Second compression for pixelated images under edge-based compression algorithms: JPEG-LS as an example

Abstract

This paper details the examination of a particular case of data compression, where the compression algorithm removes the redundancy from data, which occurs when edge-based compression algorithms compress (previously compressed) pixelated images. The newly created redundancy can be removed using another round of compression. This work utilized the JPEG-LS as an example of an edge-based compression algorithm for compressing pixelated images. The output of this process was subjected to another round of compression using a more robust but slower compressor (PAQ8f). The compression ratio of the second compression was, on average, 18%, which is high for random data. The results of the second compression were superior to the lossy JPEG. Under the used data set, lossy JPEG needs to sacrifice 10% on average to realize nearly total lossless compression ratios of the two-successive compressions. To generalize the results, fast general-purpose compression algorithms (7z, bz2, and Gzip) were used too.

Keywords

Data compression lossless lossy Pixelated images PAQ8f

1 Introduction

Data compression is the science of decreasing the size of data files. Compressed data is the final product of the compression process, and it requires less space and can be transmitted quicker. The first compression algorithm removes redundancies in the data [18], and theoretically, the data cannot be compressed further after being compressed by the first compression algorithm; therefore, instead of subjecting the compressed data to the second round of compression, scientists usually enhance the existing compression algorithms or invent other methods of compression. Enhancing the compression ratio of an algorithm can be done via pre-processing by changing the format of the data to make it more amenable for compression, or in-processing by modifying the algorithm from within to increase the compression ratio. Dealing with data in compressed format post-processing is a challenging task, and in most cases, the result of a second compression is an expansion as opposed to a shrinkage. Failing to compress compressed data results in the data being classified as random data [21], which is consistent with the Kolmogorov algorithm’s definition of randomness [23]. There is research that investigated the randomness of compressed data, but most reported the absence of meaningful correlations [3 , 11], reflecting the complexity of the nature of such data. Despite the complexity of the compressed data, the overall behaviour of compressed data is typical across the board and can be captured when analysed based on reference patterns such as the Fibonacci code [10]. However, in the case of certain types of data, compression algorithms could fail to remove (all) redundancies within it, or it creates another redundancy when compressing the data. This paper discusses the edge-based compression algorithm. The algorithm, when removing redundancies from specific data (pixelated data), creates another redundancy. Understanding the algorithm helps in the selection of a suitable algorithm for specific types of data, as certain types of data might require more than one level of compression. The concept developed in this work applies across the board for other algorithms such as PNG, which utilizes the same prediction mechanism for the next pixel value. The rest of this paper is organized in the following order: Section 2 focuses on the background, Section 3 describes the methodologies and the results, and Section 4 concludes this work.

2 Theoretical Background

This section details the foremost example of an edge-based compression algorithm called JPEG-LS. The definition of a pixelated image and how edge-based compression utilizes its pixilation will also be elucidated.

2.1 Edge-Based compressors (and JPEG-LS)

[11] detailed a famous lossless algorithm, called CALIC. The core of this algorithm is a prediction scheme called GAP (gradient- adjusted predictor). Its early work was introduced in [26] and refined in [15]. The idea behind GAP is quite simple; it predicts the current value of the pixel based on the seven neighbors on the top and the left of the current pixel. Another famous algorithm in the category of lossless compression is JPEG-LS. It is registered as a US patent No. 5,680,129 and US patent No. 5,764,374, and owned by HP Co. JPEG-LS was introduced in [22 –24] and it uses the prediction technique called Median Edge Detectors (MED). It predicts the value of the current pixel based on three neighbors (unlike GAP, which require seven neighbors). MED works in a more straightforward way than GAP, as it detects the horizontal and the vertical edge and predicts accordingly. In the case of edge-based model, a combination of the three pixels can be used to venture a guess. Two essential steps need to be carried out before encoding: prediction and error modeling. For the former, the horizontal and vertical edges detection can be done by examining the neighboring pixels of the current pixels, as shown in Figure 1.

Fig. 1

The neighboring pixels around the current pixel.

Pixel B is used when a vertical edge is detected, while pixel A is used when a horizontal edge is detected. When there are no edges, a combination of pixels A, B and C are used. This simple prediction approach is called the MED prediction. Pixel X is predicted as follows: $x = {\begin{matrix} min (A, B) if C \geq \max (A, B) \\ max (A, B) if C \leq \min (A, B) \\ A + B - C otherwise \end{matrix}$ (1) Since it was invented, JPEG-LS has seen widespread use and research efforts are mostly focused on increasing its compression ratio [5 , 25].

2.2 Pixelated image and edge-based compression algorithm

Pixilation is the process of making pixels easily visible. The pixelated images come either from low resolution in artworks, for example, as a deliberate attempt to mask imperfections of details in the images. Pixelated images are heavily used in computer games due to its high-speed requirements. A perfect pixelated image is when the similar local intensity forms a small square of four pixels (2x2) that continually varies as per Figure 2, because if pixels beyond the four pixels (the pixel D specifically) share similar intensities, the algorithm will shift to the run mode. Image processing software such as Photoshop can be used to create such pixelated images.

Fig. 2

An example of the image ideal recompression.

As the prediction mode is the dominant working mode in the pixelated image and due to the similarity in intensities in the pixelated image, the prediction error is mostly zero. One possible way to explain why the JPEG-LS produce compressible output is: When the error is zero, it causes the parameter of Colomb-Rice coding in JPEG-LS (which is called a code parameter k as in [26]) to become mostly 0, which encodes the error in a unary code. The word "mostly" is essential because the parameter of Colomb-Rice in JPEG-LS is affected by the contexts of where the error occurs, which would change the parameter from being zero. When the parameter is zero whereas the the error is not zero,Colomb-Rice is coding the error in a unary code which creates a long sequence of ones (or zeros) that could play an essential role in the creation of a compressible code. For large squares of similar pixels (more significant than 2x2), JPEG-LS will work in a predicted mode on the edges of the square, while in the heart of the square, the run mode dominates. Figure 3 shows a visualization of this concept.

Fig. 3

The regular mode and the run mode.

In the figure, the square with the "X" sign represents the pixel working under the regular (prediction) mode, where JPEG-LS will detect the horizontal (top row) and vertical (left and right column) edges. In the middle, the run mode will occur.

3 The methodology

The datasets used in our experiments were divided into two groups; the first contained images without pixilation and is called group 1, while the second is pixelated images called group 2. Both groups were compressed using JPEG-LS for its first compression phase. PAQ8f was used for the second compression due to it being a robust, lossless compression algorithm and its high compression ratio. The general-purpose compression algorithm was then applied due to its (high) speed, even at a lower compression ratio. The PNG was used alongside the JPEG-LS as a first compressor to ensure that any algorithm that follows the paradigm of edge-based compression algorithm will also produce compressible data. The edge-prediction mechanism and JPEG-2000 uses a different algorithm based on integer wavelet transform. The resulting compressed data was then fed into the second compression algorithm (PAQ8f). The following is a brief description of the algorithm and data sets used in this work.

3.1 Datasets used

The first group (group 1) comprised of 11 non-pixelated images, while the second group (group2) consist of pixelated images (group 2)[1, 2]. The pixelated images received other pixelated images to produce two by two pixels of similar intensities, as described earlier. Both groups were in the raw format (PGM) of 8 bits per pixel. Figure 4 and Figure 5 depict groups 1 and 2, respectively.

Fig. 4

Grey images without pixilation (group 1).

Fig. 5

Grey images without pixilation (group 1).

3.2 Compression algorithms used

The data sets were first compressed using the JPEG-LS compression algorithm via IrfanView. PNG and JPEG-2000 were used for comparison between JPEG-LS and other image compression algorithms.

JPEG-2000 is a wavelet-based lossy-to-lossless transform coder [20]. IrfanView can be used to apply JPEG-2000.

PNG uses a 2-stage compression process: pre-compression filtering (prediction) and the DEFLATE algorithm.

For the second compression, a reliable compressor from the family of PAQ was used, which was the PAQ8f, described in [13] and available at [12]. However, PAQ is a slow compression algorithm due to the context modeling it uses, which is a time-consuming process, and, therefore, for the second compressor, fast general-purpose compressors, such as 7z, Bz2, and Gzip were used for comparisons and generalization.

7z uses the LZMA (Lempel–Ziv–Markov chain algorithm), which includes an improved LZ77 and range encoder. The 7-ZIP software was used to implement this algorithm.

Bzip2 (Bz2 for short) concatenates RLE, Burrows-Wheeler transform, and Huffman coding. It also uses the 7-ZIP software.

Gzip is based on the DEFLATE algorithm, which is a combination of LZ77 and Huffman coding. It also uses the 7-ZIP software.

As the second compression produces a high compression ratio, the double compression was compared with the well-known lossy jpeg [19].

3.3 Second compression for non-pixelated images

The first compression for the compressed data in JPEG-LS format was compressed for the second time using PAQ8F. The measurements used for evaluating the quality of the Compression are as follows:

$CR = \frac{uncompressed_size}{compressed_size}$ (2) $Bpp = \frac{# pixels_before_compression}{# pixls_after_compression}$ (3)

$Space_saving = \frac{100 - compressedsize}{uncompressedsize} * 100$ (4)

The Bpp(bit per pixel) measurement was used due to its status as a global measurement able to show improvements via the two-phases of compression, while the only show improvements from the raw to the first compression or from the first to the second compression. It is also essential to quantify space-saving, and it is shown in percentage form in this work to make it easier to visualize and understand. The results of the group 1 experiment are shown in Table 1.

Table 1

The result of first and second compression for group 1

		First Compression				Second compression
Name	PGM	JPEG-LS	CR	Bpp	Saving %	PAQ8F	CR	Bpp	Saving %
Bee	262,182	106,880	2.453	0.408	59.234	106,090	1.007	0.405	0.739
0.405 Bird	262,182	142,043	1.846	0.542	45.823	141,427	1.004	0.539	0.434
Brain	65,574	20,956	0.320	0.318	68.042	20,862	1.005	3.129	0.449
Fish	262,182	159,669	1.642	0.609	39.100	159,337	1.002	0.608	0.208
Fruit	262,182	169,199	1.550	0.645	35.465	168,243	1.006	0.642	0.565
House	262,182	168,639	1.555	0.643	35.679	168,112	1.003	0.641	0.313
Liver	262,182	72,039	3.639	0.275	72.523	71,653	1.005	0.273	0.536
Lung	129,188	62,475	2.060	0.485	51.459	62,709	1.004	0.484	0.373
Monkey	262,182	197,804	1.325	0.753	24.555	197,319	1.002	0.754	0.245
N1	262,182	82,785	0.314	0.317	68.425	82,197	1.007	0.316	0.710
People	262,182	128,269	2.044	0.489	51.076	127,918	1.003	0.488	0.274
AVERAGE			2.219	0.499	50.126		1.004	0.497	0.440

The average compression ratio of the first compression via JPEG-LS for this group is high (2.219). The average saving is 50.126 %, with a minimum of 35.465 % and a maximum of 72.523 %. The saving is half of the image size, confirmed by its bpp value of 0.499. For the second compression via PAQ8f, the results show almost no improvement in the compression ratio, and the average bpp is nearly the same as that of the first Compression. There is only a marginal improvement in its bpp (0.002) and saving size (0.440 %) in the second compression ratio, both of which are almost negligible. The result of the second compression agrees with the common intuition in data compression, where it is assumed that the second compression is complicated, and if it does take place, it is purely by chance.

3.4 Second compression on pixelated images

Since the images in this group were pixelated similarly, it is expected that the second compression would produce a close compression ratio. Table 2 shows the result of the application of the second compression using PAQ8F.

Table 2
The result of first and second compression for group 2

First Compression Second compression

Name PGM JPEG-LS CR Bpp Saving % PAQ8F CR Bpp Saving %

Architecture 272,015 83,740 3.248 0.308 69.215 68,889 1.216 0.253 17.735

Boats 272,655 60,674 4.494 0.223 77.747 49,766 1.219 0.183 17.978

Car 272,655 68,619 3.973 0.252 74.833 56,796 1.208 0.208 17.230

House1 409,638 109,421 3.744 0.267 73.288 92,133 1.188 0.225 15.800

Jellyfish 272,655 36,013 7.571 0.132 86.792 29,411 1.224 0.108 18.332

Mosque 89,160 25,069 3.557 0.281 71.883 21,361 1.174 0.240 14.791

Old man 502,727 117,494 4.279 0.234 76.629 93,708 1.254 0.186 20.244

Old women 327,695 71,429 4.588 0.218 78.203 59,528 1.200 0.182 16.661

Orchid 272,655 51,517 5.293 0.189 81.105 42,185 1.221 0.155 18.114

Owl 307,215 77,475 3.965 0.252 74.782 56,920 1.361 0.185 26.531

Pier 272,655 64,891 4.202 0.238 76.200 53,362 1.216 0.196 17.767

Building 1,416,933 257,743 5.497 0.182 81.810 208,103 1.239 0.147 19.259

Tiger 845,642 234,571 3.605 0.277 72.261 188,384 1.245 0.223 19.690

AVERAGE 4.463 0.235 76.519 1.228 0.192 18.472

	First Compression	Second compression
Name	PGM	JPEG-LS	CR	Bpp	Saving %	PAQ8F	CR	Bpp	Saving %
Architecture	272,015	83,740	3.248	0.308	69.215	68,889	1.216	0.253	17.735
Boats	272,655	60,674	4.494	0.223	77.747	49,766	1.219	0.183	17.978
Car	272,655	68,619	3.973	0.252	74.833	56,796	1.208	0.208	17.230
House1	409,638	109,421	3.744	0.267	73.288	92,133	1.188	0.225	15.800
Jellyfish	272,655	36,013	7.571	0.132	86.792	29,411	1.224	0.108	18.332
Mosque	89,160	25,069	3.557	0.281	71.883	21,361	1.174	0.240	14.791
Old man	502,727	117,494	4.279	0.234	76.629	93,708	1.254	0.186	20.244
Old women	327,695	71,429	4.588	0.218	78.203	59,528	1.200	0.182	16.661
Orchid	272,655	51,517	5.293	0.189	81.105	42,185	1.221	0.155	18.114
Owl	307,215	77,475	3.965	0.252	74.782	56,920	1.361	0.185	26.531
Pier	272,655	64,891	4.202	0.238	76.200	53,362	1.216	0.196	17.767
Building	1,416,933	257,743	5.497	0.182	81.810	208,103	1.239	0.147	19.259
Tiger	845,642	234,571	3.605	0.277	72.261	188,384	1.245	0.223	19.690
AVERAGE			4.463	0.235	76.519		1.228	0.192	18.472

The compression ratio of the first compression, on average, is 4.463, with an average saving of 76.5 %, which is very high for lossless compression. The real saving of the files does not differ from the average, and its minimum is 69.215 %, and its maximum is 86.792 %. Relative to the first group, the compression ratio for the first compressor of this group is high. The second compression using PAQ8f resulted in a compression ratio of 1.228, with an average saving of 18.472 %, which is also a very high percentage for the data that is supposed to be random. The overall reduction in size can be obtained from the global bpp, reduced from 0.235 to 0.192, with an overall saving average of ~ 95 %. Such an effective compression needs to be compared with the lossy algorithm, which will be detailed in later sub-sections. It can be concluded from the results of the second compression that edge-based compression algorithms best compress pixelated images due to the output being compressible again at a percentage of saving.

3.5 The second Compression using general- purpose compressors

The PAQ8F compressor used in the experiments is powerful but slow. Three commonly used general-purpose compressors described earlier to ensure that the second compression can be performed using any general-purpose compressor. These compressors are typically used extensively to decrease resources, and the comparison has a practical impact. Table 3 shows the result of applying the second round of compression using fast general-purpose compressors.

Table 3
Second compression using general-purpose algorithms

Second Compression

Name PGM Jpeg-Ls Paq8f 7z Bz2 Gzip

Architecture 272,015 83,740 68,889 72,037 72,292 72,415

Boats 272,655 60,674 49,766 53,214 54,044 53,320

Car 272,655 68,619 56,796 60,153 60,887 60,328

house1 409,638 109,421 92,133 96,489 96,736 96,904

Jellyfish 272,655 36,013 29,411 31,518 32,519 31,255

Mosque 89,160 25,069 21,361 22,502 22,855 22,391

old man 502,727 117,494 93,708 99,101 100,087 100,008

old women 327,695 71,429 59,528 62,752 63,421 63,154

Orchid 272,655 51,517 42,185 45,443 46,153 45,430

Owl 307,215 77,475 56,920 69,158 69,544 69,281

Pier 272,655 64,891 53,362 56,788 57,684 57,267

Building 1,416,933 257,743 208,103 222,411 227,946 223,425

Tiger 845,642 234,571 188,384 197,482 197,814 199,433

AVERAGE 78,504 83,773 84,768 84,201

			Second Compression
Architecture	272,015	83,740	68,889	72,037	72,292	72,415
Boats	272,655	60,674	49,766	53,214	54,044	53,320
Car	272,655	68,619	56,796	60,153	60,887	60,328
house1	409,638	109,421	92,133	96,489	96,736	96,904
Jellyfish	272,655	36,013	29,411	31,518	32,519	31,255
Mosque	89,160	25,069	21,361	22,502	22,855	22,391
old man	502,727	117,494	93,708	99,101	100,087	100,008
old women	327,695	71,429	59,528	62,752	63,421	63,154
Orchid	272,655	51,517	42,185	45,443	46,153	45,430
Owl	307,215	77,475	56,920	69,158	69,544	69,281
Pier	272,655	64,891	53,362	56,788	57,684	57,267
Building	1,416,933	257,743	208,103	222,411	227,946	223,425
Tiger	845,642	234,571	188,384	197,482	197,814	199,433
AVERAGE			78,504	83,773	84,768	84,201

As can be seen in Table 3, the files for group 2 are still compressible with an excellent ratio using fast general-purpose algorithms, which can create a replacement for the lossy Compression for these images. This seems to suggest that it is better to use PAQ8f and similar compressors for offline processes, or when there is a need to decrease sizes at any cost. If speed is vital, as is the case with online compression or in a situation where time is a critical factor, a faster general-purpose algorithm should be used instead.

3.6 First Compression using JPEG-LS, PNG and JPEG-2000

Despite using JPEG-LS as a first compressor, it should be pointed out that any algorithm under edged-based also behaves similarly. For this reason, one algorithm from this category, and another algorithm from a different data compression category were examined.

One of the most widely used algorithms is PNG. It utilizes the same prediction scheme as JPEG-LS. It is therefore expected that the PNG produces a compressible code for the same set of pixelated data samples. A lossless JPEG-2000, which uses an integer-based wavelet transformation, was used to eliminate the idea that any lossless image compression could behave similarly with the edge-based algorithms. Its mechanism is far too dissimilar to the edge-based algorithms. The second compression was performed using PAQ8F, and the results shown in Table 4.

Table 4
The first compression using JPEG-LS, PNG, AND JPEG-2000

First compression Second compression

Name JPEG-LS PNG JPEG-2K JPEG-LS saving % PNG Saving % JPEG-2K Saving %

Architecture 83,740 106,28 182,37 68,889 17.735 96,235 9.450 182,44 -0.041

Boats 60,674 65,927 105,24 49,766 17.978 63,312 3.967 105,27 -0.029

Car 68,619 81,334 131,97 56,796 17.230 76,551 5.881 132,01 -0.031

House 109,42 122,68 237,86 92,133 15.800 115,40 5.935 237,96 -0.043

Jellyfish 36,013 32,676 48,730 29,411 18.332 31,351 4.055 48,722 0.016

Mosque 25,069 31,493 54,648 21,361 14.791 28,678 8.938 54,646 0.004

Old man 117,49 139,59 203,54 93,708 20.244 133,13 4.632 203,62 -0.038

Old women 71,429 73,563 137,49 59,528 16.661 71,022 3.454 137,54 -0.038

Orchid 51,517 55,161 79,915 42,185 18.114 53,054 3.820 76,925 3.741

Owl 77,475 87,103 166,27 56,920 26.531 81,529 6.399 166,34 -0.040

Pier 64,891 72,213 117,07 53,362 17.767 69,200 4.172 117,10 -0.026

Building 257,74 258,05 413,81 208,10 19.259 244,89 5.099 413,98 -0.041

Tiger 234,57 293,14 453,07 188,38 19.690 269,9 7.930 453,27 -0.045

Averages 18.472 5.672 0.261

	First compression	Second compression
Architecture	83,740	106,28	182,37	68,889	17.735	96,235	9.450	182,44	-0.041
Boats	60,674	65,927	105,24	49,766	17.978	63,312	3.967	105,27	-0.029
Car	68,619	81,334	131,97	56,796	17.230	76,551	5.881	132,01	-0.031
House	109,42	122,68	237,86	92,133	15.800	115,40	5.935	237,96	-0.043
Jellyfish	36,013	32,676	48,730	29,411	18.332	31,351	4.055	48,722	0.016
Mosque	25,069	31,493	54,648	21,361	14.791	28,678	8.938	54,646	0.004
Old man	117,49	139,59	203,54	93,708	20.244	133,13	4.632	203,62	-0.038
Old women	71,429	73,563	137,49	59,528	16.661	71,022	3.454	137,54	-0.038
Orchid	51,517	55,161	79,915	42,185	18.114	53,054	3.820	76,925	3.741
Owl	77,475	87,103	166,27	56,920	26.531	81,529	6.399	166,34	-0.040
Pier	64,891	72,213	117,07	53,362	17.767	69,200	4.172	117,10	-0.026
Building	257,74	258,05	413,81	208,10	19.259	244,89	5.099	413,98	-0.041
Tiger	234,57	293,14	453,07	188,38	19.690	269,9	7.930	453,27	-0.045
Averages					18.472		5.672		0.261

PNG, similar to JPEG-LS, produces compressible code even though the second compression of JPEG-LS produces a higher size reduction over PNG. This could be because both algorithms handle post-prediction differently.JPEG-2000, on the other hand, does not produce any compressible code because it is not edge-based algorithm; hence the result of its second compression is marginal.

3.7 Second compression against lossy compression

The previous results from the second compression lead to the comparison with the lossy compression algorithm. The lossy JPEG was selected due to its ubiquity in usage and the literature. The parameter of quality was adjusted to be as close as possible to the results of the second compression, as shown in Table 5.

Table 5
Comparing the second compression with the lossy JPEG

Name First Compression Second Compression (PAQ8F) Lossy JPEG Quality%

Architecture 83,740 68,889 69,740 81

Boats 60,674 49,766 48,682 91

Car 68,619 56,796 57,371 89

House 109,421 92,133 96,407 85

jellyfish 36,013 29,411 29,002 95

mosque 25,069 21,361 28,506 90

old man 117,494 93,708 92,109 91

old women 71,429 59,528 58,945 90

orchid 51,517 42,185 42,456 94

Owl 77,475 56,920 57,931 80

Pier 64,891 53,362 52,216 89

Building 257,743 208,103 202,673 92

Tiger 234,571 188,384 194,360 88

Name	First Compression	Second Compression (PAQ8F)	Lossy JPEG	Quality%
Architecture	83,740	68,889	69,740	81
Boats	60,674	49,766	48,682	91
Car	68,619	56,796	57,371	89
House	109,421	92,133	96,407	85
jellyfish	36,013	29,411	29,002	95
mosque	25,069	21,361	28,506	90
old man	117,494	93,708	92,109	91
old women	71,429	59,528	58,945	90
orchid	51,517	42,185	42,456	94
Owl	77,475	56,920	57,931	80
Pier	64,891	53,362	52,216	89
Building	257,743	208,103	202,673	92
Tiger	234,571	188,384	194,360	88

The quality parameter of lossy JPEG compression was adjusted manually for each file, and the last column represents the best quality percentage. The second compression, which is lossless, will retain the details of the original images, while the lossy JPEG will sacrifice a tremendous amount of detail to decrease the original file into approximately the same size. Figure 6a compares an example of an original and restored image after lossy JPEG to show the details that were removed by lossy JPEG from the image,despite it is visually challenging for the eye to differentiate.The size of the "Old_woman" becomes 59,528 bytes after the second compression. In order to lower the original size of the image using a lossy JPEG, the quality of the compression was set to ~ 90 % with ~ 10 % loss of information, the latter of which is depicted in Figure 6c to showcase the effects of loss, where grey represents the pixel values changed by lossy JPEG.

Fig. 6

The details loss by JPEG compression compared to the original.

4 Conclusion

This study addresses a rare case in data compression, where the compressed data are re-compressed. It shows how JPEG-LS and edge-based compression algorithms, in general, produce compressible data that can be compressed (again) using any general compression algorithms. This case occurs when the data under the first compression algorithm are pixelated images, where similar intensities composed of squares start from 2 by 2 pixels. The compression ratio of the second compression is very high (~ 18 % under PAQ8F) relative to that of random data. Two successive compression were compared to lossy JPEG, and it was seen that the two successive compression for this type of data are favorable relative to the lossy compressor. The quality parameter of the lossy JPEG, on average, needs to be adjusted to ~ 90 % of the quality, which translates into ~ 10 % missing details. The details removed by lossy JPEG decreased the overall quality of the reconstructed image, as shown in previous sub-sections, suggesting that the use of double compression of pixelated images gives better result than the lossy compression.However it is challenging to identify the pixelated image so the edge-based compression algorithms can be apply. This problem can be solved if the we know in advance what kind of images usually used in a particular field.For example, in computer games where pixelated images are frequently used, or when pixelated images are deliberately used as a kind of art.

References

Pixelated image | Free Photo. URL https://www.freepik.com/free-photo/pixelated-image_946034.htm.

Pattern Super Mario Pixel Art - Free vector graphic on Pixabay. URL https://pixabay.com/illustrations/pattern-super-mario-pixel-art-block.

Al-khayyat

K.A.

, Al-shaikhli

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