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Adaptive color space model based on dominant colors for image and video compression performance improvement
S. Madenda1, A. Darmayantie1 1 Computer Engineering Department, Gunadarma University, Jl. Margonda Raya. No. 100, Depok - Jawa Barat, Indonesia
Abstract
This paper describes the use of some color spaces in JPEG image compression algorithm and their impact in terms of image quality and compression ratio, and then proposes adaptive color space models (ACSM) to improve the performance of lossy image compression algorithm. The proposed ACSM consists of, dominant color analysis algorithm and YCoCg color space family. The YCoCg color space family is composed of three color spaces, which are YCcCr, YCpCg and YCyCb. The dominant colors analysis algorithm is developed which enables to automatically select one of the three color space models based on the suitability of the dominant colors contained in an image. The experimental results using sixty test images, which have varying colors, shapes and textures, show that the proposed adaptive color space model provides improved performance of 3 % to 10 % better than YCbCr, YDbDr, YCoCg and YCgCo-R color spaces family. In addition, the YCoCg color space family is a discrete transformation so its digital electronic implementation requires only two adders and two subtractors, both for forward and inverse conversions.
Keywords: colors dominant analysis, adaptive color space, image compression, image quality, compression ratio.
Citation: Madenda S, Darmayantie A. Adaptive color space model based on dominant colors for image and video compression performance improvement. Computer Optics 2021; 45(3): 405417. DOI: 10.18287/2412-6179-03-780.
Acknowledgments: Thank you to Gunadarma University for providing funding support during the research and publication process.
1. Introduction
Raw images and video frames recorded by highresolution cameras in information and communication technology (ICT) devices are in the form of three basic color components R (red), G (green) and B (blue). These color components are called RGB color spaces. Saving high-resolution raw images and video frames in RGB color space requires enormous memory. Image and video compression algorithms are the main solutions to reduce data size and minimize storage requirements. JPEG and JPEG2000 are two compression algorithms that are widely used in ICT devices. In general, these two algorithms have the same process flow, as shown in fig. 1 [1, 2, 3]. The Compression algorithm in fig. 1a consists of the following processes: color space conversion, spatial to frequency transform, quantization and coding. Contrary, the decompression algorithm (fig. 1b) consists of: decoding, inverse quantization, frequency to spatial transform and inverse color space conversion.
In image and video compression algorithms, the choice of color space is an important part, because it directly affects the compression ratio and image quality. This means that the use of the right color space can increase the compression ratio and image quality. Generally, the color space used is in accordance with the sensitivity of the human visual system to color changes, especially the color spaces that have luminance and chrominance components. The JPEG and JPEG2000 compression al-
gorithms use color spaces YCbCr and YDbDr, which Y correspond to luminance, Cb and Db are blue chrominance, and Cr and Dr are red chrominance components [3, 4, 5, 6]. The Color conversion process from RGB to YCbCr can be calculated through a mathematical transformation as given in Eq. (1), while the inverse conversion process from YCbCr to RGB is shown by Eq. (2). Matrix A is called a color transformation matrix to which [a -1] is the inverse of matrix [a] and is called an inverse color transformation matrix. Numerical implementation of RGB to YCbCr conversion requires two shift-right operations, seven multiplications and six adders/subtractors. Numerical implementation of YCbCr to RGB conversion requires four multiplications and four adders / subtractors. This color space is an irreversible color transform because it is rounded during the process.
Fig. 1. General block diagram of JPEG and JPEG2000 algorithms: (a) Compression and (b) Decompression processes
Y " "r"
Cb = [a] G , [a] =
Cr _ B
0.2990 0.5870 -0.1688 -0.3312
R" "y "
G = [ a-1] cb , [a-1] =
B .cr _
0.5000 1.0
0.1140 0.5000 -0.4187 -0.0813
0.0 1.4020
1.0 -0.3441 -0.7141
1.0 1.7720
0.0
(1)
(2)
The YDbDr color space used in the JPEG2000 compression algorithm is a variant of YCbCr [2, 7 - 9]. The matrices [a] and [A1] in Eqs. (3, 4) respectively show the transformation matrix for RGB to YDtDr conversion and inverse transformation matrix for YDDr to RGB conversion. This color space is reversible color transform (RCT) and its numerical implementation is simpler because it only requires shift-right (symbolized by "»"), addition and subtraction operations, and without multiplication operation. For example, 0.5xR is equal to one-bit shift-right of R value (R » 1) and 0.25 xB is identical to two-bits shift-right of B value (B » 2). Thus, for RGB to YDbDr conversion requires two shift-right operations and four adders / subtracters. While YDbDr to RGB inverse conversion requires three shift-right and seven addition and subtraction operations.
Y
Db
Dr
" R"
= [ a] G , [a] =
B
R" "y "
G = [ a-1] Db , [a-1] =
B . Dr _
0.25 0.50 0.25 0.0 -1.0 1.0 , (3) 1.0 -1.0 0.0 1.0 -0.25 0.75 " 1.0 -0.25 -0.25 . (4) 1.0 0.75 -0.25
Another variant of the YCbCr color space is YCoCg, which has a conversion process easier and faster than YCbCr, and it is a reversible color transform [9, 10]. YCoCg is also known as the YCgCo color model. The matrix A is used for the conversion process from RGB to YCoCg and the inverse transformation matrix [a -1] is applied for the conversion process from YCoCg to RGB which are given in Eqs. (5, 6). The numerical implementation of RGB to YCoCg conversion requires four shift-right, two addition and tow subtraction operations. Likewise for YCoCg to RGB conversion process requires only two addition and two subtraction operations.
Y R 0.25 0.50 0.25
Co = [ a] G , [a] = 0.50 0.0 -0.50
Cg _ B -0.25 0.50 -0.25
R" "y " "1.0 1.0 -1.0"
G = [ a-1] co , [a-1 ] = 1.0 0.0 1.0
B .cg _ 1.0 -1.0 -1.0
(5)
(6)
YCoCg color space is then developed into YCgC-R with the aim to speed-up the conversion process by multiplying by 2 each value of the chrominance components [11,
12] (see Eqs. (7, 8)). Numerical implementation of RGB to YCgCo-R conversion and its inverse conversion form YCgCo-R to RGB, both only require two shift-right, two addition and two subtraction operations.
[ a] =
[ a-1] =
0.25 1.0 -0.50 1.0 1.0 1.0
0.50 0.25 0.0 -1.0 1.0 -0.50 0.5 -0.5 0.0 0.5 -0.5 -0.5
(7)
(8)
In [13], the authors developed a new family of reversible low-complexity color transformation: YiUVj. The YDbDr and YCgCo-R color spaces are included in this family. The Co = (R-G) / 2 and Cg = (2G-(R+B))/4 as chrominance components of YCoCg color space (Eq. 5) are not yet included. From this family, the color space components Yi, Uj and Vj, which have computational with lower complexity, are given in table 1. The performance of each color space has been compared with the focus on lossy compression and by applying an automatic color space selection algorithm based on entropy h.
Table 1. YiUVj reversible color transformation.
i Yi j Uj Vj
1 (R+2G+B) / 4 1 G - (R+B) / 2 R - B
2 (R+G + 2B) / 4 2 B - (R + G) / 2 R - G
3 (2R + G+B) / 4 3 R - (G+B) / 2 B - G
4 (R + G) / 2 4 B - (R + G) / 2 R - G
5 (R + B) / 2 5 G - (R+B) / 2 R - B
6 (R + B) / 2 6 R - (G+B) / 2 B - G
The image in R, G and B color components format must first be converted into each color component of Yi, Uj, and Vj, and then the entropy value is calculated for each of H(Y), h(u), and H(Vj). It is assumed that the one having the smallest entropy value (h=H(Yi) + H(Uj) + H(v)), as the components ofthe color space, will be selected to be applied. To avoid high computation time, an image is divided into p x q macro blocks, where the number of blocks depends on the image size. For example, an image is divided into 9 blocks (p = q = 3), in each block the same components can be applied, or may also be different, according to their entropy calculation result. Both adaptive color space and macro block models have been developed in [14, 15] and implemented in 4: 4: 4 video coding.
The first three color spaces in table 1, Y1UV1, Y2UV2 and Y3UV3 (each for r = i = j is called YUVr: YUV1, YUV2, and YUV3), can be represented as matrix multiplication and each accompanied by its inverse transformation, respectively shown by Eqs. (9, 10, 11, 12, 13, 14). The YUV1 color space is the same as the YCgCo-R color space, while YUV2 and YUV3 are the permutations of the YUV1 color space. These three color spaces can be applied for lossless and lossy image compression.
RGB to YUV1 and YUV1 to RGB :
Y R 0.25 0.5 0.25
U = [a ] G , where [A1 ] = -0.5 1.0 -0.5 , (9)
v B 1.0 0.0 -1.0
R~ "Y "1.0 -0.5 0.5"
G = [ at' ] U , where [a-1] = 1.0 0.5 0.0 . (10)
B V 1.0 -0.5 -0.5
RGB to YUV2 and YUV2 to RGB:
= [a2
= [ a- ]
where [a2 ] =
where [a2'] =
0.25 0.25 0.5
-0.5 -0.5 1.0
1.0 -1.0 0.0
1.0 -0.5 0.5"
1.0 -0.5 -0.5
1.0 0.5 0.0
(11)
(12)
RGB to YUV3 and YUV3 to RGB :
" Y " R ] 0.5 0.25 0.25"
U = [a3 ] G , where [a3 ] = 1.0 -0.5 -0.5 , (13)
V B 0.0 -1.0 1.0
" R~ Y" "1.0 0.5 0.0"
G = [ a3-1 ] U , where [a-1] = 1.0 -0.5 -0.5 . (14)
B V 1.0 -0.5 0.5
2. Performance evaluation of existing color spaces
In terms of numerical implementation, it can be concluded that YUV1 (= ycocg-R), YUV2 and YUV3 are simpler and faster than YCoCg, YDbDr and YCbCr color spaces. So, what about the performance in terms of compression ratio and image quality, if each color space is implemented in the lossy image compression algorithm?
In this part, we describe performance evaluation of color spaces YCbC, YDDr, YCaCg, YUV1, YUV2 and YUV3, applied in JPEG compression algorithm. As known that image quality and compression ratio of color image compression algorithms are not only determined by the diversity of color contained in an image, but also influenced by texture and shape variations. For these reasons, in the experiments, 60 images were selected containing various colors, shapes and textures from six sources of image dataset [16, 17, 18, 19, 20, 21]. Twelve of them are shown in fig. 2. For example, the Lena image has the dominant colors red, orange and red-purple, many homogeneous areas, slight in texture and shape variation. The Baboon image has random textures and shapes, and its dominant colors are green-yellow, cyan and red. The Frymire image is very rich in textures and shapes, as well as containing variant colors with almost the same composition between yellow, red, orange, green, cyan, blue and purple. The Roses image has dominant colors red, red-purple (pink), blue-cyan, blue-purple, yellow, white and
black. The Woman image has a little color variation, some areas are relatively homogeneous and varying texture patterns in the hair. Yellow_orchid has a dominant homogeneous area, yellow and cyan colors, as well as various shapes and slight variations in texture.
(j) (k) (l)
Fig. 2. Twelve test images: (a) Lena, (b) Baboon, (c) Peppers, (d) Frymire, (e) Roses, (f) Tulips, (g) Sails, (h) Monarch, (i) Textile, (j) Woman, (k) yelloworchid, and (l) ucid00295
Next, we outline the performance comparison of six color space YCbC, YDDr, YCaCg, YUVj, YUV2 and YUV3, regarding their compression ratio and image quality, when each of them is used in the lossy image compression algorithm. Block size 8 x 8 pixels [1], color components without sub-sampling for high quality image compression [23, 24, 25], discrete cosine transform (8 x 8 DCT and iDCT) [1, 26, 27, 28, 29], and Huffman statistic encoding / decoding [1, 2, 8, 22, 30] are chosen to carry-out the experiments of JPEG lossy image compression. For each color space used, it is done by determining the same quality for the same image and then compares their compression ratio. In this case, the experiment was carried out by using one Photoshop's quantization matrix for medium quality (Q9) as shown in Eq. (15) [3, 22]. QLum and Qcr are respectively quantization matrices for luminance and chrominance components, and q is a variable that determines the quantization value, so that the seven color spaces can produce the same quality for the same image, thus the compression ratio can be compared.
Qcr = q.
4 6 12 22 20 20 17 17
6 8 12 14 14 12 12 12
12 12 14 14 12 12 12 12
22 14 14 12 12 12 12 12
20 14 12 12 12 12 12 12
20 12 12 12 12 12 12 12
17 12 12 12 12 12 12 12
17 12 12 12 12 12 12 12
and
QLum = q.
4 3 4 7 9 11 14 17
3 3 4 7 9 12 12 12
4 4 5 9 12 12 12 12
7 7 9 12 12 12 12 12
9 9 12 12 12 12 12 12
11 12 12 12 12 12 12 12
14 12 12 12 12 12 12 12
17 12 12 12 12 12 12 12
(15)
Table 2. Compression ratio of nine images using JPEG algorithm for six color spaces
File Image (png) Quality PSNR (dB) Compression Ratio (CR) Using Color Space:
YCbCr YDbDr YCoCg YUVi YCoCg-R YUV2 YUV3
Lena 36.117 9.490 8.430 10.024 8.910 7.987 9.076
Baboon 32.805 3.554 3.486 3.798 3.543 3.446 3.506
Peppers 34.057 6.161 5.952 6.580 6.230 6.419 5.995
Frymire 34.227 3.696 3.500 3.765 3.577 3.585 3.597
Roses 46.776 19.96 19.118 19.709 18.960 19.213 19.340
Tulips 33.764 3.784 3.405 3.679 3.500 3.669 3.601
Sails 37.456 7.451 7.228 7.750 7.220 7.081 7.013
Monarch 39.788 12.288 11.560 12.553 11.834 11.788 11.702
Textile 36.838 5.442 5.422 5.464 5.280 5.439 5.166
Woman 38.011 10.156 10.400 10.442 9.021 8.862 9.062
Yellow Or 41.050 21.398 22.915 23.518 23.355 24.131 22.996
Ucid00295 36.614 7.642 7.794 7.908 7.228 7.086 7.174
CR Average 9.252 9.101 9.599 9.055 9.059 9.019
Note: ¿Increase ¿Decrease 41.6% |3.8% 42.1% 42.1% 42.5%
Table 2 shows the compression ratio (CR) of JPEG algorithm using color spaces: YCbCr, YDbDr, YCoCg, YUVi, YUV2 and YUV3. In the first line, for Lena image with compression quality of PSNR = 36.117 dB, the CR produced by YChCr is 9.490, YDbDr is 8.430, YCoCg is 10.024 and respectively for YUVi, YUV2 and YUV3 are 8.910, 7.987, and 9.076. Similarly, for Baboon image in the second row with a compression quality of PSNR = 32.805 dB, six consecutive color spaces produced CR of: 3.554, 3.486, 3.798, 3.543, 3.446 and 3.506. Furthermore, the CR for Peppers, Frymire, Roses, Tulips, Sails, Monarch, Textile, Woman, yellow_orchid and ucid00295 images can be seen in the next lines.
From the compression ratio results in table 2, it can be seen that, YCoCg color space yields highest CR for Lena, Baboon, Peppers, Frymire, Sails, Monarch, Woman and
Ucid00295 images compared to the five others. YCbCr results in better CR for Roses and Tulips images, while Yellow_Orchid image has highest CR given by YUV2. In the two last rows of table 2, the CR average and the performance produced by each color space is given. When referring to these CR average values and comparing them to the CR average value of JPEG-standard YCbCr color space, YCoCg provides better performance with increased CR of 3.8 % on average, while YDbDr, YUVi, YUV2 and YUV3 resulted CR averages of 1.6 %, 2.1 %, 2.1 %, and 2.5 % lower than YCbCr respectively.
The experimental results of the other forty-eight images are given in tables 4 - 5. Table 4 represents the compression ratios for the same image quality and table 5 reflects the image quality for the same compression ratio. For now, we focus on the first seven columns to evaluate the compression results of the forty-eight images using YCbCr, YCoCg, YUVi, YUV2 and YUV3 color spaces. There are thirty-seven images (75.51 %) that have the highest compression ratio and image quality generated by the YCoCg color space (in the fourth column), nine images (18.37 %) given by the YCbCr color space (in the third column), and the remaining two, one and zero images respectively resulted by YUVi, YUV2 and YUV3 color spaces (in the fifth, sixth and seventh column). In the last two rows of each table, the CR average and the performance yielded by each color space is given. YCoCg color space has the highest average value of 9.599, followed by YCbCr = 9.252, YDbDr = 9.101, YUV2 = 9.059, YUVi = 9.055 and YUV2=9.019. These CR average values show that for those forty-eight images, the use of YCoCg in the JPEG lossy compression algorithm can increase the CR average of 3.623 %, while for YUVi, YUV2 and YUV3 there is a decrease of 3.158 %, 5.056 % and 4.693 % respectively.
These results indicate that in general YCoCg color space provides better performance than the five other color spaces and YCbCr has a higher compression ratio than YUVi, YUV2, YUV3 and YDbDr color spaces. It may be assumed that the compatibility between the percentage composition of each color in a color space formula and the dominant colors contained in an image can affect the quality and compression ratio. The first analysis is about the percentage of color representation in a color space formula. For example, a pixel has pure red or pure blue, in YCoCg color space, its color will be accommodated 100 % (25 % in Y, 50 % in Co and 25 % in Cg components), while in YCbCr, YDbDr and YCgCo-R family (YUVi, YUV2, YUV3) color spaces respectively accommodate 97.775 %, 125 % and 175 %. Furthermore, for pure green, it will be recorded 100 %, 250 %, 150 % and 133.695 % respectively by YCoCg, YCbC, YDbDr and YCoCg-R. Ideally to get good quality and compression ratio, the color conversion formula must still record 100 % of the dynamic value for each color component R, G and B. This ideal condition is only owned by YCoCg color space and it is proven that its performance is better than the three other color spaces. The second analysis con-
cerns chrominance covered by the color space formula. For example, YCbCr color space tends to be dominant in color combinations with hues (for all chrominance and luminance): red, orange, yellow, green, green-yellow, cyan, and blue, whereas the YCoCg color space covers more color variations with hues: red, orange, green-yellow, green, green-cyan, blue, purple. This means, there are several hues that have not been well covered by each color space formula. The third analysis is the compatibility between the color space used and the dominant colors contained in an image. Based on the three thoughts above, this paper proposes a color dominant analysis algorithm and an adaptive color space model.
3. Proposed methods
The proposed methods consist of three parts: developing adaptive color space, analyzing dominant colors in an image to determine which color space will be used, and then the experimentations. The development of adaptive color space model refers to YCoCg color space which provides better quality and compression ratio in lossy image
compression (see results in table 1). It has been described above that this color space has not evenly covered all existing chrominance. This weakness has an impact on quality and compression ratio: it is best suited for images having colors according to their characteristics and decreased for images having less suitable color.
3.1. Dominant colors analysis
As described in the example of twelve images (fig. 2), where each image has a different dominant color. Thus, there is a need to adapt the suitability of the color space used and the image to be compressed. For this reason, the dominant color analysis contained in the image must be carried out first. The colors information can be presented in the form of cylindrical coordinates hue-saturation as shown in fig. 3a. We propose to divide hue coordinates into 12 parts, so that 12 different hues will be formed with angle range: red=0° -15° and 345° - 360°, orange = 15° - 45°, yellow=45° - 75°, green-yellow=75° - 105°, green =105° - 135°, green-cyan = 135° - 165°, cyan = 165° - 195°, blue-cyan = 195° -225°, blue=225°- 255°, blue-purple = 255°- 285°, purple = 285° - 315°, red-purple = 315° - 345°.
Number of pixels
250 300 350 Hue {degrees)
Number of pixels
Number of pixels
(c)
150 200 250 300 350
Hue (degrees) (d)
150 200 250 300 350 Hue (degrees)
Fig. 3. (a) Cylindrical coordinates of hue; and hue histograms of (b) Lena, (c) Roses and (d) Textile images
The Hue of each pixel of an RGB image can be calculated using H (hue) component formula of HSL, HSV or HCL color spaces [31, 32]. From the hue value of each pixel, a histogram hue can be calculated. A Histo-
gram hue is a distribution of the number of pixels having the same hue value in an image. Furthermore, this histogram hue can be used to determine what chrominance are dominants in an image. figs. 3b - d respective-
ly show histogram hues for Lena, Roses, and Textile images. The dominant hue in Lena image is red, orange, and red-purple. These three hues are more in line with YCoCg that is why its compression ratio performance is 5.63 % better than YCbCr (see table 2). Roses image has dominant hues: red, red-purple, blue-cyan, blue-purple, yellow, white, and black. The majority of these hues are less compatible with YCoCg, this has an impact on decreasing its compression ratio performance to 1.27% lower than YCbCr. For Textile images, its dominant hues are yellow, orange, cyan, blue, red-purple. For this Textile image, YCoCg and YChCr provide a relatively similar compression ratio.
The proposed algorithm for the dominant colors analysis process in an image is given in Algo-1. The syntax of Hue_histo(red), Hue_histo(cyan), and so on represent the number of pixels in an image that have the red hues (0° - 15° and 345° - 360°), cyan hues (165° -195°), and so forth. The dominant colors are grouped into three parts according to the three color space models described in section 3.2. The first part (Model-1) is a combination of red, cyan, green-yellow, blue-purple, and gray-level colors. The second part (Model-2) is a combination of green, purple, orange, blue-cyan, and gray-level colors. The last part (Model-3) is a combination of blue, yellow, green-cyan, red-purple, and gray-level colors.
Algo-1. Dominant color analysis algorithm
Input : RGB_Image Output: Color_ Space 1. Huehisto = Calculate_hue_histogram(RGB_Image) DC_I = Hue_histo(red) + Hue_histo( cyan) +
Hue_histo(green-yellow) + Hue_histo(blue-purple) Y R 0.25 0.25 0.50
3. DC_2 = Hue_histo(green) + Hue_histo(purple) + Cy = [ a] G , [a] = 0.50 -0.50 0.0
Hue_histo(orange) + Hue_histo( blue-cyan) Cb B -0.25 -0.25 0.5
4. DC_3 = Hue_histo(blue) + Hue_histo(yellow) +
Hue_histo(green-cyan) + Hue_histo(red-purple) " R' "y - 1.0 1.0 -1.0-
5. if (DC_I > DC_2) and (DC_I > DC_3)
6. ColorSpace = "Modell" G = [ a1] Cy , [a-1 ] = 1.0 -1.0 -1.0
7. else if (DC_2 > DC_I) and (DC_2 > DC_3) B Cb 1.0 0.0 1.0
else
8.
9.
10. 11. end if
ColorSpace = "Model_2"
ColorSpace = "Model_3"
3.2. Proposed adaptive color space model
In this part, we adopted the permutation model proposed in [13] to produce two additional color spaces which are variants of YCoCg and to be a solution to its weaknesses. The two color spaces are shown in Eqs. (16, 17), and Eqs. (20, 21). Thus, the proposed adaptive color space model (ACSM) consists of three color spaces and can be said as the YCoCg color space family (ACSM-YCoCg). As a side note, if each of their all chrominance
components is multiplied by 2, they will be identical to the ycgco-R color space family (YUVh YUV2 and YUV3).
Model-1: YCcCr (luminance y, chrominance cyan Cc and chrominance red cr) with dominant hues (colors) coverage: red, cyan, green-yellow, blue-purple, and grey-level.
(16)
Y - " R - "0.50 0.25 0.25 -
cc = [ a] G , [a] = 0.0 0.50 -0.50
cr B 0.50 -0.25 -0.25
" R - "y - "1.0 1.0 -1.0
G = [ a-1] cc , [a-1] = 1.0 -1.0 -1.0
B cr 1.0 0.0 1.0
(17)
Model-2: YCpCg (luminance y, chrominance purple Cp and chrominance green cg) is equal to YCoCg (Eq. 5) with dominant hues coverage: green, purple, orange, blue-cyan, and grey-level.
(18)
Y " R - " 0.25 0.50 0.25 -
CP = [ a] G , [a] = 0.50 0.0 -0.50
Cg _ B -0.25 0.50 -0.25
R Y 1.0 1.0 -1.0
G = [ a-1] CP , [ a-1] = 1.0 0.0 1.0
B Cg _ 1.0 -1.0 -1.0
. (19)
Model-3: YCyCb (luminance y, chrominance yellow Cy and chrominance blue Cb) with dominant hues coverage: blue, yellow, green-cyan, red-purple, and grey-level.
(20)
. (21)
The color image conversion algorithm from RGB space to ACSM and its inverse conversion from ACSM to RGB are presented by Algo-2 and Algo-3. The choice of color s pace (Color Space), for the color image conversion process, depends on the dominant colors calculated using Algo-1. If the Color Space = "Modell", then the color space YCcCr will be used, or the color space YCpCg that will be selected if Color Space = "Model_2", whereas if Color Space = "Model_3", then the color space YCyCb will be used. The color image conversion process from RGBImage to ACSM_ Image is done in the last line of the algorithm. This conversion process is carried out pixel by pixel. The Algo-3 is used for the inverse color conversion process from ACSM_ Image to RGB Image.
%% Color model 1
%% Color model 2
%% Color model 3
Algo-2. RGB_Image to ACSM_ Image conversion algorithm
Input : RGB_Image, Color_ Space Output: ACSM_ Image
1. if Color_ Space = "Model l"
2. ACSM=[0.50 0.25 0.25
0.00 0.50 -0.50 0.50 -0.25 -0.25]
3. else if Color_ Space = "Model_2
4. ACSM=[0.25 0.50 0.25
0.50 0.00 -0.50
-0.25 0.50 -0.25]
5. else
6. ACSM=[0.25 0.25 0.50
0.50 -0.50 0.00
-0.25 -0.25 0.50]
7. end if
8. ACSM_ Image = ACSM * RGBImage
Algo-3. ACSM_ Image to RGB_Image conversion algorithm
Input : ACSM_ Image, Color_ Space
Output: RGB_Image
1. if Color_ Space = "Model_1"
2. iACSM = [1.0 0.0 1.0
1.0 1.0 -1.0 1.0 -1.0 -1.0]
3. else if Color_ Space = "Model_2
4. iACSM = [1.0 1.0 -1.0
1.0 0.0 1.0 1.0 -1.0 -1.0]
5. else
6. iACSM = [1.0 1.0 -1.0
1.0 -1.0 -1.0 1.0 0.0 1.0]
7. end if
8. RGB Image = iACSM * ACSM_ Image
4. Results and discussions
The proposed dominant color analysis and ACSM algorithms have been integrated into the JPEG lossy image compression algorithm. Besides that, we also implemented the ACSM algorithm using YCgCo-R color space family (YUVi, YUV2 and YUV3). Both were tested using sixty images from [17, 18, 19, 20, 21]. The experimental results of the first twelve images are given in table 3 and the next forty-eight images are shown in tables 4 - 5. In table 3, there are eleven of the twelve images with the highest CR value offered by the ACSM-YCoCg color space family (last column), while the ACSM-YCgCo-R family only produces one image with the highest CR value (fourth column).
For Lena image, the adaptive color algorithm automatically selects and uses model-1 YCcCr color space, and obtained CR of 10.34 % better than YChCr. Color space YUV3 is also automatically selected when ACSM-ycgco-R family is implemented. This color space is 4.362 % lower than YCbCr. Color space Model-1 is also selected for Roses and Ucid00295 images and their CR
%% Color model 1
%% Color model 2
%% Color model 3
are better than YCbCr and ACSM-ycgco-R family. An increase in CR is also seen in Peppers, Frymire, Tulips, and Textile images, where the color space chosen is model-3 YCyCb. Furthermore, for Baboon, Sails, Monarch, and Woman images, model-2 YCpCg color space is used, where the compression ratios results are also better than YCbCr and ACSM-ycgco-R family. The higher CR for Yel-low_Orchid image is given by YUV3 of ACSM-YCgCo-R family. Its compression ratio is 12.77 % better than YCbCr and 2.607 % better than the ACSM-YCoCg family.
Furthermore, in tables 4 - 5, it can be observed that there are forty-one out of forty-eight images having the highest quality and compression ratio produced by the proposed ACSM-ycocg family. YCbCr and ACSM-YCgCo-R family provide the highest quality and compression ratio of the other four and three images, respectively. On average, ACSM-YCoCg family can enhance the CR by 5,046 % for the first 12 images, while for the next 48 images the CR and compression quality increase 4,555 % and 0.303 dB comparatively to YCbCr. Conversely, there was a decrease in CR of 0.420 % for the first 12 images and a decrease in CR of 2.087 % and compression quantity of 0.439 dB for the next 48 images, when ACSM-ycgco-R family was used.
Table 3. Compression ratio of YCbCr, YCoCg and adaptive color space: YCcCr, YCpCg, YCyCb
File Image (png) Quality PSNR (dB) Compression Ratio (CR) Using Color Space:
YCbCr ACSM appled to:
YUVi, YUV2, YUV3 YCcCr, YCpCg, YCyCb
Lena 36.117 9.490 9.076 (YUV3) 10.471 (YCcCr)
Baboon 32.805 3.554 3.543 (YUVi) 3.798 (YCpCg)
Peppers 34.057 6.161 6.419 (YUV2) 6.695 (YCyCb)
Frymire 34.227 3.696 3.597 (YUV3) 3.771 (YCyCb)
Roses 46.776 19.96 19.340 (YUV3) 20.145 (YCcCr)
Tulips 33.764 3.784 3.669 (YUV2) 3.926 (YCyCb)
Sails 37.456 7.451 7.220 (YUVi) 7.750 (YCpCg)
Monarch 39.788 12.288 11.834 (YUVi) 12.553 (YCpCg)
Textile 36.838 5.442 5.439 (YUV2) 5.650 (YCyCb)
Woman 38.011 10.156 9.062 (YUV3) 10.442 (YCpCg)
Yellow_0rc 41.050 21.398 24.131 (YUV2) 23.518 (YCyCb)
Ucid00295 36.614 7.642 7.228 (YUVi) 7.908 (YCcCr)
CR Average 9.252 9.213 9.719
Note: t Increase j Decrease 1 0.420% t 5.046%
Furthermore, the adaptive color space performance test is performed using seven Photoshop's quantization matrices from the high Q12 to the low Q6 compression quality (i.e. Q12, Q11, Q10, Q9, Q8, Q7, Q6) [22, 30]. Tables 6 - 8 show the quality (PSNR) and compression ratio for Lena, Baboon and Textile images and graphically show by the curves in Figs. 4 - 6. The adaptive color space curves for the three images are above the YCbCr color space curve. This shows that the proposed adaptive model has a better performance.
Table 4. Compression ratio of YCbCr, YCoCg, ACSM-YCgCo-R (YUVi, YUV2, YUV3) and ACSM-YCoCg (YCcCr, YCpCg, YCyCb)
Image file name YCbCr YC0Cg YUV1 YCgC0-R YUV2 YUV2 ACSM: YUVi, YUV2, YUV3 ACSM: YCcG, YCpCg, YCyCb
PSNR (dB) CR CR CR CR CR CR CR
5colors_544x544 38.611 7.468 7.569 7.309 7.322 7.385 7.385 7.583
408px-Killersudoku_color 41.071 11.429 11.205 10.756 10.756 10.868 10.868 11.730
73755 39.277 15.136 15.140 14.639 14.436 14.855 14.855 15.297
3975590069_7d5e05207e_o 45.767 37.588 39.581 38.840 39.484 40.538 40.538 39.638
article-0-0B9771B5000005... 44.027 17.167 17.509 16.092 16.354 16.093 16.354 17.509
Best-Science-Images-2007-I... 47.342 20.269 18.591 18.353 17.759 18.346 18.353 19.147
Best-Science-Images-2007-II... 40.302 10.604 10.245 11.039 10.268 10.883 11.039 10.775
bike_orig_1280x1600 36.740 8.383 8.785 7.435 7.754 7.683 7.754 8.785
butterfly _3 45.780 19.965 19.933 19.184 19.442 19.399 19.442 20.062
cafe_orig_1280x1600 34.084 4.365 4.598 4.200 4.239 4.154 4.239 4.598
computer-science-ultimate 38.722 8.3158 7.658 7.289 7.634 7.187 7.634 8.095
dc7b126a-20f9-4569-bfd4-ce... 39.482 9.139 9.489 8.671 8.541 8.564 8.671 9.489
F1_large 40.337 10.828 10.718 10.446 10.647 10.740 10.740 11.056
glas_coloured_6 41.043 17.102 17.389 17.084 17.344 17.020 17.344 17.617
p-radiologist-art1 _1467422c 37.968 6.709 7.076 7.125 6.810 6.797 7.125 7.076
p01_orig_1280x1600 39.844 11.145 10.604 10.098 10.793 10.495 10.793 11.020
p06_orig_1280x1600 39.026 12.194 12.303 11.505 11.373 11.510 11.510 12.303
p30_orig_1280x1600 36.627 9.296 8.581 7.863 8.490 8.031 8.490 9.236
Screen-Searchmetri_968x576 40.886 14.033 15.431 14.640 13.719 13.979 14.640 15.431
Spectrscopic_mapping_speeds. 44.479 11.834 11.717 11.251 11.195 11.177 11.251 11.878
stadtplan-museum-o_880 *600 35.788 5.641 5.750 5.228 5.319 5.108 5.319 5.776
stewart_tartan_2 39.212 7.33 7.373 6.689 6.842 6.881 6.881 7.373
surface_2 42.713 20.925 22.584 22.143 21.481 21.555 21.481 22.584
ucid00032 36.554 7.995 8.564 7.537 7.049 7.213 7.537 8.564
ucid00041 37.931 11.579 12.815 11.217 10.565 10.399 11.217 12.815
ucid00045 37.645 11.031 12.140 10.323 9.691 9.432 10.323 12.140
ucid00059 37.414 10.691 11.495 9.417 9.276 8.954 9.417 11.495
ucid00066 38.694 14.181 15.383 13.215 12.588 12.126 13.215 15.383
ucid00110 33.792 5.597 5.962 5.265 5.013 4.889 5.265 5.962
ucid00262 37.118 8.702 8.710 8.009 7.872 8.522 8.522 9.235
ucid00275 35.955 6.611 6.876 6.317 6.039 6.438 6.438 6.905
ucid00295 36.614 7.642 7.908 7.228 7.086 7.174 7.228 7.908
ucid00302 37.754 9.697 10.531 9.709 9.148 9.446 9.446 10.531
ucid00317 38.474 15.023 16.341 14.326 13.878 13.723 14.326 16.341
ucid00368 35.466 5.635 6.255 5.798 5.726 5.446 5.798 6.255
ucid00410 34.695 4.793 5.008 4.673 4.534 4.545 4.673 5.066
ucid00456 36.374 6.892 7.193 6.639 6.431 6.565 6.639 7.193
ucid00457 39.619 14.076 14.367 12.804 12.447 12.900 12.900 14.367
ucid00489 37.097 8.831 8.946 8.043 7.881 8.041 8.043 8.946
ucid00514 34.844 5.053 5.055 4.650 4.608 4.744 4.744 5.172
ucid00648 36.711 8.827 9.440 8.443 7.982 8.197 8.443 9.440
ucid00687 34.979 5.153 5.444 5.027 4.812 5.016 5.027 5.444
ucid00758 36.705 8.854 9.563 8.618 8.340 8.100 8.618 9.563
ucid00804 39.598 16.251 19.805 19.041 15.760 15.950 19.041 19.805
ucid00811 38.649 12.234 12.820 11.524 10.998 11.412 11.524 12.820
ucid00860 37.882 11.197 11.251 10.604 10.467 10.272 10.604 11.251
ucid00884 35.413 6.021 6.439 5.731 5.397 5.619 5.731 6.439
WFCAM_JHK_colour-comp... 42.822 14.177 14.819 14.718 15.038 14.194 15.038 14.819
CR average: 11.117 11.520 10.766 10.555 10.595 10.885 11.623
Note: t Increase 4 Decrease t3.626% 43.158% 45.056% 44.693% 42.087% t4.555%
Table 5. Compression quality of YCbCr, YCoCg, ACSM-YCgCo-R (YUVi, YUV2, YUV3) and ACSM-YCoCg (YCcCr, YCpCg, YCyCb)
Image file name YCbCr YCgCo YUVi YCgCo-R YUV2 YUV3 ACSM: YUVi, YUV2, YUV3 ACSM: YCcCr, YCpCg, YCyCb
CR PSNR (dB) PSNR (dB) PSNR (dB) PSNR (dB) PSNR (dB) PSNR (dB) PSNR (dB)
5colors_544x544 7.468 38.611 38.875 38.084 38.131 38.329 38.329 38.944
408px-Killersudoku_color 11.429 41.071 40.697 39.511 39.511 39.857 39.857 41.530
73755 15.136 39.277 39.278 39.165 39.112 39.225 39.225 39.308
3975590069_7d5e05207e_o 37.588 45.767 45.927 45.859 45.918 45.961 45.961 45.927
article-0-0B9771B5000005... 17.167 44.027 44.338 42.735 43.074 42.736 43.074 44.344
Best-Science-Images-2007-I... 20.269 47.342 41.826 43.761 42.977 43.719 43.761 45.231
Best-Science-Images-2007-II... 10.604 40.302 39.729 40.836 39.814 40.673 40.836 40.579
bike_orig_1280 x 1600 8.383 36.740 37.053 35.866 36.123 36.125 36.125 37.053
butterfly _3 19.965 45.780 45.762 45.330 45.465 45.452 45.465 45.833
cafe_orig_1280x 1600 4.365 34.084 34.559 33.592 33.716 33.439 33.716 34.559
computer-science-ultimate 8.3158 38.722 36.989 36.445 37.058 35.884 37.058 38.254
dc7b126a-20f9-4569-bfd4-ce... 9.139 39.482 39.982 38.640 38.386 38.456 38.640 39.982
F1_large 10.828 40.337 40.210 39.788 40.086 40.216 40.216 40.581
glas_coloured_6 17.102 41.043 41.097 41.039 41.091 41.024 41.091 41.144
p-radiologist-art1_1467422c 6.709 37.968 38.448 38.472 38.141 38.128 38.128 38.448
p01 _orig_1280 x 1600 11.145 39.844 39.486 39.041 39.581 39.361 39.581 39.760
p06_orig_1280x 1600 12.194 39.026 39.090 38.530 38.443 38.526 38.530 39.090
p30_orig_1280x1600 9.296 36.627 36.132 35.202 35.761 35.423 35.761 36.583
Screen-Searchmetri_968x576 14.033 40.886 42.320 41.709 40.424 40.809 41.709 42.320
Spectrscopic_mapping_speed... 11.834 44.479 44.400 43.772 43.592 43.617 43.772 44.507
stadtplan-museum-o_880x600 5.641 35.788 36.008 34.766 34.961 34.437 34.961 36.062
stewart_tartan_2 7.33 39.212 39.350 36.897 37.722 37.746 37.746 39.350
surface_2 20.925 42.713 42.987 42.930 42.812 42.827 42.930 42.987
ucid00032 7.995 36.554 37.073 36.052 35.464 35.636 36.052 37.073
ucid00041 11.579 37.931 38.482 37.756 37.446 37.321 37.756 38.482
ucid00045 11.031 37.645 38.137 37.302 36.995 36.791 37.302 38.137
ucid00059 10.691 37.414 37.810 36.621 36.649 36.387 36.649 37.810
ucid00066 14.181 38.694 39.014 38.419 38.269 38.069 38.419 39.014
ucid00110 5.597 33.792 34.105 33.182 32.668 32.334 33.182 34.105
ucid00262 8.702 37.118 37.125 36.379 36.243 36.949 36.949 37.547
ucid00275 6.611 35.955 36.279 35.530 35.052 35.715 35.715 36.535
ucid00295 7.642 36.614 36.919 36.041 35.861 35.995 36.041 36.921
ucid00302 9.697 37.754 38.344 37.763 37.287 37.555 37.763 38.344
ucid00317 15.023 38.474 38.764 38.296 38.197 38.131 38.296 38.764
ucid00368 5.635 35.466 36.443 35.783 35.642 35.081 35.783 36.443
ucid00410 4.793 34.695 35.170 34.358 33.859 33.975 33.975 35.265
ucid00456 6.892 36.374 36.770 35.979 35.666 35.879 35.979 36.770
ucid00457 14.076 39.619 39.765 38.984 38.825 39.045 39.045 39.765
ucid00489 8.831 37.097 37.195 36.332 36.093 36.318 36.332 37.195
ucid00514 5.053 34.844 34.847 33.866 33.750 34.113 34.113 35.050
ucid00648 8.827 36.711 37.176 36.421 36.000 36.212 36.421 37.176
ucid00687 5.153 34.979 35.527 34.682 34.132 34.651 34.651 35.527
ucid00758 8.854 36.705 37.260 36.514 36.294 36.068 36.514 37.260
ucid00804 16.251 39.598 40.755 40.465 39.417 39.487 39.487 40.755
ucid00811 12.234 38.649 38.962 38.231 37.919 38.178 38.231 38.962
ucid00860 11.197 37.882 37.920 37.471 37.382 37.249 37.471 37.920
ucid00884 6.021 35.413 36.007 34.897 34.266 34.707 34.897 36.007
WFCAM_JHK_colour-comp... 14.177 42.822 43.251 43.290 43.371 42.836 43.371 43.251
PSNR average (dB): 38.707 38.826 38.179 38.013 38.055 38.268 39.009
Note: t Increase j Decrease (dB): Î 0.119 1 0.528 1 0.693 1 0.652 | 0.439 T 0.303
Table 6. PSNR and CR of YCbCr and ACSM for Lena image
Matrix Quality YCbCr ACSM: YCcCr, YCpCg, YCyCb
PSNR (dB) CR PSNR (dB) CR
Q6 34.545 13.027 34.691 13.719
Q7 35.365 11.504 35.509 12.072
Q8 35.396 11.170 35.550 11.757
Q9 36.117 9.490 36.275 9.957
Q10 36.934 7.457 37.105 7.789
Q11 39.111 4.512 39.386 4.621
Q12 46.143 2.401 46.564 2.429
Fig. 4. PSNR vs CR curves of YCbCr and ACSM for Lena image
Table 8. PSNR and CR of YCbCr and ACSM for Textile image
Matrix Quality YCbCr ACSM: YCcCr, YCpCg, YCyCb
PSNR (dB) CR PSNR (dB) CR
Q6 33.246 7.048 33.461 7.168
Q7 35.442 6.208 35.622 6.303
Q8 34.961 6.236 35.219 6.324
Q9 36.838 5.442 37.140 5.537
Q10 38.873 4.654 39.075 4.717
Q11 42.191 3.572 42.411 3.60
Q12 48.269 2.453 48.4971 2.426
Besides its better performance, the implementation of the proposed adaptive color space in the form of an electronic circuit is very simple and only requires adders and subtrac-tors. It is as simple as the electronic implementation of ycgco-R color space family [13]. Suppose each color data R, G and B of an image is encoded with eight bits, that is: R = r7, ..., r0; G = g7,..., go; and B = b7,..., b0. Arithmetic operations for these data are carried out in binary operations: addition, subtraction, and logic. The symbol "»1", is a one-bit shift-right operation, used instead of multiply by 0.5. For example, the Eq. (10) can be simplified as:
Y = 0.5r + 0.25g + 0.25b ^ Y = (r + ((g + b) »1)) »1, Cc = 0.5G - 0.5B ^ Cc = (G-B)»1,
Table 7. PSNR and CR of YCbCr and ACSMfor Baboon image
Matrix Quality YCbCr ACSM: YCcCr, YCpCg, YCyCb
PSNR (dB) CR PSNR (dB) CR
Q6 30.914 4.152 31.452 4.180
Q7 32.050 3.872 32.509 3.906
Q8 31.912 3.857 32.492 3.883
Q9 32.805 3.554 33.403 3.582
Q10 33.814 3.144 34.417 3.17
Q11 37.696 2.328 38.262 2.347
Q12 46.102 1.534 46.567 1.545
Compression Ratio
Fig. 5. PSNR vs CR curves of YCbCr and ACSM for Baboon image
Compression Ratio
Fig. 6. PSNR vs CR curves of YCbCr and ACSM for Textile image
Cr = 0.5R - 0.25G - 0.25B ^ Cr = (R - ((G + B) »1)) »1.
Referring to this simplification model, the electronic schematic of RGB to YCcCr conversion can be created as shown in Fig. 7. This scheme only requires 2 adders and 2 subtractors. The luminance Y component requires 10 bits, consisting of 8 bits for integer (s7,..., s0) value and 2 bits for fractional (s-1, s-2) value. While the cyan chrominance Cc component needs 9 bits, that are 1 bit of borrow-out (s7 as sign bit: "0" positive or "1" negative), 7 bits integer value (s6,..., s0), and 1 bit fractional (s -1). Furthermore, the red chrominance Cr component takes 10 bits consisting of 1 bit borrow-out (s7 as sign bit), 7 bits inte ger (s6, ..., s0), and 2 bits (s -1, s -2) fractional.
S7...So'S-lS-2 S7,S6...So,S-lS-2 S7,S6...So,S./
yt cr? c)
Fig. 7. Electronic schematic of RGB to YCcCr color conversion
"gl *-/>T
Fig. 9. Electronic schematic of RGB
to YCpCg color conversion
Fig. 11. Electronic schematic of RGB to YCyCb color conversion
The inverse conversion process from YCcCr to RGB in Eq. (11): R = Y + C„
G = (y - Cr) + Cc, B = (y - Cr) - Cc. The electronic schematic of this equation is given by fig. 8. It can be seen that this inverse conversion only needs 2 adders and 2 subtractors.
In the same ways, the color model-2 from RGB to YCpCg can be simplified as:
S7...So\S-jS-2 S7,S6...So,S-]S-2
(it fit R
Fig. 8. Electronic schematic of YCcCr to RGB color conversion
Fig. 10. Electronic schematic of YCpCg to RGB color conversion
Fig. 12. Electronic schematic of YCyCb to RGB color conversion
Y = 0.25r + 0.5g + 0.25b ^ Y = (g + ((r + b) » 1)) »1,
Cp = 0.5R - 0.5B ^ Cp = (R - B)»1,
Cg = - 0.25R+0.5G - 0.25B ^ Cg = (G - ((R+B) »1)) »1.
and its inverse conversion from YCpCg to RGB is:
R = (Y - Cg) + Cp, G = (Y + Cg), B = (Y - Cg) - Cp.
The electronic schematics diagrams of both RGB to YCpCg and YCpCg to RGB colors conversion are sequentially presented in figs. 9 - 10.
Similarly for the color model-3 RGB to YCyCb is simplified as:
Y = 0.25R + 0.25G + 0.5B ^ Y = (B + ((R + G) »1)) »1,
Cy = 0.5R - 0.5G ^ Cy = (R - G) »1,
Cb = - 0.25R - 0.25G + 0.5B ^ Cb = (B - ((R + G) »1)) »1.
and its inverse conversion from YCyCb to RGB is:
R = (Y - Cb) + Cy,
G = (Y - Cb) - Cy,
B = (Y + Cb).
The electronic schematics diagrams of both RGB to YCyCb and YCyCb to RGB colors conversion are sequentially presented in figs. 11 - 12.
5. Conclusion
In this paper, three color spaces YCcCr, YCpCg, and YCyCb (YCoCg color space family) have been developed that can be adapted according to the dominant colors contained in an image. The color analysis algorithm can calculate and determine the dominant colors in an image, and then automatically determines the appropriate color space to be applied in that image. The experimental results using sixty test images, which have varying colors, shapes, and textures, indicate that the proposed adaptive color spaces model provides improved performance of 3 % to 10 % better than other color spaces. Likewise, their electronic schematics require only two adders and two subtracters, both for forward and inverse conversions.
Our future research is to apply the dominant color analysis and adaptive color space model (ACSM) algorithm to the JPEG2000 image compression algorithm, and MPEG for video compression.
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Authors' information
Sarifuddin Madenda is a researcher and professor at Gunadarma University, Indonesia. He was born in Raha, Indonesia 7th April 1963. He finished his: B.S degree in Physic Instrumentation at University of Indonesia in 1989; M. S. degree in Electronics from INSA-Lyon, France in 1992; and Ph.D degree in Electronics and Image Processing from Universite de Bourgogne, France in 1995. He is also lecturer at UQO, Quebec - Canada since 2003. Actually, he is Director of Doctoral Program in Information Technology. His research interests are focused on image and video processing, multimedia data compression, content based image and video retrieval, steganography (encryption, decryption, coding) and decoding of multimedia secret documents, real time system architecture (FPGA and ASIC design). E-mail: sarif@staff.gunadarma.ac.id .
Astie Darmayantie was born in Jakarta, Indonesia 27th March 1990. She acquires her Bachelor Degree in Computer Science 2011. She finished her master in 2013, in which brings her to be entitled as Master in Information System Management from Universitas Gunadarma and Master in Computer Vision and Robotics from Universite De Bourgogne. She completed her doctoral degree in information technology in 2018. Her research interests vary from machine learning to health informatics and socio-technical aspects in technology. E-mail: astie@staff.gunadarma.ac.id .
Received July 2, 2020. The final version - February 16, 2021.
