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Relation Between Video Bitrate And Frame Size

In Arbitrary Downsizing Transcoding

HAIWEI SUN, YAPPENG TAN and YONGQING LIANG

School of Electrical & Electronic Engineering

Nanyang Technological University

Singapore

pg01533119@ntu.edu.sg

Abstract: - Video downsizing transcoding is a common technique for adapting the bitrate or spatial/temporal resolution of a compressed video to suit different transmission bandwidths or receiving devices. In arbitrary downsizing video transcoding [1], although the transcoder can adjust the size of a pre-coded video to meet the requirements of different transmission channels or receiving devices, there is however no model to illustrate the relation between bitrate and frame size. In this paper, we propose a new method to model the relation between bitrate and frame size under low bitrate condition. With this new method, we can re-estimate the bitrate according to required frame size or select a suitable frame size for a given target bitrate, while maintaining good video quality. Experimental results are presented to demonstrate the effectiveness of the proposed video transcoding methods.

Key-Words: - Arbitrary downsizing transcoding, bitrate, frame size

1 Introduction

Video transcoding is a common technique for adapting the bitrate or spatial/temporal resolution of a compressed video to suit different transmission bandwidths or receiving devices. By using arbitrary downsizing video transcoding technique [1] which can downsize a pre-coded video by an arbitrary factor, we have more choices in adjusting the spatial resolution of a pre-compressed video according to the available channel bandwidth. Given a target bitrate, however, it is not clear that which educed size can provide optimal video quality. Moreover, if users want to select the display size, the bitrate what is required for the size is also not clear. Thus, we focus on modelling the relation between the frame size of the transcoded video and its required bitrate. With the relation between bitrate and frame size, we can apply it into two applications as follows:

1) If the available channel bandwidth is insufficient, we can select a reduced frame size or the transcoded video to meet the available bandwidth.

2) If users want to change frame size during video transmission, we can estimate a suitable bitrate what is required to transcode the video.

In this paper, we focus on developing an efficient model to build the relation between video bitrate and frame sizes. In order to estimate the relation between bitrate and frame size, we want to build a model to estimate the required bitrate given a precoded video with its frame size and bitrate, while maintaining video quality or distortion from precoded video. To simplify the estimation of the relation, the same mean quantization parameter Q for all macroblocks is used in both precoded video and downsizing transcoded video. Since we care more for downsizing transcoding under low bitrate, we set Q as 32 and frame rate as 10 to stimulate low bitrate case in our experiments. Six standard test videos, ``Tempete", ``Foreman", ``Stefan", ``Mobile & Calendar (MC)", ``Mother & Daughter (MD)", and ``News" are used in our experiments.

2 Video Bitrate And Frame Size

The total number of bits allocated for a frame can be estimated by the total number of bits used to code motion vectors (RMV), frame residue (Rr), overhead (RH) as follows [3].

[pic] (1)

where parameter RH in our experiments is treated as bits allocated to express layer information, including bits allocated for picture layer, bits allocated for macroblock layer, bits allocated for block layer, etc [6]. To estimate the relation between bitrate and frame size, we consider RMV, Rr, RH separately.

2.1 Bitrate For Motion Vector

Considering the relation between bitrate for motion vector and frame size, we notice that papers [3,4,5] present methods to estimate motion vector rate, or bits/pixel for motion vector as follows:

[pic] (2)

where parameters [pic] and [pic] are the average variance and average correlation coefficient of motion vectors for one frame. Parameter [pic] is the accuracy of motion vectors. Parameter B is the size of motion compensated block for frame residue. So the total number of bits for motion vectors RMV within a frame can be expressed as the total number of pixels times the motion vector rate. Thus, we obtain an expression for RMV as:

[pic] (3)

where parameter S is the total number of macroblocks in a frame. Parameter A is the total number of pixels in a macroblock (i.e., A=162). Thus, S×A stands for the total number of pixels in one frame. Moreover, after a further analysis, we ignore the second part on the right of the equation (2) and simplify the expression for RMV. The reason is illustrated as below. As for the first part on the right of the equation (2), if we fix B as 8 for the size of block, [pic] as 0.5 for half pixel resolution, we obtain a approximation of the first part:

[pic] (4)

while the second part in (2):

[pic] (5)

where [pic]is set as 0.998 [3]. We calculate the value of [pic] by measuring the variance for the x and y components of the block (8×8 pixels) motion vectors and average the two variance [3]. If the value of 0.002[pic]in (5) is comparable with 947 in (4), we should not ignore the second part. However, parameter [pic] is not large enough. For example, we calculate the the value of [pic] from ``Foreman". The results from different frame size are:

|frame size |variance |

|336×272 |35.1 |

|304×240 |31.7 |

|256×208 |25.7 |

|224×176 |21.3 |

|176×144 |15.2 |

|128×96 |7.9 |

Table 1. Variance for motion vector in "Foreman"

Table 1 show that the variance is no more than 40 in ``Foreman". So the value of 0.002[pic] is less than 0.08 which is far less than 947. Moreover, video ``Foreman" includes a lot of motions compared to other videos. In other word, the variance of motion vectors from other videos should not be much larger than ``Foreman". Thus, we ignored the second part compared with the first part in (2). We simplify Equation (2) to (6) by using the same block size B and

resolution [pic]:

[pic] (6)

From (6), we obtain the total number of bits for motion vectors in a frame in the precoded video:

[pic] (7)

where, parameter Spre is the total number of macroblocks in a frame in the precoded video.

Combining (6) and (7), we obtain an expression for the total number of bits allocated for motion vectors in a frame:

[pic] (8)

Assuming the the size of the precoded video is CIF, we compare the results estimated from Equation (8) with the results obtained from Fullsearch method. Results are shown as follows.

|frame size |bitrate from fullsearch for motion vector |

| |foreman |news |md |

|336×272 |5363.06 |1812.50 |2194.28 |

|304×240 |4419.66 |1399.90 |1666.84 |

|256×208 |3326.04 |1048.16 |1191.12 |

|224×176 |2510.74 |737.04 |860.26 |

|176×144 |1629.34 |482.12 |508.34 |

|128×96 |761.74 |224.78 |222.48 |

Table2. Bitrate from fullsearch for motion vector

The difference of the results for motion vectors is as follows.

|frame size |bitrate from (8) for motion vector |

| |foreman |news |md |

|336×272 |35.48 |49.97 |-24.02 |

|304×240 |166.55 |-7.17 |-104.08 |

|256×208 |222.02 |21.25 |-101.34 |

|224×176 |212.57 |-23.27 |-96.66 |

|176×144 |151.95 |-6.65 |-106.82 |

|128×96 |45.43 |-12.20 |-75.78 |

Table3. Difference between bitrate from fullsearch and bitrate from (8) for motion vector

From Table 3, we find all values of absolute difference is less than 300 bits for motion vector in a frame. So the overall difference can be acceptable. Thus, we apply (8) to estimate bits for coding the motion vectors.

2.2 Bitrate For Frame Residue

With the assumption that DCT coefficients of frame residue are approximately uncorrelated and are Laplacian distributed [7], papers [3,4] present an expression of frame residue rate, or bits/pixel for frame residue:

[pic] (9)

So the total number of bits for frame residue (Rr ) within a frame can be expressed as the total number of pixels times the frame residue rate. We select H2(Q) for low bitrate case [5]. We obtain an expression for Rr:

[pic] (10)

where parameter [pic] is the average variance for a frame in the transcoded video. Parameter S is the total number of macroblocks within a frame in the transcoded video. Parameter A is the total number of pixels in a macroblock. However, Equation (9) is obtained before Zig-Zag scan and run length coding. This will make the estimation for frame residue rate higher when (10) is used to estimate the total number of bits for frame residue in a frame. So we revise Equation (10), by keeping [pic]in (10) as a relative part for frame residue rate, to:

[pic] (11)

From (11), we obtain the total number of bits for frame residue in a frame in the precoded video:

[pic] (12)

where, parameter Spre is the total number of macroblocks within a frame in the precoded video. Parameter [pic] is the average variance within a frame in the precoded video. Combining (11) and (12), we obtain an expression for the total number of bits allocated for frame residue in a frame as follows:

[pic] (13)

Assuming the the size of the precoded video is CIF, we compare the results estimated from Equation (13) with the results obtained from Fullsearch method. Results are shown as follows.

|frame size |bitrate from fullsearch for motion vector |

| |foreman |news |md |

|336×272 |2968.08 |2564.42 |1272.46 |

|304×240 |2635.40 |2283.50 |1130.24 |

|256×208 |2329.08 |1953.94 |966.74 |

|224×176 |1992.24 |1580.26 |810.08 |

|176×144 |1480.10 |1048.04 |561.20 |

|128×96 |965.48 |542.64 |307.76 |

Table4. Bitrate from fullsearch for frame residue

The difference of the results for frame residue is as follows.

|frame size |bitrate from (8) for motion vector |

| |foreman |news |md |

|336×272 |-17.60 |27.45 |97.98 |

|304×240 |58.08 |148.05 |200.27 |

|256×208 |41.71 |212.56 |287.92 |

|224×176 |-7.98 |275.79 |291.31 |

|176×144 |-43.32 |221.11 |195.27 |

|128×96 |-86.75 |135.02 |113.49 |

Table5. Difference between bitrate from fullsearch and bitrate from (13) for frame residue

From Table 5, the absolute difference for most value (90%) is less than 300 bits for frame residue in a frame. The overall difference can be acceptable. Thus, we apply Equation (13) to estimate bits coded for frame residue.

2.3 Bitrate For Overhead

Since most bits for overhead is allocated for macroblock and block layer [6], the total number of macroblocks in a frame will affect the overhead mostly. So we use the function of frame size (S) to build the model for the relation for overhead and frame size. To further simplify this model, we assume the average number of bits for overhead per macroblock (Rh) will not change much after downsizing. Then we set an expression of overhead in a frame:

[pic] (14)

From (14), we obtain the total number of bits for overhead within a frame in the precoded video:

[pic] (15)

where, parameter Spre is the total number of macroblocks within a frame in the precoded video. Parameter [pic] is the average number of bits for overhead within a frame in the precoded video. Combining (14) and (15), we obtain an expression

for the total number of bits allocated for overhead in a frame:

[pic] (16)

2.4 Bitrate And Frame Size

Combining (8), (13) and (16), we obtain the overall bitrate (R) model for the relation between video bitrate and frame size:

[pic] (17)

3 Experimental Results

Simple linear model by connecting precoded bitrate and zero bitrate is used to make a comparison with our proposed method (17). Here, the simple linear model is assumed to be the model of relation between bitrate and frame sizes before our investigation in this paper.

The bitrate (Rl) in the linear model can be expressed as follow.

[pic] (18)

Assuming the size of the precoded video is CIF, we compare the results estimated from Equation (17) with the results obtained from the simple linear model. Results are shown in Table 6,7 and Figure 1.

|number of |Overall bitrate from |

|MBs |fullsearch |

| |stefan |news |

|357 |24173.73 |6133.89 |

|285 |20414.17 |5122.62 |

|208 |16384.07 |4168.61 |

|154 |12993.10 |3209.82 |

|99 |8438.99 |2180.23 |

|48 |3939.30 |1130.09 |

Table6. Overall bitrate from fullsearch

|number of |proposed (17) |Linear (18) |

|MBs | | |

| |stefan |news |stefan |news |

|357 |202.05 |-72.57 |951.88 |95.50 |

|285 |314.18 |78.66 |-355.90 |-302.06 |

|208 |90.32 |19.31 |-1745.05 |-650.44 |

|154 |-204.51 |142.86 |-2154.60 |-605.02 |

|99 |-212.44 |51.04 |-1471.38 |-505.72 |

|48 |-66.20 |14.05 |-561.06 |-318.21 |

Table7. Difference between overall bitrate from fullsearch and bitrate from proposed method (17) and linear method (18)

From Table 7, we find the overall absolute difference from our proposed method (17) is smaller than the overall absolute difference from simple linear model (18) for a frame. In other word, using our proposed method will get a more accurate model to build the relation between bitrate and frame sizes.

Figure1. Overall bitrate from fullsearch, proposed method (17) and linear method (18)

4 Conclusion

We develop a model that can estimate the relationship between bitrate and video frame sizes in arbitrary downsizing transcoding. Using this model, we can choose a bitrate according to the frame size required by users or we can select a suitable frame size for a given bitrate, while maintaining a good video quality.

References:

[1] L. P. Chau, Y. Q. Liang, and Y. P. Tan, ``Motion Vector Re-Estimation for Fractional-Scale Video Transcoding'', International Conference on Information Technology: Coding and Computing, pp. 212-215, April 2001.

[2] G. Shen, B. Zeng, Y.-Q. Zhang and M.L. Liou, ``Transcoder with arbitrarily resizing capability'', IEEE International Symposium on Circuits and Systems, pp. 25-28, May 2001.

[3] Jordi Ribas-Corbera, and David L. Neuhoff, ``Optimizing Block Size in Motion-Compensated Video Coding'', Journal of Electronic Imaging, pp. 155-165, 2001.

[4] Jordi Ribas Corbera, and David L. Neuhoff, ``Optimal Bit Allocations for Lossless Video Codecs: Motion Vectors VS. Difference Frames'', International Conference on Image Processing, IEEE Proceedings, VOL. 3, 1995.

[5] Chia-Wen Lin and Te-Jen Liou, and Yung-Chang Chen, ``Dynamic Rate Control in Multipoint Video Transcoding'', International Sysmposium on Circuit and System, IEEE Proceedings, pp. II-17-II-20, 2000.

[6] ITU-Telecommunications Standardization Sector, ``Video Coding for Low Bit Rate Communication'', pp. 9-18, 1996.

[7] Jordi Ribas-Corbera, and Shawmin Lei, ``Rate Control in DCT Video Coding for Low-Delay Communcations'', IEEE Trans. on Circuits and Systems for Video Technology, VOL. 9, pp. 172-185, May 1999.

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