Adaptive Rate Control in Object-Based Video Coding Using

Non-Cooperative Game Theory El-Sayed Youssif1, Mohamed E. Khedr2, Shawki Shabaan1, and Nour El Din El Madany2

1Electrical Engineering Department, College of Engineering Alexandria University, Alexandria, Egypt

2Electronics and Communications Engineering Arab Academy of Science and Technology, Alexandria, Egypt

Email: khedr@vt.edu. Email: nourelmadany@gmail.com

Abstract – This paper introduces a rate distortion scheme that adaptively allocates bits for objects in a video. This scheme allocates bits to objects using non-cooperative game theory. Every object is considered as a player in game where each player fights for the bits that best represent its contents. Simulations of the proposed scheme show promising results. These results show that our system has maintained the buffer at the half of its capacity with efficient bit allocation and accuracy of nearly 99.5 %. Index – non-cooperative, multiple video object, Game theory, Rate distortion model, adaptive bit allocation.

I. Introduction

Advanced digital video coding techniques (ADVCT) have been developed in recent years. This is due to the wide range of applications that require high bit rate as well as standardization of many communication systems (such as IEEE 802.11, IEEE 802.16, and IEEE 802.22). Whatever the video coding technique that is used or if the coding architecture is frame based or object based, there is a main block in the coder that is responsible for controlling the rate, which is the rate controller. The rate controller is a mechanism which is responsible for controlling video encoding in order to meet certain specific constrains such as complexity, delay, and visual quality. Due to the coding and compression techniques used in ADVCT ,video coders provide variable bit rates , but the underlying network and video quality of service require constant bit rate(CBR). In order to accommodate the variable bit rate of the video data a buffer is used. Therefore, there is a probability that the buffer may overflow or under-flow. So, in this situation the target of the rate controller is preventing the buffer from overflowing and under-flowing. In video coding, rate distortion can be used to model the output of the encoder as this encoder is a lossy encoder. The video source is modeled as Laplacian distribution [1]. So that, the Rate-Distortion model can be easily derived as (1) [1].

(1)

Fig.1 Rate – distortion function

Figure 1 shows the theoretical curve of the rate-distortion

function. As shown in the figure, increasing the distortion decreases the output rate. So, by choosing a suitable operating point on the R-D, the rate can be regulated. The main source of distortion in the encoder is the quantization process, which means that the higher the quantization level, the higher the video rate is and lower the distortion is.

The rate control techniques can be classified into two types: frame-based rate control and object-based rate control. The former is dedicated to encoders such as H.263 and MPEG-2. The later is dedicated to object-based rate control such as MPEG-4. H.263 Test Model Near-term version 5 TMN5 is one of earliest model. The allocation of target bits for the next frame is estimated using the complexity of the pervious frame. This model uses linear rate distortion model. In order to enhance the accuracy of the rate estimation several rate distortion models have been proposed. Chiang and Zhang have proposed a quadratic model that can be applied to DCT and Wavelet based encoders [1]. He and Mitra have proposed a model that is based on ρ, which is the percentage of zeros among quantization DCT coefficients [2]. H.263+ rate controller was based on the rate distortion model that was proposed by Ribas-Corbera and Lei [3]. There is also framing based rate controllers like the algorithm which was developed by Vetro and Sun [4].

This paper proposes an improved rate control algorithm that depends on Game theory. This algorithm allows multi-objective optimization among different decision makers (e.g.

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objects of each frame) under specific constrains (e.g. Bit budget).

The rest of paper is organized as follows. Section II presents the Game theory concept and system model. Section III describes the proposed approach for controlling rate of video encoder. Section IV presents the simulation and results of the suggested model. Finally Section V concludes the paper and presents the future work.

II. Game theory object-based video coding using game theory

Game theory was originated by Von Neumann. Von Neumann introduced the theory of min and max [5]. Several contributions have proposed by John Nash in cooperative and non-cooperative game theory [6]. Game theory is used in solving problems that contains competitions. It was widely used in economics [7]. Recently, game theory has been used in resource allocation in networks [8]. Game theory can be classified according to the interaction among the players into cooperative and non-cooperative. In the cooperative type, players try to maximize the overall gain and not the individual gain. On the other hand, non-cooperative type, each player maximizes its gain even on the expense on other players. In this paper non-cooperative game theory is deployed. In a non-cooperative game, decision makers are called players, who have conflicting interests. Those players are considered rational, which means that players want to maximize their utilities. In order to maximize their utilities the players change their strategy. The system consists of video encoder which is responsible for video encoding. There is also a buffer that has the main function of absorbing the variation in the video data rates. The rate controller is used to adjust the encoder output video rate in order to prevent the buffer from underflow and overflow. The overall system architecture is shown in Figure 2.

The rate controller should estimate the target bits for each video object plane (VOP) for specific frame in a specific time [2].

(2)

Where R is the bit budget, N is the number of video objects and is number of remaining VOPs. For maintaining the change in target bit budget smooth, the current frame target bits should be related to the pervious frame actual bits

. . (3)

Where is the actual bits used of the pervious object plane. The total number of bits for specific time instant is the sum of all estimated bits for all VOPs.

∑ (4)

Fig.2 Game theory based Video encoder

A buffer is placed after the video encoder to maintain the constant bit rate constant. To avoid the buffer from overflowing and under-flowing, the buffer fullness should be at 50 % of buffer size. A Proportional-Integral-Derivative (PID) is used to change the target bits according to the buffer level [9]. Figure 3 illustrates the controlling system that was used in changing target bits.

(5) ∑ (6)

Where is the buffer level, is the buffer size, is the proportional control parameters, is the integral control parameters and is differential control parameters. In this paper , and were taken to be 1, 0.01 and 0.5 respectively.

Fig.3 Target bits PID controller

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It should be noted that the target bits is bounded by [0.25 / , 2 / ], where is frame rate. This bound is to prevent the buffer from overflow and to maintain the video at an acceptable quality.

III. Proposed approach for controlling rate of

video encoder In multi object coding each object is encoded using a quantization parameter, the higher the quantization parameter, the less the number of bits. If the objects have the ability to choose the quantization parameter, the object will be considered as rational players. Each player, Video Object plane (VOP), takes a decision simultaneously without knowing the decision of the other players. So, this game is considered strategic game. Each player has strategy space of (1 to 31). This numbers are the quantization parameters of the MPEG-4.The utility function will be the number of bits for each object. , (7) , (8) , (9) , (10) Where and are the utility functions of VOP1 and VOP2 respectively. and are the rate of VOP1 and VOP2 respectively. and are the quantization parameters of the of VOP1 and VOP2 respectively. is the total number of bits that will be used of texture encoding of the objects. In this paper, the rate-quantization model that will be chosen is the quadratic model [1].

. . (11)

Where and are the model parameters for object are calculated using linear regression and is the quantization step value and it takes 31 values. This model is modified by choosing the pervious frames that minimize the error between the actual bits and R-Q model bits. So it can be modified to

. . (12)

Choosing quantization parameter will be based on Nash equilibrium strategy. The non-cooperative game theoretical based rate control pseudo code is as follows While (Total_number_of_bits< Bit_budget) For Qstep=1:31 Rate_of_object_1=Rate –Quantization model Rate_of_object_2=Rate –Quantization model

End Construct the utility matrix Find Nash equilibrium of the game

Total_number_of_bits =Total_number_of_bits + bit_ith_frame End

IV. Simulation Results

The proposed model is implemented using MATLAB. Four QCIF video sequences have been used in our experiments which are Claire, news, Mother and daughter, and container. The bit rates that have been used are 128, 256 and 384 Kbps.

Fig.4 buffer level of claire at 384 Kbps

Fig.5 PSNR for the 2 objects of "claire" at 384 Kbps.

Fig.6 Buffer level of "news" at 384.

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Fig.7 PSNR for the 2 objects of news at 384 Kbps.

Fig.8 buffer level "mother and daugther" at 384 Kbps.

Fig.9 PSNR for 2 objects of "mother and daugther" at 384 Kbps.

It can be noted from figure 4, figure 6, figure 8, and figure 10 that the rate controller based of the proposed game theory made the buffer level at 50 % of its buffer size which is the target of the rate controller with different sequences. The buffer level did not exceeding 80 % and is not below 20 %. So that, there will be no buffer over flow or under flow. It can also be noted from figure 5, figure 7, and figure 9 that the PSNR for VOP1 is less than VOP2. The reason of that is VOP2 contains more texture than VOP1. On the other hand figure 11 which represents PSNR of "Container" the PSNR of VOP1 is similar to VOP2 because VOP1 has nearly same texture as VOP2.

Table.1 shows the performance of the proposed system. It shows that the proposed system has high accuracy and high Average PSNR for each VOP.

Fig.10 buffer level "container" at 384 Kbps.

Fig.11 PSNR "container" at 384 Kbps.

Table.1 The performance of the proposed rate control algorithm.

Sequence Target

Bit Rate

Accuracy (Target –

Actual)/Actual

Average PSNR VOP1 (dB)

Average PSNR VOP2 (dB)

Claire 384 99.5% 42 45 256 99.4% 40.2 42.1 128 99.2% 39.5 41.2

News 384 99.6% 41.6 44.3 256 99.7% 40.1 43.3 128 99.65 38.4 40.2

Mother and

daugther

384 99.5% 43.1 47.2 256 99.7% 41.6 44.8 128 99.9% 40.2 42.8

Container 384 99.6% 47 48 256 99.3% 44.3 45.7 128 99.1% 42.6 43.3

V. Conclusion and Future Work

Rate control plays a great role in providing nearly constant bit rate for multi-object video coding over wireless communication networks. The work in this paper is limited to two objects and non cooperative game theory. To optimize the

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work in this paper several enhancements should be applied like cooperative game theory in rate control and applying this algorithm on more than two objects.

References

[1] T. Chiang, and Y. Q. Zhang, ‘‘A New Rate Control Scheme using Quadratic Rate Distortion Model,’’ IEEE Transactions on Circuits and Systems for Video Technology, vol. 7, no. 1, pp. 246-250, Feb. 1997.

[2] Z. He, Y. K. Kin, and S. K. Mitra, ‘‘Low-Delay Rate Control for DCT Video Coding via -domain Source Modeling,’’ IEEE Transactions on Circuits and Systems for Video Technology, vol. 11, no. 8, pp. 928-940, Aug. 2001.

[3] J. Ribas -Corbera and S. Lei, ‘‘Rate Control in DCT Video Coding for Low-Delay Communication,’’ IEEE Transactions on Circuit and System for Video Technology, vol. 9, no. 1, pp. 172-185, Feb. 1999.

[4] A. Vetro, H. Sun, and Y. Wang, “MPEG-4 Rate Control for Multiple Video Objects,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 9, no. 1, pp. 186-199, Feb. 1999.

[5] J. Von Neumann, and O. Morganstern, Theory of Games and Economic Behaviors. Princeton (Princeton University Press), 1944, 1947.

[6] J. Nash, “Non-Cooperative Games,” Annals of Mathematics, vol. 54, pp. 286-295, Sept. 1951.

[7] Montet and D. Serra, Game Theory and Economics, Palgrave, 2003.

[8] T. Roughgarden, “Stackelberg Scheduling Strategies,” in Proc. of ACM STOC, pp. 104-113, 1991.

[9] Sun Yu and Ishfaq Ahmad, “A New Rate Control Algorithm for MPEG-4Video Coding,” in Visual Communications and Image Processing, Proc. SPIE 4671, pp. 698-709, San Jose, CA. Jan. 2002.

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