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THE METHOD OF EFFICIENT CODING OF COLOR IMAGES UNDER THE CONDITION OF PERMISSIBLE AND FORBIDDEN
VALUES OF COLOR GAMUT
DOI 10.24411/2072-8735-2018-10282
Anastasiya Y. Kudryashova,
Moscow Technical University of Communications and Informatics, Moscow, Russia, asykka@bk.ru
Keywords: binary code, effective coding, error-correcting coding, gamma-correction, RGB signal.
In modern communication systems, when transmitting a color image, the issues of ensuring the required transmission quality are highly relevant. In turn, intercompatible coding is an important factor in ensuring the necessary noise immunity of communication systems. When transmitting signals, several color models are used, for example, RGB or YCrCb. At the same time, an important role is played by the fact that the color gamut has several forbidden values that can be discarded when encoding the transmitted image. R, G and B channels use gamma correction, which is not optimal from the point of view of minimizing the number of quantization levels when visually observing an image, and on the other hand, these models do not have the same contrast, i.e. change, for example, color tone or saturation at a certain value will differ significantly depending on the choice of the initial values of the coordinates of the selected color. The paper proposes to optimize the choice of code combinations for color image transmission. An algorithm for estimating the efficiency of coding a color image is proposed, taking into account the derivation from acceptable values of chromaticity, the estimation algorithm takes into account indicators of risks or distortions when coding with a binary code, and also takes into account the types of errors that occur in a digital signal. This approach allows us to identify more and less efficient methods for coding a color image. It was found that, depending on the type of errors in the digital signal, different coding options provide significantly different distortions in the restored signal.
Для цитирования:
Кудряшова А.Ю. Метод адаптации психоакустической модели к вейвлетному пространству на основе матрицы шумов квантования // T-Comm: Телекоммуникации и транспорт. 2019. Том 13. №6. С. 65-70.
For citation:
Kudryashova A.Yu. (2019). A method of efficient coding of color images under the condition of permissible and forbidden values of color gamut. T-Comm, vol. 13, no.6, pр. 65-70.
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Introduction
An analogue factor to be taken into account when operating a video signal is the understanding that the video display accurately reproduces the brightness of each picture element. A cathodc ray tube (CRT) - based display is basically a nonlinear device, and as a result, the light output at the output is a non-linear dependence on the voltage applied to the display. This dependence is called the gamma device indicator. In order for this relationship to have a linear appearance, a correction factor must be introduced into the television system.
For this reason, the RGB signals in a video camera are gam ma-corrected using the inverse CRT function. Gamma-corrected signals are designated R, G and B. New LCD and plasma displays have recently become more common, so some may think that gamma correction will no longer be needed in the future. However, human vision also has a non-linear characteristic of the perception of light intensity, which is described by a power function with an exponent of approximately 1/3. To ensure the best image contrast and signal-to-noise ratio (S / N), the video signal is encoded using the same power function. This is called abstract coding.
Gamma correction
The gamma correction required for CRT-based displays is practically optimal for abstract correction. For this reason, in the framework of the use of methods with gamma correction, it is necessary to especially carefully evaluate systems that use correction factors.
Figures 1 and 2 show the gamma correction, presented as a power function with an exponent equal to 0.45, as defined by ITU-R BT.709, the main standard for high-definition digital video. This gamma correction is used in video cameras to eliminate non-linear distortions in CRT-based displays and to conduct abstract coding. Nonlinearities in CRT displays are described by a power function with an exponent that lies in the range from 2.2 to 2.6, for most CRTs it is about 2.5.
o OS I
Fig. 1. Gamma curvc on BT.709
The resulting gamma value for the entire system is approximately 1.2, which is almost ideal for typical viewing conditions. This characteristic introduces an approximate correction. On the human perception of the brightness of the image, which, in turn, reduces the number of bits that are required when converting a video signal into digital form for its transmission.
Converting an R'G'B 'signal to a luminance signal
and color difference signal
Red, green, and blue video components are characteristic of video signal capture devices, and they are almost always used by operators to control the video color. The RGB color rendering system, however, is not the most efficient, in terms of bandwidth, method of transmitting an image during video processing, because all three components must have the same bandwidth. Human vision is more sensitive to changes in brightness levels than to changes in color.
Therefore, we can improve bandwidth efficiency by allocating the full bandwidth of the luminance information and providing any part of the remaining available frequency band under the color difference information. Converting video components to luminance and color difference values reduces the amount of information transmitted. With one luminance channel (Y') with foil frequency band, which provides information about the brightness of the image and the signal fragment, two color difference channels (R* — Y' and B' — Y") can be almost twice the frequency band smaller than the luminance channel bandwidth, and yet still provide sufficient color information.
Some types of equipment, especially in the past, distributed RGB signals outside the camcorder (or camera control unit), while video signals were almost always converted or encoded to other formats for recording, interconnection or long-distance transmission, and then dccoded for display on the display. Another way of describing the primary colors - red, green, and blue — is to present it using the three-dimensional R'G'B 'color cube. As shown in Figure 3, all colors can be displayed inside the edges of the RGB color cube.
Blus
Magenta
Red
Gimh
o o j t
Fig. 2, Gamma curve on BT.709, CRT and systems
Fig. 3. Three-dimensional color cube RGB
In the development of color television systems, special attention was paid to the problem of compatibility with the black-and-white television receivers that existed at that time. The gam m a-corrected luminance signal, Y is created from the red, green, and biue channel signals received from a video camera in order to transmit to a black and white or color television receiver in the form of a monochrome image. Knowing the difference
¥
between a monochrome signal or a luminance channel signal, and signals from either of the two color channels, you can easily restore red, green and blue components for kinescope feed.
Since the sensitivity of human vision to green color is most relevant to the perception of brightness, most of the information of this color signal is used to obtain the brightness signal, and the remaining red and blue color difference signals can be transmitted in a narrower bandwidth.
The luminance signal and two coior difference signals contain all the information necessary to display any color from the entire color spectrum of the original image. The main set of three components (R\ G' and B') by a simple matrix transformation is transformed into a new set of three components (Y\ R' - Y\ B* - Y'). The color difference form of signal representation has two advantages compared to R'G'B \
First, a narrower bandwidth is required to transmit the necessary information: the color difference system needs only one broadband channel, because ihc fine details of the image are carried by the luminance signal. In the RTrB 'system, on the other hand, high bandwidth is required for all three channels. Secondly, the set of color difference components is less susceptible to distortion of the gain compared to the components of the R'G'B'.
A low level in any of the color difference channels can cause only minor changes in hue or color saturation. And a low level in any of the R'G'B 'components can lead to a noticeable distortion of the image color. The idea of converting R'G'B 'signals into one luminance signal and two color difference signals was very useful. Currently, such signals, with relatively minor changes, are the basis of all existing component video formats, as well as composite broadcasting standards around the world.
Among the professionals involved component video, component R'G'B 'signals are often called «G'B'R'», because most of the information carried by the luminance signal, consists from the green channel information. Therefore, there is some analogy between Y'P'bP'r and G'B'R' formats.
To simplify the processing of color difference signals in different systems, their values are first scaled so that they have the same dynamic range of ± 350 mV. Such an analog component signal is referred to as Y'P'bP'r. In the digital component system, an offset has been made to the color difference signals, allowing for the same processing ranges for the luminance signals Y and the color difference signals. Such a system is referred to as Y'C'bC'r.
/7 N \ y ii^vttÜ
/ ¡7
Black
Performing matrixing and scaling prevents possible damage to the Y'C'bC'r signals when they are converted back to RGB. As shown in Figure 4, only about 25% of all possible signal values in the Y'C'bC'r region are used to represent the full spectrum of colors in the RGB region. In this regard, when transferring signals to other formats, care must be taken to ensure that the dynamic range does not exceed the established limits during the conversion process.
Color spectrum - allowed and valid values.
The term «color gamut» is used to designate a range or palette of colors reproduced by a television system when the subject of the photograph is illuminated with a reference white (standard light source D65 for NTSC/PAL), The color gamut is. determined by the value of the chromaticity or ehromatieity coordinates of the ICE for this system. This range of colors with, variable saturation is reproduced on the video monitor screen with the values of red, green and blue signals or R'G'B' signals. When the values of the components are equal (i.e., R'= G' = B')_ the image becomes colorless to the extent necessary to display shades of gray on a properly adjusted video monitor. Otherwise, for nonzero saturation values, a color hue will appear. All reproducible colors in the palette are available with independent setting of the values of the signals R'G'B'.
Since the values of the R'G'B 'signals directly embody these colors, the term «color gamut» is often used to denote the range of colors represented by all combinations R'G'B' signals that lie within the allowed limits from 0 to 700 mV. R'G'B 'signals that go beyond this voltage range can create the desired color on this video monitor, but they are outside the permissible color gamut. They can be cut or compressed during post-processing of signals, which will lead to color distortion when displayed on another video monitor, but they arc out of the permissible color range. They can be cut or compressed during post-processing of signals, which will lead to color distortion when displayed on another video monitor.
The same happens in the R'G'B 'color space. Any signal that goes beyond the upper or lower bounds is unacceptable because the color falls out of the permissible color gamut. In addition, it is also unresolved, since one or more components exceed the allowed limits.
Allowed signals are those signals that do not violate the voltage limits of the signal set for a particular format, i.e.. allowed signals limits for this format. Similarly, a resolved signal in a color difference format, such as Y'C'bC'r, may be invalid in a format in which it represents a signal that goes beyond the permissible color gamut. Such an invalid signal will always generate an unresolved signal when converted to the R'G'B 'format.
A valid signal is a signal that is in the color gamut and remains allowed when converting to any other format. Valid signal will be always allowed, but the allowed signal is not necessarily valid. The latter most often happens with color-difference component signals, the levels of which not independent, unlike RGB systems.
Fig. 4. 3D color space Y'C'bC'r
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............1...LI...............if.............
0.5' Of-
OA
03- ■■
0.2
0.1
•0.1
Fig, 5. Allowed and allowable color difference signal (lop) converted to an allowed RGB signal (bottom)
as-
0-716-OS 4*
02 0.1 00
Figure fi shows the color di Iference signal (above), which has distortions in the brightness channel: in it, the relative gain is only y0% of the desired one. When this distorted signal is converted to the RGB format (below), the result is an unresolved signal: in it all three components tie below ¡he minimum acceptable level, signal. Since it distorted color difference signal cannot be converted to an allowed RGB signal, it is invalid. Note that other types of distortion contribute to the formation of unacceptable signals. Valid signals can be converted, encoded and entered into any part of the video system without causing amplitude problems.
If we consider two color image coding standards for digital transmission - ITU 523 / 59.94 and ITU 625/50, then the number Of samples in both standards lot* the luminance signal is 720. and the number of samples for color difference signals is 360 each. The number of bits per sample is the quantization levels from 1 to 254 are reserved for the video signal, die levels 0 and 255 arc reserved for synchronization.
Based on the above, we can assume that it is possible to choose the variant of encoding the image in such a way as not to take into account the forbidden values of the color gamut. To assess die quality of signal transmission, it is necessary to introduce some measures of error due to the effect of interference, if a signal value different from the transmitted value is accepted. Let us name these errors as risks, and for their display we introduce the matrix Ibrni of the record.
To quantify this, we introduce a risk matrix:
f *.
R =
•i J
rK-U\ \ rNA
ri2 >1.2
'Vu fir.a
r2-J
HA.) rSJ
r.
|uV
... fi
... r.
S.N
(1)
r. . is the magnitude of the errors (risks, losses), if instead Of the transmitted value of the signal Sj, the recipient accepts the value
os j
o?.. 0.6 0504 0J
OiJ-
0,1 01
■0,1
Fig. 6, Distorted color difference signal (top) and signal converted to RGB format (bottom)
Figures 5 and 6 show how a simple distortion of the gain in the color difference component signal can make the signal unacceptable, but it still remains resolved. Figure 5 shows the allowed and allowed color difference signal (top) converted to an allowed RGB signal (bottom).
However, we must understand that every risk must arise with some probability. For the convenience of reflecting the probabilities of occurrence of each risk, we introduce a matrix of probabilities. We take into account that the sum of the probabilities in each row of the matrix must he equal to one.
In general, the probability matrix will look like:
Pu Pi. I
J°.-V I.I
V Ph
Phi Pi.i
Ps 1.3
Phi Ps.J
P I.A-
Pl.N
Py I..V
f>m
(2)
in addition to the likelihood of distortion, it is necessary to take into account the probability of a symbol appearing in the transmission channel. To record these probabilities, we use the probability vector of the signal value appearing in the channel, in general, the vector looks like:
¥
n -
n
K
(3)
After the introduction of all coding characteristics, it is necessary to calculate the distortion risk factor and variance (considering thai) M(R) = K'.
M M
D(R)= M(R")-{M(R))~
(4)
(5)
It should be noted that ihcsc calculations must be carried out for all possible CO(ling options, their total number can be found by the formula:
N
= (2")!
(6)
n is the number of characters in the code pattern.
After calculating the risk coefficient and variance for all possible coding options, it can be concluded about the "best" coding method. To search for it. it is necessary to determine the coding method with the smallest distortion coefficient and the smallest variance value.
Conclusion
Thus. We were able to propose an algorithm for choosing the most "effective" version of the coding of a color image, taking into account the discarding of the "forbidden" v alues of the color gamut. The algorithm is based on the method of average risks. It takes into account the risk values when a transfer element is transferred to another one and itself, as well as the likelihood of these risks occurring.
References
I. Adzfiemov A. S. Code Distance Table and its Application. In proceedings of the IEEE Wave Electronics and its Application in Information and Telecommunication Systems (WECONFi, Si Petersburg, 2018. pp. 1-5.
2. Adzhemov A.S., Adzhemov S.A. On some features of binary code combinations. In proceedings of the IEEE International Scientific Conference Systems of Signals Generating and Processing in the Field of on Board Communications (ON BOARD), Moscow, 2019. pp. 1-7.
3, Actehemov A.S., Kudryashova A.Y. features of assessing the quality of signal transmission in various metric spaces. Fundamental problems of radio-electronic instrument-making. 2017. Vol. 17. No. 4. pp. 886-888. (in Russian)
Adzhemov A.S.. ICudryasliova A.Y, About features of evaluation of the quality of generation and signai processing at stage transformations in wiring and optical communication systems. In proceedings of the IEEE International Scientific Conference Systems of Signals Generating and Processing in the Field of on Board Communications (ON BOARD). Moscow, 20IS. pp. 1-4.
5. Adzhemov A.S., Kudryashova A.Y. Features rate estimation options binary codewords with the digitalizatien of the signal. In proceedings of the IEEE International Scientific Conference Systems of Signal Synchronisation, Generating and Processing in Telecommunications (SWCUROIMFO). Minsk, 2018, pp. 1-5.
6. Adzhemov A.S., Kudryashova A.Y. Li wilding an Algorithm for Estimating ihe Effective Coding of a Source when Converting Signals in Various Metric Spaces. In proceedings of the IEEE Wave Electronics and its Application in Information and Telecommunication Systems (WECONF). S.-Peters burg, 2018. pp. I -4.
7. Adzhemov A.S., Kudryashova A Y. On the peculiarities of the evaluation of the quality of signal conversion under successive transformations in various metric spaces, In proceedings of the XII International Industrial Scientific and Technical Conference Information Society Technologies, 2018. pp. 211-213. (in Russian)
8. Adzhemov A.S., Kudryashova A.Y. Features of estimating the pow er of a se) of choices for binary code combinations when digitizing a signal. Synchronisation systems, signal generation and processing. 2018. Vol, 9. No. t. pp. 5-8. (inRussian)
9. Kudryashova A.Y. Features of encoding evaluation in various source space configurations. DSP A: Issues of application of digital signal processing, 2018. Vol. 8. No. 3 pp. 228-232. {in Russian)
10. Adzhemov A.S., Kudryashova A.Y, features of estimating die power of multiple choiecs of binary code combinations. Fundamental problems of radio-electronic instrument-making. 2018, Vol. 18. No. 4, pp. 926-929. (in Russian)
11. Adzhemov A.S., Kudryashova A.Y. Evaluation program of an efficient source coding algorithm under the condition of converting metric spaces. In proceedings of the IEEE Wove Electronics and its Application in Information and Telecommunication Systems (WECONF). S, Petersburg, 2019. pp. 1-5.
12. Adzhemov A.S., Kudryashova A.Y., Viàsyuk I.V. Application of Weber-Fechner Law in Image Transmission in the Field of Onboard Communications. In proceedings of the IEEE International Scientific Conference Systems of Signals Generating and Processing in the Field of on Board Communications (ON BOARD), Moscow, ¿019, pp. 1-0.
T-Comm Vol.13. #6-2019
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МЕТОД ЭФФЕКТИВНОГО КОДИРОВАНИЯ ЦВЕТНЫХ ИЗОБРАЖЕНИЙ ПРИ УСЛОВИИ ДОПУСТИМЫХ И ЗАПРЕЩЕННЫХ ЗНАЧЕНИЙ ЦВЕТОВОЙ ГАММЫ
Кудряшова Анастасия Юрьевна,
Московский технический университет связи и информатики, Москва, Россия, asykka@bk.ru
Аннотация
В современных системах связи при передаче цветного изображения вопросы обеспечения требуемого качества передачи являются весьма актуальными. В свою очередь помхоустойчивое кодирование является важным фактором в обеспечении необходимой помехоустойчивости систем связи. При передаче сигналов используются несколько цветовых моделей, например, RGB или YCrCb. В то же время важную роль играет тот факт, что цветовая гамма имеет несколько запрещенных значений, которые могут быть отброшены при кодировании передаваемого изображения. В каналах R, G и B используется гамма-коррекция, которая не является оптимальной с точки зрения минимизации количества уровней квантования при визуальном наблюдении за изображением, а с другой стороны, эти модели не имеют одинаковой контрастности, то есть изменение, например, цветового тона или насыщенности на определенное значение будет заметно отличаться в зависимости от выбора начальных значений координат выбранного цвета. В работе предлагается оптимизировать выбор кодовых комбинаций для передачи цветного изображения. Предложен алгоритм оценки эффективности кодирования цветного изображения с учетом вывода из допустимых значений цветности, алгоритм оценки учитывает показатели рисков или искажений при кодировании двоичным кодом, а также учитывает виды возникающих ошибок в цифровом сигнале. Данный подход позволяет выявить более и менее эффективные методы кодирования цветного изображения. Было выявлено, что в зависимости от вида ошибок в цифровом сигнале различные варианты кодирования обеспечивают существенно отличные искажения в восстанавливаемом сигнале.
Ключевые слова: двоичный код, эффективное кодирование, кодирование с исправлением ошибок, гамма-коррекция, сигнал RGB. Литература
1. Аджемов А.С. Таблица кодовых расстояний и ее применение / В материалах Международной конференции "Волновая электроника и ее применение в информационных и телекоммуникационных системах" (WECONF). С.-Петербург, 2018. С. 1-5.
2. Аджемов А.С., Аджемов С.А. О некоторых особенностях комбинаций двоичного кода / В материалах Международной научно-практической конференции IEEE "Системы формирования и обработки сигналов в области бортовых коммуникаций" (ON BOARD). Москва, 2019. С. 1-7.
3. Аджемов А.С., Кудряшова А.Ю. Особенности оценки качества передачи сигналов в различных метрических пространствах // Фундаментальные проблемы радиоэлектронного приборостроения. 2017. Т. 17. № 4. С. 886-888.
4. Аджемов А.С., Кудряшова А.Ю. Об особенностях оценки качества генерации и обработки сигналов на этапных преобразованиях в системах электропроводки и оптической связи / В материалах Международной научно-практической конференции IEEE "Системы формирования и обработки сигналов в области бортовых коммуникаций" (ON BOARD). Москва, 2018. С.1-4
5. Аджемов А.С., Кудряшова А.Ю. Особенности оценки скорости вариантов двоичных кодовых слов с оцифровкой сигнала / В материалах Международной научной конференции IEEE "Системы синхронизации, генерации и обработки сигналов в телекоммуникациях" (SYNCHROINFO). Минск, 2018. С. 1-5.
6. Аджемов А.С., Кудряшова А.Ю. Построение алгоритма оценки эффективного кодирования источника при преобразовании сигналов в различных метрических пространствах" / В материалах Волновой электроники IEEE и ее применения в информационных и телекоммуникационных системах (WECONF). С.-Петербург, 2018. С. 1-4.
7. Аджемов А.С., Кудряшова А.Ю. Об особенностях оценки качества преобразования сигналов при последовательных преобразованиях в различных метрических пространствах" / В материалах XII Международной промышленной научно-технической конференции "Технологии информационного общества", 2018. С. 211-213.
8. Аджемов А.С., Кудряшова А.Ю. Особенности оценки мощности набора вариантов для комбинаций двоичного кода при оцифровке сигнала // Системы синхронизации, генерация и обработка сигналов. 2018. Том. 9. № 1. С. 5-8.
9. Кудряшова А.Ю. Особенности оценки кодирования в различных конфигурациях исходного пространства // DSPA: проблемы применения цифровой обработки сигналов, 2018. Т. 8. № 3. С. 228-232.
10. Аджемов А.С., Кудряшова А.Ю. Особенности оценки мощности множественного выбора комбинаций двоичных кодов // Фундаментальные проблемы радиоэлектронного приборостроения. 2018. Т. 18. № 4. С. 926-929.
11. Аджемов А.С., Кудряшова А.Ю. Программа оценки эффективного алгоритма кодирования источника в условиях преобразования метрических пространств" / В материалах Международной конференции IEEE "Волновая электроника и ее применения в информационных и телекоммуникационных системах" (WECONF). С.-Петербург, 2019. С. 1-5.
12. Аджемов А.С., Кудряшова А.Ю., Власюк И.В. Применение закона Вебера-Фехнера при передаче изображений в области бортовых коммуникаций / В материалах Международной научной конференции IEEE "Системы генерации и обработки сигналов в области бортовых коммуникаций" (ON BOARD). Москва, 2019. С. 1-6.
T-Comm ^м 13. #6-2019
