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ABSTRACT. In this paper, we propose a lifetime maximization method for battery- and flash-constrained blackbox surveillance node. (BSN) consisting of image ...
LIFETIME MAXIMIZATION OF VIDEO BLACKBOX SURVEILLANCE CAMERA Sangkwon Na†, Giwon Kim‡, and Chong-Min Kyung‡ †Magnachip Semiconductor, ‡ Korea Advanced Institute of Science and Technology [email protected], [email protected], [email protected] ABSTRACT In this paper, we propose a lifetime maximization method for battery- and flash-constrained blackbox surveillance node (BSN) consisting of image sensor, event detector, video encoder, flash memory and battery. Because it is not economically feasible to transfer all the recorded images to the base station due to the limited energy in BSN, the recorded images are stored in flash memory for offline event recognition. In BSN, balancing the usage of battery and flash memory is critical to prolong the lifetime, because the shortage of either battery charge or flash capacity could lead to a complete loss of events, or a significant loss of quality in the recorded image of events. The lifetime of BSN is determined by the remaining battery charge and flash memory space. In this work, we assume that the resources of BSN, i.e., battery and flash memory are refreshed every system maintenance period (SMP). The proposed method controls the bit-rate of encoded videos and sampling rate, i.e., resolution and frame rate, to prolong the BSN lifetime till the SMP. Experimental results show that the proposed method prolongs the BSN lifetime by up to 136.36% compared with an existing bit-rate allocation method which does not consider the resource usage balancing. 1. INTRODUCTION Recent progress of low-power video and non-volatile memory technology along with growing interest in safety has led to a growth in demand on the video blackbox surveillance camera which captures events of interest for offline interpretation. Moreover, as the cost of flash memory has been falling and the demand on prolonged operating time of BSN (blackbox surveillance node) is growing, flash memory is used in BSN for the disposal of gathered data due to lower energy consumption for flash writing than wireless transmission. The main function of BSN, which consists of sensor, event detector, video encoder, flash memory and battery, is to detect suspicious objects in its camera scope, and store the captured images with recognizable quality. Because BSN is This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MEST) (No.20100000823).

978-1-61284-350-6/11/$26.00 ©2011 IEEE

powered by battery and has limited flash capacity, it is crucial to balance between the usage of battery charge with that of flash storage in the operation of BSN. To avoid battery energy and flash memory being wasted for recording uncritical events, most BSNs operate in an event-driven manner where all functional blocks, except the event detector, are normally power-gated and only wake up when an event is detected by the event detector [1–4]. The video encoding complexity can be scaled by adjusting encoding parameters, i.e., frame size and type, number of reference frames, block partition size, motion search method, etc. [5]. Encoding configuration which gives low compression efficiency and, therefore, high bit-rate for encoded frames generally has low computational complexity [5] [6]. We can reduce the energy consumption of video encoding by increasing the bit-rate, which, however, increases the energy consumption for writing the encoded data into flash. Various methods for finding trade-off between the energy consumption of video encoding and flash writing have been proposed by finding the optimal video encoding configuration in terms of total energy consumption [7–11]. In addition, joint source-channel coding schemes [10] [11] were introduced to allocate bitrate of source and channel coding with the given bandwidth of wireless channel. In this paper, we present a method of finding the video encoding configuration to minimize the energy consumption of BSN and maximize the utilization of the flash memory under the given image quality requirement. In [14] [15], an energyoptimal bit-rate allocation was proposed without considering the lifetime of either battery or flash memory. In case of blackbox, no more events can be recorded and stored in flash memory full of encoded video stream even if the remaining battery charge is sufficient. Thus, the proposed method finds the optimal output bit-rate which is expected to simultaneously wear out battery and flash memory. In addition, we present a method of controlling a sampling rate such that BSN survives the system maintenance period (SMP) for replenishing the resources. The output quality of the proposed scheme is evaluated by using structural similarity (SSIM) [12]. This paper is organized as follows. Section 2 introduces a P-R-D model of video encoding. Section 3 explains the sampling rate. Section 4 presents the proposed solution. Section 5 reports experimental results.

2. POWER-RATE-DISTORTION (P-R-D) MODEL 2.1. Subjective Quality Assessment To evaluate the image/video quality, the approaches for objective image/video quality assessment such as peak signal to noise ratio (PSNR) and mean square error (MSE) which are based on the error sensitivity are widely used. However, the error sensitivity based methods do not accurately reflect the degradation of image/video quality since the large errors do not always lead to the large perceptual distortions [12]. Z. Wang et al. [12] proposed the new image/video quality metric based on the structural distortion measurement for an image/video quality assessment, namely structure similarity (SSIM). Let x = {xi |i = 1, 2, . . . , N } and y = {yi |i = 1, 2, . . . , N } be the original and the distorted image, respectively. In SSIM, the index of image/video quality is defined as followings [12]. Q=

¯ · y¯ 4σxy · x ,0 ≤ Q ≤ 1 (σx2 + σy2 ) · [(¯ x)2 + (¯ y )2 ]

(1)

where x ¯, y¯, σx2 , σy2 , and σxy are the estimated of the mean of x, the mean of y, the variance of x, the variance of y, and the covariance of x and y, respectively. When xi equals yi for i = 1, 2, . . . , N , Q has the best value, namely 1. In other words, the value of 1 − Q can be used to evaluate the distortion. 2.2. P-R-D Model of Video Encoding A power-rate-distortion model [9] was proposed integrating classical Laplacian-based rate-distortion model and the computational complexity model, which is represented as a function of the power consumption of the software-based video codec. This paper deals with the variation of achievable rate and/or distortion according to the power consumption based on the power model of the energy-aware hardware codec-based system using Cauchy-density-based ratedistortion model. An operational framework for power-ratedistortion (P-R-D) analysis is prepared based on [20] as follows. Based on the encoder power model obtained through the gate-level simulation of the target video encoder, we developed a power-distortion (P-D) model. Inputs of the modeling process are encoder power model, reference frame buffer (DRAM) power model, input video sequence, and target bitrate. The total power consumption of video encoding is given as the sum of the video encoding power and the reference frame buffer access power. Reference frame buffer storage power including refresh is assumed as negligible. Based on our P-D model and Cauchy-density-based ratedistortion model [13], we proposed the power-rate-distortion (P-R-D) model of the target video encoder [20] as follows. D = c0 (c1 e−c2 P + 1)R−γ

(2)

Table 1. Comparison of structural similarity (SSIM) [12] between full resolution and other sampling rates Mean SSIM between 4CIF@30fps Sequence ↔ CIF@30fps ↔ QCIF@15fps City 0.771 0.444 Crew 0.881 0.660 Harbour 0.839 0.371 Ice 0.930 0.832 Soccer 0.836 0.551 Average 0.859 0.593 where c0 , c1 and c2 are fitting parameters, γ is CauchyDensity parameter and P is the encoding power consumption normalized by its maximum value. R2 of the curve fitting was about 0.98 with c0 = 3.055, c1 = 5.086 and c2 = 11.15. 3. SAMPLING RATE In addition to bit-rate and distortion of the encoded video, the overall power and bit-rate can be controlled by changing the resolution and/or frame rate, i.e., sampling rate. In this work, we define sampling rate, ψ, as the combination of the image resolution (the product of the image width and height in pixels) and frame rate as follows; ψ = nw ∗ nh ∗ rf where nw and nh are the image width and height, respectively, and rf is the frame rate (frames per second, hereafter fps). We used four sampling rates, i.e., QCIF (176x144)@15 fps, CIF (352x288)@15 fps, CIF@30 fps, and 4CIF (704x576)@30 fps. Fitting parameters c0 , c1 and c2 in Eq. (2) are separately adjusted according to the given sampling rate. Lowering resolution and frame rate leads to reduced power consumption of the video encoder at the increase of the distortion. With limited resource (battery and flash), it is required to decide the sampling rate to maximize the BSN lifetime under the distortion requirement corresponding to the given sampling rate. In section 4.4, we discuss on how to determine the sampling rate according to the remaining battery charge and flash storage. To evaluate the subjective quality difference between sampling rates, we use structural similarity (SSIM). As shown in Table 1, SSIM between full resolution (4CIF@30fps) and other sampling rates can be used to assess the distortion caused by under-sampling, i.e., CIF@30fps, QCIF@15fps, etc. 4. PROPOSED LIFETIME MAXIMIZATION APPROACHES 4.1. Energy Model of Blackbox Surveillance Node BSN operates based on event-driven manner. When the sum of absolute difference between the pixel intensity of two consequence frames is bigger than the given threshold, the event detector activates BSN. After the event detector detects the

10

monitoring the remaining resources. The remaining lifetime of BSN at time i, fi , can be defined by

9

Energy (mJ)

8

Etot

7 6

fi =

Eenc

5 4 3 2

Eacc

1

Ropt

0 0.035

0.085

0.135 0.185 Bit-rate (bpp)

0.235

0.285

Fig. 1. Total energy consumption of BSN, Etot , (the sum of the video encoder, Eenc , and flash access energy, Eacc ) with respect to bit-rate for news sequence where Ropt denotes the optimal bit-rate in terms of the energy consumption of BSN. occurrence of an event, the video encoder compresses the number of bits representing captured frames and stores the coded bit-stream in flash memory. We used the proposed PR-D model for the video encoder and calculated the power consumption of flash memory using the parameters presented in [16]. Etot in Fig. 1, the sum of video encoding energy (Eenc ) and flash access energy (Eacc ), is given by ψ Etot = Eenc + Eacc = [Penc (R, D) + Pacc (R)] · tevent

(3)

ψ where Penc and Pacc are the power consumption of video encoding for the given sampling rate (ψ) and flash access, respectively; D is the distortion represented as 1-SSIM (structural similarity, Q); R is the bit-rate represented as bit per pixel; and tevent is the total event time duration. The power consumption of the video encoder can be derived from Eq. (2) as follows. ψ Penc (R, D)

1 = Pmax · ψ ln c2



ψ cψ 0 · c1 D · R γ − cψ 0



(4)

ψ ψ where cψ 0 , c1 and c2 are the fitting parameters for the given sampling rate ψ and Pmax denotes the maximum power consumption of video encoding. The power consumption of memory access is given by

Pacc (R) = eacc · ψ · R

(5)

where eacc denotes the energy consumption of the flash per writing a bit, modeled in [16]. Total energy consumption of BSN, i.e., the video encoder and flash memory, can be controlled by the bit-rate of the encoded video. As shown in Fig. 1, the energy consumption of the video encoder decreases as the bit-rate of the encoded output increases. On the other hand, the energy consumption of flash access is proportional to the bit-rate. Then, there is a trade-off point in terms of energy consumption, i.e., Ropt in Fig. 1. 4.2. Battery- and Flash-Constrained Optimization To maximize the lifetime of the resource-constrained BSN, it is necessary to utilize the given resources effectively while

min

κ∈{bat,f la}

giκ , for ∀i = 0, 1, . . .

(6)

where giκ is called the resource lifetime of the BSN at time i (Launch of BSN is assumed to occur at i = 0.) as defined by the exhaustion of resource κ, i.e., either battery (bat) or flash memory (f la). The battery lifetime is affected by the power consumption of BSN, and the flash lifetime is affected by the bit-rate of encoded video. As the lifetime of BSN is defined as the time to exhaustion of whichever of the two resources wears out first, it is important to evenly wear out both resources. For example, if the flash memory is filled with encoded bits while there is some remaining battery charge, the remaining lifetime is still zero. The BSN lifetime also depends on event characteristics such as the probability of events and statistics of the event time duration. The lifetime of the resource can be predicted as dividing the remaining capacity of the corresponding resource by the rate of the resource use. Because the power consumption of BSN and the amount of encoded bits per second can be expressed as a function of Ri , the bit-rate at time i, the battery lifetime, gibat and the flash lifetime, gif la at time i are defined by Ebat,i

gibat

=



gif la

=

Cf la,i ψi · Ri · π ˆi

ψi Penc (Ri , Di )



+ Pacc (Ri ) π ˆi



1 Etot

(7)

(8)

where Ebat,i and Cf la,i are the remaining battery energy and remaining flash capacity at time i, respectively; Ri and Di denote the bit-rate (represented as bit per pixel) and distortion at time i, respectively; π ˆi is the estimated duty cycle of BSN at time i based on prior event statistics. Duty cycle denotes the probability of events, i.e., the ratio of the event-recording time ψi of BSN to the total operation time. In Eq. (7), Penc denotes the power consumption of the video encoder at the current sampling rate, ψi . The battery lifetime, gibat , is an inverse function of total energy consumption of BSN, Etot . 4.3. Bit-Rate Control (BRC) for Balancing Lifetime Maximizing the BSN lifetime is achieved by balancing the lifetime of two resources, i.e., battery and flash memory. Fig. 2 shows the tendencies of two resource lifetimes, i.e., battery lifetime and flash lifetime according to the bit-rate. Because battery and flash lifetime have reverse relationship to the bit-rate, the BSN lifetime, which is defined as the minimum between them, is maximized at the bit-rate shown as Rbal . (If there are multiple intersection points between two tendency curves, one with the larger lifetime is simply chosen as Rbal .) The problem is formulated as follows     Ribal = arg min gibat − gif la  Ri

such that Di ≤ D∗ (ψi )

(9)

g ifla

1000 900

Flash lifetime WSC lifetime

800 Lifetime (ksec)

rate, i.e., 4CIF@30fps; fi is the remaining lifetime of BSN at time i; τi is the remaining time till the SMP at time i; μ(≥ 1) is the lifetime fitting ratio which determines the degree of the lifetime margin; and Ψ is the set of the sampling rate candidates. The lower the value of ψi , the longer fi . As shown in Table 1, however, the higher the value of ψi , the higher Q(ψf ull , ψi ). Thus, Eq. (12) finds the highest sampling rate, ψi , which makes BSN survive through the SMP.

Battery lifetime

g ibat

700 600 500 400 300 200 100

Rbal

0 0.035

Rmin

Rmax

0.085

0.135 Bit-rate (bpp)

0.185

Fig. 2. Lifetime curves of battery and flash memory (gibat and gif la ) with respect to bit-rate where solid lines denote the resource lifetimes and a dashed line denotes the BSN lifetime for news sequence where R´bal means the balanced bit-rate which is out of the feasible bit-rate range. where Ribal denotes the bit-rate where the battery lifetime and flash lifetime are balanced, and D∗ (ψi ) is the required distortion level for the given sampling rate, ψi . When Ribal lies outside the bit-rate range supported by the video encoder, it means that the BSN lifetime is dominated by one of the two resources. When Ribal is lower than Rmin , i.e., the lower bound of the feasible bit-rate in the video encoder, the flash memory determines the overall lifetime of BSN. In this case, Ribal is given by Ribal = Rmin

(10)

because the flash lifetime is monotonically decreasing. When the battery lifetime determines the BSN lifetime, i.e., Ribal is higher than Rmax (the upper bound of the feasible bit-rate in the video encoder), actual Ribal is determined to maximize the battery lifetime as follows Ribal = arg

max

Rmin ≤Ri ≤Rmax

This is because the gibat (∼ as shown in Fig. 1.)

1 Etot )

gibat .

(11)

is concave. (Etot is convex

4.4. Sampling Rate Control (SRC) for Maximizing Lifetime Even if the BSN lifetime is maximized by dynamically balancing the resources, the expected lifetime of BSN may be shorter than the system maintenance period (SMP). To make BSN survive through the SMP, we propose to control another feature of video, i.e., sampling rate. In other words, sampling rate (resolution * frame rate), is adaptively determined to prolong the lifetime of BSN till the SMP while the distortion caused by under sampling is minimized. The optimal sampling rate at time i, ψiopt , is given by ψi opt = arg



max

{ψi |ψi ∈Ψ}

   fi Q(ψf ull , ψi )  ≥ μ τi

(12)

where Q(a, b) is the value of SSIM between two video sequences with sampling rate a and b; ψf ull is the full sampling

5. EXPERIMENTAL RESULTS 5.1. Configuration We used the simulation environment and assumptions as follows: 1) event detector: OpenCV [17], 2) video encoder: our power-scalable H.264/AVC video encoder with baseline profile, 3) flash: NAND flash memory [16], 4) the system maintenance period: 120 days, 5) the initial battery charge: 3600 mWh and 6) the initial flash space: 100 Gbyte. We used three test sequences captured for the purpose of surveillance, namely, PetsD1C1, ThreePersons Circles and IndoorGTTest2 [18]. Eventually, we characterized these three sequences to obtain the event parameters used in our simulator. We generated the event trace from the characterized event parameters, and models the energy consumption of BSN. Our simulator takes an event from the event trace, calculates the total energy consumed to process the event, and updates the remaining battery and flash capacity. This process is repeated until any one of the two resources is exhausted. 5.2. Bit-rate and Sampling Rate Control Table 2 shows the comparison of the proposed BRC (bitrate control) and proposed BRC+SRC (sampling rate control) scheme VS. the joint source-channel coding (JSCC) [10], the battery-oriented rate allocation (BORA) without flash [11] and with flash [9] in terms of lifetime and remaining resource capacities. The JSCC scheme adaptively determines the bitrate of source and channel coding while minimizing the endto-end distortion. Each distortion caused by source and channel coding is modeled as SSIM [12]. The BORA scheme decides the bit-rate in terms of the energy consumption only considering the battery. In particular, the encoded data are transmitted immediately to the base station in case of the BORA scheme without flash [11]; the energy consumption of the wireless transmitter is modeled based on [19]. The distortion of the JSCC scheme is lower than the BORA scheme without flash. However, the energy consumption of the JSCC scheme is not optimized compared to other schemes because this scheme decides the bit-rate in terms of the end-to-end distortion. Because the energy consumption per bit disposal of wireless transmission is higher than that of flash writing, the BORA scheme with flash has a lifetime 46.81% longer than the BORA scheme without flash.

Table 2. Comparison of battery-oriented bit-rate allocation (BORA) without flash [11] and with flash [9], with the proposed BRC (bit-rate control) and BRC+SRC (sampling rate control) scheme in terms of the lifetime and the remaining resources when the system maintenance period (TSM P ) is 120 days, the initial battery charge is 3600 mWh, and the initial memory capacity is 100 Gbyte JSCC BORA BORA Proposed Proposed † [10] w/o flash † [11] w/ flash [9] (BRC) (BRC+SRC) hours (days) 1138 (47) 1331 (55) 1657 (69) 2195 (91) 3124 (130) Δ improvement VS. JSCC 17.02 % +46.81 % +93.62 % +176.60 % Lifetime Δ improvement VS. BORA w/ flash +25.45 % +65.45 % +136.36 % Remaining battery (%) 0.00 % 0.00 % 35.94 % 0.00 % 0.00 % Remaining flash (%) 0.000 % 0.000 % 0.001 % Distortion (≡ 1 − SSIM ) [12] 0.0828 0.1076 0.0778 0.0827 0.0978 †: the encoded data are transferred to the base station immediately. In case of the BORA scheme with flash, the bit-rate obtained from the optimization of the energy consumption of BSN belongs to the flash-bound region. It means that the flash memory dominates the BSN lifetime. Accordingly, the BORA scheme with flash achieves relatively short lifetime compared with the proposed BRC (bit-rate control) and BRC+SRC (sampling rate control) scheme, and 35.94% of battery charge remains when the flash memory is full. The BRC scheme achieved 93.62% and 65.45% increased lifetime compared with the JSCC scheme and the BORA scheme with flash, respectively, by evenly wearing out all the resources. On the other hand, BSN with the BRC+SRC scheme can survive through the SMP (system maintenance period) by adaptively changing the sampling rate. Eventually, the BRC+SRC scheme achieved 176.60% and 136.36% increased lifetime compared with the JSCC scheme and the BORA scheme with flash, respectively. Fig. 3 shows the expected lifetime (left y-axis) and the bit-rate (right y-axis) for PetsD1C1. In this work, the step of the bit-rate control is 0.01 bpp (bit per pixel). In case of the BORA scheme with flash in Fig. 3(a), the weighted mean bit-rate [9] obtained with training sequences which have the similar event characteristics is applied to the video encoder. Because the bit-rate in Fig. 3(a) is allocated just in terms of energy consumption, the flash lifetime determines the BSN lifetime in case of BORA with flash. As shown in Fig. 3(b) and (c), the result of BRC and BRC+SRC represented the bitrate is adaptively allocated due to lifetime balancing. In case of BRC+SRC scheme, the sampling rate changed on the 62nd day. Fig. 4 shows the expected lifetime (left y-axis) of the resources till the death of BSN, and the sampling rate index (right y-axis) for the BRC and BRC+SRC scheme for PetsD1C1. The initial sampling rate was set to 4CIF(704x576)@30 fps. In case of the BRC scheme, the expected lifetime of both resources is always shorter than the remaining time till the SMP as shown in Fig. 4(a). On the other hand, the BRC+SRC scheme started with the sampling rate as CIF(352x288)@30 fps by Eq. (12) at the first

decision point because the expected lifetime of BSN with 4CIF(704x576)@30 fps, fi , is shorter than the remaining time till the SMP, τi . On the 62nd day, the sampling rate was switched back to 4CIF@30 fps. As a result, BSN survived the SMP with the BRC+SRC scheme as shown in Fig. 4(b). 6. CONCLUSION In this paper, we proposed a lifetime maximization method for the battery- and flash-constrained blackbox surveillance node (BSN). We built P-R-D model of the video encoder based on Cauchy-density-based rate-distortion model. With an analytic formulation for energy-rate-distortion relationship in our BSN, the optimal operating point can be found such that the BSN lifetime is extended till the system maintenance period. Experimental results show that the proposed method prolongs the BSN lifetime by up to 136.36% on average compared to the existing battery-oriented bit-rate allocation (BORA) method which does not consider the flash lifetime [11]. The proposed scheme provides the dynamic scheduling of BSN to maximize its lifetime. 7. REFERENCES [1] M. Valera and S. Velastin, “Intelligent distributed surveillance systems: a review,” in IEE Proc. Vision, Image and Signal Processing, vol. 152, no. 2, Apr. 2005. [2] A. Talukder, et al., “Optimal sensor scheduling and power management in sensor networks,” in Proc. SPIE, 2005. [3] S. Hengstler, et al., “MeshEye: a hybrid-resolution smart camera mote for applications in distributed intelligent surveillance,” in Proc. IPSN, 2007. [4] W. Feng, et al., “Panoptes: scalable low-power video sensor networking technologies,” ACM TOMCCAP, vol. 1, no. 2, May 2005. [5] R. Vanam, et al., “Distortion-complexity optimization of the H.264/MPEG-4 AVC encoder using GBFOS algorithm,” in Proc. IEEE Data compression conference, 2007.

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Fig. 3. Comparison of (a) BORA (battery-oriented rate allocation) with flash [9] (b) proposed BRC (bit-rate control) and (c) proposed BRC+SRC (sampling rate control) in terms of the expected lifetime (left y-axis) and the bit-rate (right y-axis) for PetsD1C1 where the initial battery capacity is 3600 mWh and the initial flash capacity is 100 Gbyte. Sampling Rate

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Fig. 4. Comparison of (a) proposed BRC (bit-rate control) and (b) proposed BRC+SRC (sampling rate control) in terms of the expected lifetime, the remaining time till the SMP (left y-axis) and the sampling rate index (right y-axis, 3=4CIF@30fps, 2=CIF@30fps, 1=CIF@15fps, and 0=QCIF@15fps) for PetsD1C1 where the initial battery capacity is 3600 mWh and the initial flash capacity is 100 Gbyte. [6] Z. He, et al., “Power-rate-distortion analysis for wireless video communication under energy constraints,” IEEE TCSVT, vol. 15, no. 5, May 2005. [7] Q. Zhang, et al., “Power-minimized bit allocation for video communication over wireless channels,” IEEE TCSVT, vol. 12, no. 6, June 2002. [8] Y. Liang, et al., “Joint power and distortion control in video coding,” in Proc. SPIE, 2005. [9] Z. He, et al., “Energy minimization of portable video communication devices based on power-rate-distortion optimization,” IEEE TCSVT, vol. 18, no. 5, May 2008. [10] V. Vukadinovie and G. Karlsson, “Trade-Offs in Bit-Rate Allocation for Wireless Video Streaming,” IEEE TCSVT, vol. 11, no.6, Aug. 2009. [11] X. Lu, E. Erkip, Y. Wang and D. Goodman, “Power efficient multimedia communication over wireless channels,” IEEE Journal on Selected Areas in Communications, vol.21, no.10, pp. 1738- 1751, Dec. 2003. [12] Zhou Wang, Ligang Lu and A.C. Bovik, “Video quality assessment using structural distortion measurement,” in Proc. of IEEE ICIP, vol.3, no., pp. III-65- III-68 vol.3, 2002. [13] N. Kamaci, Y. Altunbasak, and R.M. Mersereau, “Frame bit allocation for the H.264/AVC video coder via Cauchy-densitybased rate and distortion models,” IEEE TCSVT, vol. 15, no.8, Aug. 2005.

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