Effective Video Compression with two Quantization Parameters

Journal of Broadcast Engineering.
2019.
Dec,
24(7):
1199-1208

This is an Open-Access article distributed under the terms of the Creative Commons BY-NC-ND (http://creativecommons.org/licenses/by-nc-nd/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited and not altered.

- Received : September 30, 2019
- Accepted : November 26, 2019
- Published : December 01, 2019

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In this paper, we propose the novel methodology to improve the rate-distortion characteristics by the difference of the quantized DCT coefficients using two different quantized parameters in HEVC. Under the special condition of the quantization property in HEVC, we evaluate the binary difference of the quantized DCT coefficients derived from two different quantized parameters and compressed it with simple CABAC algorithm based on the characteristics of the binary difference. The experimental result shows that the proposed algorithm improves the compression performance of the rate-distortion property in comparison to the conventional HEVC compression method.
X
∈
R
^{(n×n)}
, and a prediction image evaluated by a video codec is
where the subscript denotes a time index. Under this assumption, we set a residual image
such that
Therein, we define the DCT of the residual as following matrix form:
Herein, we set the quantization as the function of the quantization parameter
q
and DCT such that
where
q^{s}
∈R is a scale factor for the DCT coefficients as the function of quantization parameter,
N_{q}
∈R is the quantization error at
q
such as −1 <
N_{q}
≤ 0, and the symbol ⌷ is the round symbol such as [
x
]∈Z for all
x
∈R defined as follows[
6]
[7]
:
Since
N_{q}
≤ 0, for convenience, we introduce a positive quantization error
ε_{q}
= −
N_{q}
such that 0 ≤
ε_{q}
< 1. Subsequently, the quantization of the DCT coefficients is illustrated as follows:
Considering the inverse quantization, we can find a Quantization error occurred as the proportion to the scale factor or the quantization parameters from the following equation.
q
_{2}
and we set the other to be
q
_{1}
, the quantized DCT parameters can be denoted abbreviately as
and
.
According to the HEVC standard, the relation of the scale factor and the quantization parameter
q
is represented as follows
[1]
:
where mod is a modulo operation, and
k
is a proportional constant approximated to 0.17.
Generally, the quantization of DCT coefficients is defined such that
where
qbits
is the constant value which is equal to 14, as defined in the HEVC standard , is an additional 5-bit shift considering the coding of DCT and the bit depth, which is also defined in the HEVC.
From (7) and (8), we can obtain the following approximated equation:
where
f
is a round factor defined in the HEVC standard.
Therefore, by (9), when there exists a difference of 6 between two quantization parameters
q
_{1}
,
q
_{2}
, the scale of DCT coefficients is twice difference such as
However, practically, the DCT coefficients in video codec are integer values, so that there exists the quantization error represented in (3)(5). For
q
_{1}
<
q
_{2}
, and i.e.
q
_{2}
=
q
_{1}
+ 6 i.e.
, suppose that ||
Q
_{1}
|| ≥ ||
Q
_{2}
||. Considering the quantization error, we can evaluate the error model such that
Since −1 <
N_{q}
≤ 0, we can obtain
Thereby, since
ΔQ
_{q1,q2}
∈ Z, the difference
ΔQ
_{q1,q2}
is only equal to {0, 1} (in case of positive. for negative, it is equal to {−0, 1}).
On the other hand, for ||
Q
_{1}
|| ≤ 2 ||
Q
_{2}
||, as like (11), since the difference
ΔQ
_{q1,q2}
is equal to 1,
Consequently,
,so that
ΔQ
_{q1,q2}
∈ {0, −1}. The detailed proof is provided in the appendix, which is shown as theorem Ⅵ.1.
Encoder Structure for the proposed algorithm
In our implementation, we set the standard quantization parameter is larger than the other quantization parameter so that the main result of compression such as the CU(Computational Unit) and PU (Prediction Unit) size is optimized to the standard quantization parameter. Consequently, the proposed algorithm does not provide the same encoding results in comparison to the coding result only with the . Moreover, when the absolute distortion value with the standard quantization parameter is less than those of the other quantization parameter, we select the coding results of the standard quantization parameter such as the quantized DCT coefficients, CBF, and the quantization parameter itself. Finally, when there is not any compressed data such as all zero CBF, we select the reference quantization parameter which is derived from the quantization parameters in the neighbor CUs. As a result, the general rate-distortion property of the proposed algorithm follows that of the standard quantization parameter.
ΔQ
_{q1,q2}
is based on the DCT, the event of the
x
_{1}
(
k
) = 1 occurs more frequently as the
k
is small. Therefore, as the length of the code-word is relatively shorter, the probability of the event is similar to 0.5. Conversely, when those of the code-word is relatively longer, the probability approaches the 0.25. However, even though the length is relatively long, it is possible that there exists a lot of "1" in a unit code-word. Consequently, we set three probability models for the arithmetic coder. One is the simple model that the probability of "1" is initially 0.5, and it is updated by the number of "1" or "0" in a code-word as follows
[7]
[8]
:
, where
x_{y}
(
k
) ∈ {0, 1} is a random variable to represent the kth difference data in a TU(Transform Unit) of a unit CU(Computation Unit) for
yin
{0, 1}, and
Δ
is a positive integer value for the initial probability. Besides, it controls the rate of probability updating.
Another model is the complex model that the probability of "1" is defined as follows:
, where
E
(Σ
x_{y}
(
k
)) is the expectation sum for
y
in a unit code-word which is evaluated with the probability from the Theorem Ⅵ.1, and the
L
is the length of the code-word such as
. The other model is the complex model of which the probability is the same as that of the simple model.
To improve the coding efficiency and to avoid additional indication bits to the models, we set the criteria for the selection of the probability model to the arithmetic coding with analysis of the DCT/Q about the quantization parameter
q
_{2}
. When the length of the nonzero signal in the DCT/Q data for
q
_{2}
is less than 5, we employ the simple model for the binary arithmetic coder. When the length of the nonzero signal in the DCT/Q data for
q
_{2}
is less than 5, we employ the simple model for the binary arithmetic coder. On the other hand, when the length is longer than 5, and the number of the larger than 2 signal for is less than 6 in a 4 × 4 unit TU, we set the complex model for coding, otherwise, we select the complex model with the probability of the simple model.
E
Σ
x
_{0}
(
k
) is 12, and the
E
Σ
x
_{0}
(
k
) is 4, respectively. In addition, we set
Δ
to be 4 for the complex model.
Decoder Structure for the proposed algorithm
Moreover, we use a rate-distortion optimization for the coding of the difference. For some CU’s, by the effect of the rate-distortion optimization in DCT/Q for each quantization parameters, it is possible that the rate-distortion cost of the
q
_{2}
is less than that of the proposed algorithm. At those case, we select the result of DCT/Q for as the best result, instead of the proposed method.
The experiments are achieved under the all-Intra encoding configuration for 32 frames, and other encoding parameters, such as the size of CU or QuadTreeTU and others, are the same as the encoding parameters for the HEVC common test condition
[9]
with two modifications: AMP (Asymmetric Partition) is turned off and SAO(Sample Adaptive Offset) is selectively turned off. Since the proposed method employs two quantization parameters, we expect that the edge filtering between units would be more effective, if processing units are coded by different quantization parameters. However, to confirm the validity of the proposed method without such filtering effects, we skip the SAO and AMP.
As mentioned above, we apply the proposed algorithm only to the I-frames and a luminance component. The experimental results show that the improvement of BD-rate(Bjøntegaard delta bit rate) averagely about 1.2% when we use constant QP.
However, as shown in the
Table 1
, some experimental results with constant quantization parameters represent the large difference to bitrates between the proposed method and the anchor. Since those large differences of bitrate can distort the experimental results, we achieve another experiment with rate control appropriate to the bitrate of the proposed method. The
Table 2
shows that the improvement of BD-rate averagely about 0.0217% with similar bitrates.
Experimental Results to 4 HD1080P Test Contents with Constant QP
Experimental Results to 4 HD1080P Test Contents with Similar Bitrates
q
_{2}
=
q
_{1}
+ 6, i.e.
. When
Q
_{1}
is even,
ΔQ
_{q1,q2}
=
Q
_{1}
− 2
Q
_{2}
∈ {0, 1}, and
Q
_{1}
is odd,
ΔQ
_{q1,q2}
=
Q
_{1}
− 2
Q
_{2}
∈ {0, −1}.
Proof.
Let
X
=
q
_{1}
∙
k
+
m
where 0 ≤
m
<
q
_{1}
, then
Thereby,
For
q
_{2}
, by the same way, we can obtain
Let
k
= 2 ∙
k
+
n
. In (19), since
m
<
q
_{1}
,
, we can obtain
The equation (20) means that, if the
k
is odd number,
is
k
+ 1 in spite of which value the remainder
m
has.
•When
k
is odd value and
,
Therefore,
When
k
is odd value and
,
Therefore,
When
k
is even value and
,
Therefore,
When
k
is even value and
Therefore,
■
Theorem Ⅵ.2 The fundamental equation of quantization parameter is defined as the equation (7) and (8), the quanti- zation of DCT is approximated as follows:
Proof.
■
q^{s}
∈
R
to the quantized DCT coefficients as follows.
However, since the quantization step is a real value, we have to change it as an integer value in encoding and decoding processes. To make an integer quantization step, we use it an integer scale variable and rewrite the equation such that:
In the HEVC standard, the scale parameter, which is equal to 2
^{4}
, to the quantization, is added, and the value of inverse quantization is divided by 2
^{shift}
for the bit-depth of an input image and coding scale appropriate to the range of the DCT transformation. Moreover, since the division of 2
^{shift}
, it is necessary to add the term which integrase the inverse quantized value by round calculation. As a result, the final formulation of inverse quantization can be written such that:
※ This work was supported by Institute for Information and communications Technology Promotion(IITP) grant funded by the Korea government (MSIP) (2017-0-00072, Development of Audio/Video Coding and Light Field Media Fundamental Technologies for Ultra Realistic Tera-media).
Jinwuk Seok
- 1993. 2. : Dept. of Electrical and Control Engineering, Hong-Ik University (B.S.)
- 1995. 2. : Dept. of Electrical and Control Engineering, Hong-Ik University (M.S.)
- 1998. 8. : Dept. of Electrical Engineering, Hong-Ik University (Ph.D.)
- 2000 ~ Current : Principal Researcher, ETRI
- 2009 ~ Current : Adjunct Professor, UST
- Research interests : Video Processing/Coding. Machine Learning, Nonlinear Control
Seunghyun Cho
- 2003. 8. : Dept. of Electronic and Electrical Engineering, Kyungpook National University (B.S.)
- 2006. 2. : Dept. of Electronic and Electrical Engineering, KAIST (M.S.)
- 2015. 8. : Dept. of Electronic and Electrical Engineering, KAIST (Ph.D.)
- 2006. 6. ~ Current : Principal Researcher, ETRI
- Research interests : Video Processing/Coding, Computer Vision, Machine Learning, Digital Circuit Design
Jin Soo Choi
- 1990. 2. : Dept. of Electronic Engineering, Kyungpook National University (B.S.)
- 1992. 2. : Dept. of Electronic Engineering, Kyungpook National University (M.S.)
- 1996. 2. : Dept. of Electronic Engineering, Kyungpook National University (Ph..D.)
- 1996. 5. ~ Current : Principal Researcher, ETRI
- Research interests : Video Processing/Coding, UHDTV Broadcasting, 3DTV Broadcasting

Ⅰ. Introduction

The issue of the quantization for a DCT(Discrete Cosine Tangent) coefficients in a video codec has been a traditional and crucial problem in video compression. In the HEVC (High Efficient Video Codec), as the newest ITU-T standard of video compression, 6 binary signal flags are employed to compressed the DCT coefficients more effectively so as to solve the mentioned issue
[1]
. In spite of which all techniques for the issue of the quantization of the DCT coefficients in the video compression show improved performance, it is still important to reduce the number of bits in the DCT coefficients describing the video without serious degradation of quality
[2]
[3]
[4]
[5]
.
In the viewpoint of improving the coding efficiency in the context coding, we propose a novel coding technique about quantized DCT coefficients. In standard video codecs such as HEVC, for the purpose of obtaining the coding efficiency in DCT coefficients, it is necessary to code a difference between levels of quantized DCT coefficients described by several level flags. As similarly, we propose the coding methodology based on the properties of the quantization in HEVC using two different quantization parameters.
If an original video is compressed under a specific quantization parameter, we derive new quantized DCT coefficients with another quantization parameter and evaluate the difference between two quantized coefficients. When we select an appropriate quantization parameter with respect to the original quantization parameter, the difference of the quantized coefficients is generated to a binary form, which is easily coded by a compressing algorithm such as a simple CABAC(Context-Based Adaptive Binary Arithmetic Coding).
As a result, it is possible to improve video quality with fewer bits in comparison to a conventional compressing technique.
This paper is organized as follows. Section 2 discusses the fundamental property of the quantization parameters in HEVC. In Section 3, we present the methodology of the implementation based on our main idea. Section 4 provides the result of computer simulation. In Section 6, we conclude this paper.
Ⅱ. Fundamental Theory

- 1. Fundamental Property of quantization

Suppose that an input image is defined as
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- 2. Quantization Error and Estimation Model

As the equation (6) illustrates that, for improvement of video quality, we should use a smaller quantization parameter. However, since the smaller quantization parameter generates more bits in compression for the DCT coefficients, an efficient coding scheme for decreasing the bits to the DCT coefficients is required.
In the sense of which an efficient coding is an encoding of a difference data between a standard signal and the other data, we set the quantized DCT coefficients by a general quantization parameter as standard data. In addition, we set the other quantized DCT coefficients as comparative data, by another quantization parameter. When we set a standard quantization parameter as
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Ⅲ. Implementation of the proposed algorithm

- 1. Coding Structure

To provide two DCT coefficient sets under two different quantization parameter, we implement an operational function corresponding the DCT, quantization, inverse DCT and the inverse quantization. In addition, we make additional buffers for the reconstruction image, the CBF(Coded block flag) and the DCT coefficients. The concept schematic of encoder is shown in the
Fig 1
.
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- 2. Simple CABAC coding

As illustrated in the theorem Ⅵ.1, since the difference between the quantized DCT coefficients has three state value such as −1, 0, 1, we divided the difference set to make a binary difference space. The one space includes 0 and 1 data, and the other includes common 0 and −1 data. Consequently, it is possible to represent three state difference to be a two binary difference space, and we can employ an arithmetic binary coder to code the difference data on such spaces. In contrast to the other signals in the HEVC, the probability of which the value of data represents 0 or 1 is different from the other context models, so that we should set a simple model for arithmetic coding. Considering the distribution of the difference, since the difference
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Ⅳ. Experimental Results

We have implemented the proposed method using HEVC reference encoder HM 15. The test sequences used in the experiments are four HD1080P (1920x1080, 4:2:0, 8bit) videos of 32 frames. For the simple probability model of the asthmatic coding, the parameter is 1. For the complex model with simple probability, we set it as 12. In complex model, the
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Experimental Results to 4 HD1080P Test Contents with Constant QP

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Experimental Results to 4 HD1080P Test Contents with Similar Bitrates

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Ⅴ. Conclusion

We propose the novel quantization scheme for video compression using two quantization parameters in this paper. Using the property of the scale factor depending on the quantization parameter, we provide an effective coding methodology by generating a binary difference of two quantized DCT coefficients. Experimental results represent that the proposed algorithm improves the rate-distortion property in comparison to the conventional HEVC video compression. Even though we employ a simple CABAC compression arisen from the characteristics of the proposed algorithm to compress the binary difference, there exist more techniques to encode the DCT coefficients more effectively. For instance, we suppose some technique using appropriate conventional HEVC signals for encoding the DCT coefficients to decrease the context bits. Moreover, it is possible to optimize the rate-distortion in the coding of the binary difference using artificial intelligence. In addition, we will apply the proposed algorithm to Inter frames and we will extend it to obtain more efficient coding performance, through the conventional signals for DCT compression.
Ⅵ. Appendix

Herein, we provide the detailed theorem and the proof for the main analysis of the proposed method.
- 1. Propositions

Theorem Ⅵ.1 Let
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- 2. Mathematical Formulation of Inverse Quantization

The inverse quantization is basically formulated by multiplication of the quantization step
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Citing 'Effective Video Compression with two Quantization Parameters
'

@article{ BSGHC3_2019_v24n7_1199}
,title={Effective Video Compression with two Quantization Parameters}
,volume={7}
, url={http://dx.doi.org/10.5909/JBE.2019.24.7.1199}, DOI={10.5909/JBE.2019.24.7.1199}
, number= {7}
, journal={Journal of Broadcast Engineering}
, publisher={The Korean Institute of Broadcast and Media Engineers}
, author={Seok, Jinwuk
and
Cho, Seunghyun
and
Choi, Jin Soo}
, year={2019}
, month={Dec}