant QP approach. The Dquant method provides an optimal rate control algorithm, fully compatible for the video coding standard of the MPEG-4 or H.263+ and an optimal R-D bound when used for the benchmark.

5 3342 Table 1 Performance of analysis of optimal RC (Foreman.Qcif). Mquant Dquant Target Actual PSNR Actual PSNR Gain Rate Rate Rate (kbps) (kbps) (db) (kbps) (db) Conclusions In this paper, we propose an optimal rate control algorithm fully compatible for use in the MPEG-4 or H.263+ coding standard. In this coding standard, the quantization parameter of each macroblock is coded as the Dquant which has a value in the range of 2 to +2. The proposed algorithm calculates the optimal quantizer set through the Viterbi algorithm with regard to the dependency of quantization parameters. It is not suitable for real-time applications because the process calculating the rate and distortion of all kinds of quantization parameters repeats the quantization and VLC. However, it provides optimal R-D bounds for the benchmark used in optimal rate control and which is used for off-line rate control. References [1] Y. Shoham and A. Gersho, Efficient bit allocation for an arbitrary set of quantizers, IEEE Trans. Acoust. Speech Signal Process., vol.36, no.9, pp , Sept [2] J. Ribas-Corbera and S. Lei, Rate control in DCT video coding for low-delay communication, IEEE Trans. Circuits Syst. Video Technol., vol.9, no.1, pp , Feb [3] K. Ramchandran and M. Vetterli, Best wavelet packet bases in a ratedistortion sense, IEEE Trans. Image Process., vol.2, no.2, pp , April [4] J. Ribas-Corbera and S. Lei, A frame-layer bit allocation for H.263+, IEEE Trans. Circuits Syst. Video Technol., vol.10, no.7, pp , Oct [5] L. Lin and A. Ortega, Bit-rate control using piecewise approximated rate-distortion characteristics, IEEE Trans. Circuits Syst. Video Technol., vol.8, no.4, pp , Aug [6] A. Ortega, K. Ramchandran, and M. Vetterli, Optimal trellis-based buffered compression and fast approximations, IEEE Trans. Image Process., vol.3, no.1, pp.26 40, Jan [7] K. Ramchandran, A. Ortega, and M. Vetterli, Bit allocation for dependent quantization with applications to multiresolution and MPEG video coders, IEEE Trans. Image Process., vol.3, no.5, pp , Sept [8] ISO/IEC, Information technology Coding of audio-visual objects Part 2: Visual, ISO/IEC , Dec [9] ITU-T, Video coding for low bit rate communication, Draft, ITU-T Recommendation H.263, Sept Dong-Wan Seo was born in Sunchon, Korea, on December 28, He received his B.S. degree in electrical engineering from the Yonsei University in He received M.S. degree in electrical and electronic engineering from the Yonsei University in He is working toward the Ph.D. degree in electrical and electronic engineering at the same university. His current research interests include multimedia communication system, transcoding technique, and bit-rate control. Seong-Wook Han received the B.S. and M.S. degrees from Yonsei University, Seoul, Korea, in 2000 and 2002, respectively. Until 2002 he worked as a Research Assistant in the Image Information laboratory at Yonsei University. He has been with ontimetek Co., Ltd, multimedia laboratory, Seoul, Korea, where he is a senior engineer, focusing on a realtime Encoding Server for VOD services and Digital Multimedia Broadcasting. His current research interests include multimedia signal processing and communication, image/video compression, and multimedia system engineering necessary to implement a functional. Yong-Goo Kim received the B.S. and M.S. degrees in electrical engineering from the Yonsei University, Seoul Korea in 1993 and 1995, respectively, and received the Ph.D. degree in electrical and computer engineering at the same university in Since 2001, He has been with ontimetek Co. Ltd, multimedia laboratory, Seoul, Korea, where he is a research director focusing on a 3rd generation multimedia service with the back-bone of CDMA 1X, EVCO and WCDMA. His current research interests include multimedia signal processing and communication for mobile environment. Yoonsik Choe received the B.S. degree in electrical engineering from the Yonsei. University, Seoul Korea in 1979, and the M.S.E.E. in systems engineering, M.S. and Ph.D. degrees all in electrical engineering from the Case Western Reserve University, Cleveland, OH, the Pennsylvania State University, University Park, PA and the Purdue University, West Lafayette, IN, in 1984, 1987, and 1990, respectively. From 1990 to 1993 he was a Principal Engineering at the industrial electronics research center in the Hyundai Electronics Industries, Co. Ltd. Since 1993 he has been with the Department of Electrical and Electronic Engineering at the Yonsei University, Seoul Korea, where he is Associate Professor. His research interests include video coding, video communication, statistical signal processing and digital image processing.