A spatial image compression algorithm based on run length encoding

Bulletin of Electrical Engineering and Informatics
Vol. 10, No. 5, October 2021, pp. 2607∼2616
ISSN: 2302-9285, DOI: 10.11591/eei.v10i5.2563 ❒ 2607
A spatial image compression algorithm based on run length
encoding
Abdel Rahman Idrais1
, Inad Aljarrah2
, Osama Al-Khaleel3
1,2,3
Department of Computer Engineering, Jordan University of Science and Technology, Irbid, Jordan
1
Department of Electrical and Computer Engineering, Concordia University, Montreal, Canada
Article Info
Article history:
Received Apr 22, 2020
Revised Apr 29, 2021
Accepted Jul 29, 2021
Keywords:
Artificial intelligence
Compression algorithms
Image coding
Inter-pixel redundancy
Run-length coding
ABSTRACT
Image compression is vital for many areas such as communication and storage of data
that is rapidly growing nowadays. In this paper, a spatial lossy compression algorithm
for gray scale images is presented. It exploits the inter-pixel and the psycho-visual
data redundancies in images. The proposed technique finds paths of connected pixels
that fluctuate in value within some small threshold. The path is calculated by looking
at the 4-neighbors of a pixel then choosing the best one based on two conditions; the
first is that the selected pixel must not be included in another path and the second is
that the difference between the first pixel in the path and the selected pixel is within the
specified threshold value. A path starts with a given pixel and consists of the locations
of the subsequently selected pixels. Run-length encoding scheme is applied on paths to
harvest the inter-pixel redundancy. After applying the proposed algorithm on several
test images, a promising quality vs. compression ratio results have been achieved.
This is an open access article under the CC BY-SA license.
Corresponding Author:
Inad Aljarrah
Department of Computer Engineering
Jordan University of Science and Technology
Irbid, Jordan
Email: inad@just.edu.jo
1. INTRODUCTION
With the vast increase of usage of social media among people, the amount of images and videos
transmitted is increasing dramatically [1], [2]. For example, on January 2019; over 240 billion photos had
been uploaded by Facebook website users, with 350 million new daily photos. This requires a huge amount
of storage and a very high-speed communication link [3]. Therefore, a scheme to reduce the size of images
while maintaining an acceptable image resolution and quality is needed [4]. Image compression is a technique
that reduces the size of an image by minimizing the number of bits needed to represent it [5]-[8]. Image
compression methods evaluation is an application dependent. A good image compression technique for a given
application is not necessarily good for another one [9]-[11].
There are two main categories of image compression techniques; lossless and lossy. In lossless im-
age compression, the quality of the compressed image is similar to the quality of the original image. All
information of the original image are preserved in the compressed one [12]. On the other hand, lossy im-
age compression slightly alters the information of original image in a way that decreases the quality of the
compressed image comparing to the original one [13]-[15]. In order to judge the efficiency of a compression
scheme, a performance measurement is required [16]. The most commonly used performance measurements
are: the compression ratio, the execution time of the compression and decompression processes, and the signal
Journal homepage: http://beei.org

2608 ❒ ISSN: 2302-9285
to noise ratio [17]-[19]. The compression ratio (CR), which is calculated using (1), is defined as the ratio
between the size of the original image (N1) and the size of the compressed image (N2).
CR =
N1
N2
(1)
High speed compression and decompression are necessary for real time applications. In lossy ap-
proaches, the peak signal to noise ratio (PSNR) measures the quality of the decompressed image [20]. The
value of the PSNR in lossless techniques is useless as the original and the decompressed images are identical.
The PSNR is calculated using (2) and (3).
PSNR = 10 log10
2552
RMSE2
(2)
RMSE =
r
1
MN
X X
((f(x, y) − f′(x, y)))2) (3)
where (RMSE) is the root mean square error, M and N represent the length and width of image
respectively, f(x, y) is the pixel value in the original image at x and y coordinates, and f′
(x, y) is the pixel
value in the decompressed image at x and y coordinates.
Every image contains some redundant data that can be exploited in image compression [21], [22].
By eliminating such redundant data, the amount of data required to represent the image is reduced. Three
different types of redundancy can be found in an image: inter-pixel redundancy, psycho-visual redundancy, and
coding redundancy. Inter-pixel redundancy means that the intensities of neighboring pixels are not statistically
independent and a correlation do exist among them. Inter-pixel redundancy (also called the spatial redundancy)
is related to the fact that a pixel value can be predicted from its location and the values of its neighboring pixels.
The human eye does not respond to all incoming visual information with equal vulnerability; some
information has less relative importance. This property is called psycho-visual redundancy and can be used
to remove some redundant information without affecting how the human eye perceive the image. Most of
image compression algorithms exploit the psycho-visual redundancy, like the discrete cosine transform (DCT)
[23]-[25].
Different image compression schemes have been proposed in literature. These schemes are either
lossy or lossless. In either case, the ultimate goal is to achieve high compression ratio with reasonable execution
time. Some of these schemes are summarized in this section. A review of the compression techniques in digital
image processing and a brief description of the main technologies and traditional format that commonly used
in image compression have been presented in [26]. Moreover, the formats that are used to reduce redundant
information in an image are presented.
The work in [27] presents a new method to find the most redundant image structure elements; like
patterns, textures, and edges to compress and encode them. This method is called super-spatial prediction.
The goal of super-spatial prediction method is to recognize the best prediction of structure elements by using
the idea of motion prediction in video coding. To find the prediction of current image block the super-spatial
prediction scheme search for best prediction by calculating the minimum difference between the blocks.
Khalil the authors of [28] introduce a new method of run-length coding; the new method is easier
and more efficient than the standard one. It computes the discrete cosine transform (DCT) and works on its
quantized coefficients. The experimental results of Khalil enhance the compression ratio compared with the
older version of run-length coding method. Because of the speed and the simplicity of his method; it may be
used in data compressors such as video compression.
A new compression scheme based on the pixels’ locations is proposed in [29]. The scheme simply
divides the image into 4×4 non-overlapping blocks and works on each block separately. It takes the most
frequent pixel in that block and deletes all of its occurrences, and does that for the other less frequent pixels
with the same way. They compare their scheme with known schemes like GIF, TIFF, and PNG. When applying
them on 200 textbook images, they claim gaining better compression ratio in 83% of the cases.
Adaptive thinning algorithms by using recursive point removal methods is a new concept for compres-
sion that has been proposed by [30]. This scheme is more appropriate for modeling sharp edges and related
features in digital images. Their results are compared with another compression method called SPIHT, and the
Bulletin of Electr Eng & Inf, Vol. 10, No. 5, October 2021 : 2607 – 2616

Bulletin of Electr Eng & Inf ISSN: 2302-9285 ❒ 2609
quality is represented by the peak signal to noise ratio (PSNR). Their scheme is tested on some sample images
and got better results than SPIHT at the sharp edges in the decompressed image.
Azman authors in [31] have combined predictive differential pulse code modulation (DPCM) and in-
teger wavelet transform (IWT) in order to achieve a hybrid prediction lossless image compression approach.
They have analyzed the performance of their proposed algorithm by calculating the entropy and the compres-
sion ratio. Experimentally, sequence of DPCM-IWT-huffman gives the best compression results.
The work of [32] presents two lossless compression schemes, the min-max differential (MMD) and
the min-max predictive. The two methods are combined with the existing compression methods to enhance
them. The authors apply the proposed schemes for medical images. They test some images of CT brain scans
and the results show an improvement over other compression methods such as Huffman encoding, arithmetic
coding, and Lempel-Zif.
Two algorithms are proposed by [33] to maximize the performance of JPEG by combining the op-
timization of discrete cosine transform, huffman code, and quantization of JPEG encoder. The goal of first
algorithm is to find the optimal discrete cosine transform indices in the form of run-size pairs. Then, the second
algorithm iteratively optimized run-length coding, quantization, and Huffman coding. Both of the proposed
algorithms can be used in digital camera image compression, transcoding, and MPEG frame optimization.
A new predictive lossless image compression scheme is found in [34]. The proposed algorithm uses
the gradient edge detector as a predictor to remove the spatial data redundancy. The performance of the pro-
posed algorithm is efficient for 12-bit medical images and has a good compression ratio versus JPEG-LS.
A novel medical image compression approach has been proposed in [35]. The approach combines
geometric active contour model and quincunx wavelet transform. A level set for an optimal reduction is has
been used to localize all the part that contain the pathological. The quincunx wavelet coupled is then used with
the set partitioning in hierarchical trees (SPIHT) algorithm. A satisfactory results have been achieved.
The rest of this paper is organized is being as: section 2 discusses the proposed compression technique
and illustrates it using an example. The experimental results are presented and discussed in section 3. Finally,
the conclusions are provided in section 4.
2. RESEARCH METHOD
The proposed algorithms exploit the psycho-visual and inter-pixel data redundancies. They are lossy
compression algorithms that work with pixels’ values in the spatial domain. Thus, the decompressed image
will not be exactly similar to the original image.
The proposed method finds paths between neighboring pixels that have same values within some
threshold. The path is calculated by investigating the 4-neighbors of a pixel, as shown in Figure 1 (a). One of
the neighbors of the central pixel is chosen according to a certain technique. The location of the selected pixel
with respect to the central pixel is stored in the path and marked as visited. The locations are relative to the
middle pixel. A location can be UP, DOWN, LEFT, or RIGHT as illustrated in Figure 1 (b). A path consists
of a starting pixel value and continues with a sequence of pixels locations that are subsequently selected. The
criterion to select a pixel out of 4-neighbors is based on two conditions: the selected pixel must be unvisited
and the difference between the starting pixel value and the selected pixel value is within a threshold. When
there are two or more pixels, among the 4-neighboring pixels, satisfy the conditions, the selection is performed
based on the values of the neighbors of those neighbors. In such case, the pixel that has the minimum difference
with one of its neighbors is selected. A path ends once none of the 4-neighbors of a selected pixel satisfies the
condition. The image is investigated from top-left moving down-right column by column.
183
183
183 173
173
173 182
182
182
(a)
Left Right
Up
Down
Pixel
(b)
Figure 1. The 4-neighbors pixels and their directions: (a) the 4-neighbors of a centered pixel, (b) the
directions of 4-neighbors pixels
A spatial image compression algorithm based on run length encoding (Abdel Rahman Idrais)

2610 ❒ ISSN: 2302-9285
In the compression stage, the compressed image consists of a series of connected paths. Each path
is represented using the value of the starting pixel followed by the consecutive pixels’ locations (UP, DOWN,
LEFT, or RIGHT). Finally, a STOP code is inserted at the end to indicate the termination of the path. One
example of a path is shown in Figure 2. The number of bits needed to represent the value of the starting pixel
is 8. The four directions that are used to specify the location of a pixel can be replaced by three path directions
(LEFT, RIGHT, and STRAIGHT), because the previous pixel will not be chosen again. Also, it should be noted
that a right location will be added at the beginning of any path so that when the path directions are calculated
the length of the path is preserved due to the fact that the number of directions will be one less than the number
of locations.
RIGHT,LEFT,LEFT...
Value Locations Stop Code
{100, STOP}
Figure 2. A sample path which contains: value of starting pixel, the following pixels directions and a stop code
Table 1 shows how to map the location of a pixel by the equivalent path direction. It should be pointed
out that the STOP code can be represented using three consecutive LEFT or RIGHT direction codes. This can
be done because such a sequence is impossible to occur in a real path. This leads to having any path being
represented using only the path directions (LEFT, RIGHT, and STRAIGHT) and the starting 8-bit pixel value.
Table 1. Conversion from pixel location to path direction and from path direction to pixel location
Conversion from pixel location to path direction Conversion from path direction to pixel location
Location 2*
Path
direction
Direction 2*Location
Current pixel Next pixel Current Next
4*UP UP STRAIGHT 3*STRAIGHT LEFT UP
LEFT LEFT RIGHT DOWN
RIGHT RIGHT STRAIGHT RIGHT
DOWN ——- 3*LEFT LEFT LEFT
4*DOWN UP ——- RIGHT RIGHT
LEFT RIGHT STRAIGHT UP
RIGHT LEFT 3*RIGHT LEFT DOWN
DOWN STRAIGHT RIGHT UP
4*LEFT UP RIGHT STRAIGHT LEFT
LEFT STRAIGHT 3*DOWN LEFT RIGHT
RIGHT ——- RIGHT LEFT
DOWN LEFT STRAIGHT DOWN
4*RIGHT UP LEFT
LEFT ——-
RIGHT STRAIGHT
DOWN RIGHT
As an example, Figure 3 (a) shows a path of pixels (R, D, R, D, D, R, U, R, U, L, U). The path is
created based on the location of next pixel with respect to current one. After adding a right at the beginning, the
path locations become (R, R, D, R, D, D, R, U, R, U, L, U). All selected pixels must be within the threshold,
and each pixel value will be replaced by the value of the first pixel. Figure 3 (b) shows how to construct the
path using its direction (S, R, L, R, S, L, L, R, L, L, R).
In the decompression stage, we need to reconstruct the compressed image using all paths. Each path
contains the value of the starting pixel, path directions (LEFT, RIGHT, and STRAIGHT), and ends with the
STOP code. The directions of each path are converted to pixel locations (as shown in Table 1). Then the
decompressed image is constructed by filling the value of the starting pixel on each pixel location.
There are three different approaches that will be explained in the next three sections. For selecting and
choosing the most appropriate neighbors of a given pixel, three different approaches have investigated. These
approaches are: compression with search depth (D=1), compression with search depth (D=2), and compression
with search depth (D=5).

R
R
U
R
D
D
R
U
L
D
U
(a)
R
S
L
L
R
R
S
L
L
L
R
(b)
Figure 3. Example of construction the path based on pixels locations and using the path directions: (a) the
path based on pixels locations, (b) the path using path directions
2.1. Compression with search depth (D=1)
In the (D=1) approach, initially, the top-left pixel value is chosen as a starting pixel and is added to the
path. Then, one of the 4-neighbors (UP, DOWN, LEFT, or RIGHT) that is unvisited and has minimum differ-
ence within the threshold value is selected. The process is repeated for the selected pixel until all neighbors of
the newly selected pixel are visited or none of them is within the threshold value. The Stop code is then added
to the path. An unvisited pixel from top left moving down right is chosen to be a starting pixel in the second
path. The pseudo-code in Figure 4 demonstrates this approach. During constructing the path, if there are two
or more neighbors that have the same difference then one of them is randomly chosen. Once all pixels in the
image are marked as visited, the path set is completed and is ready to be converted from path location codes to
path direction codes.
Figure 4. A pseudo-code which presents (D=1) approach
In Figure 4, Image Matrix is the matrix that contains all pixel’s values, Visited Matrix is the matrix
that marks each pixel as ’visited’ or ’not visited’, First Value is the pixel value of the current path, path is
an array that stores the pixels values and locations, threshold is the threshold value, Path location contains
one value form four pixels locations (UP, LEFT, RIGHT, and DOWN), UP Neighbor is the upper neighbor
of a pixel, Left Neighbor is the left neighbor of a pixel, RIGHT Neighbor is the right neighbor of a pixel,

2612 ❒ ISSN: 2302-9285
DOWN Neighbor is the down neighbor of a pixel, I is the x Coordinate of the pixel, J is the y coordinate of the
pixel, and counter is incremented when a new pixel is marked as visited.
2.2. Compression with search depth (D=2)
In search depth (D=2), the top-left pixel value is initially added to path as in search depth (D=1).
However, the next pixel in the path is not directly determined based on investigating the 4-neighbors. Instead,
in this case all neighbors pixels that are within the specified threshold are determined. Let assume that these
pixels belongs to group A. Then the 4-neighbors of each pixel in group A are investigated and those satisfy the
criteria are specified. Hence, the pixel from group A that owns more pixels that satisfy the criteria is chosen
to be in the path. When all neighbors of selected pixel are visited or none of them is within the threshold
value, the stop code is added to path and we select an unvisited pixel from the top left moving down right.
The pseudo-code of this approach is depicted in Figure 5. After visiting all pixels in the image, the paths are
complete and are ready for conversion from path location to path direction.
Figure 5. A pseudo-code which presents (D=2) approach
2.3. Compression with search depth D=5
Similarly as in search depth (D=1) and (D=2), in this approach, the top-left pixel value is initially
added to the path. The 4-neighbors of the pixel are investigated and their neighbors are investigated and the
neighbors of the neighbors are investigated up to 5 levels as long as the pixels do satisfy the unvisited and
threshold criteria. Therefor, this approach covers the search depth (D=3)and (D=4). The direction which has
more pixels that satisfy the criteria is adopted and the pixel in that direction is added to the path. This added
pixel should have up to five unvisited sub-neighbors that are within the threshold. It might have four or three
sub-neighbors depending on how many levels we could span. When all neighbors of the selected pixel are
visited or none of them is within threshold value, the stop code is added to path and we select an unvisited pixel
from top left moving down right. The pseudo-code of this approach is depicted in Figure 6. After visiting all
pixels in the image, the paths are complete and are ready to be converted from path location to path direction.

Figure 6. A pseudo-code which presents (D = 5) approach
3. RESULT AND DISCUSSION
The compression techniques presented above have been implemented using Matlab. The efficiency
of the algorithms has been tested using some standard images like Peppers, Lena, and Cameraman. The test
is carried out by compressing and decompressing the images and then comparing the output (decompressed)
image with the input (original) image. For each image, the signal to noise ratio and the root mean square error
is calculated as measures for the quality of the output image. Also, the compression ratio for the compressed
images are calculated. All of these results have been studied versus increasing the threshold value. The results
have been collected for threshold values of 4, 8, 12, 16, and 20. All the different search depth approaches
(D=1), (D=2), and (D=5) have been considered. All of the collected results have been listed in Table 2.
Table 2. Compression ratio and PSNR in all depths with threshold equal to 4, 8, 12, 16, and 20
2*Threshold 2*Image (D = 1) (D = 2) (D = 5)
CR PSNR CR PSNR CR PSNR
3*4 Peppers 1.89 43.33 2.01 41.84 2.00 41.84
Lena 1.88 43.32 1.98 41.79 1.99 41.86
Cameraman 2.27 44.34 2.40 41.78 2.39 41.68
3*8 Peppers 2.37 38.39 2.63 35.99 2.64 35.96
Lena 2.34 38.4 2.60 35.99 2.62 36.12
Cameraman 2.67 39.55 2.94 36.12 2.92 36.19
3*12 Peppers 2.62 35.69 3.02 32.73 3.04 32.71
Lena 2.57 35.79 2.99 32.68 3.01 32.87
Cameraman 2.87 37.08 3.24 32.91 3.23 32.71
3*16 Peppers 2.76 33.94 3.26 30.37 3.28 30.25
Lena 2.70 34.12 3.23 30.35 3.25 30.54
Cameraman 2.99 35.26 3.43 30.70 3.41 30.57
3*20 Peppers 2.84 32.71 3.43 28.67 3.44 28.46
Lena 2.79 32.86 3.40 28.51 3.42 28.67
Cameraman 3.06 34.03 3.54 28.34 3.53 28.13

2614 ❒ ISSN: 2302-9285
To demonstrate the impact of increasing the threshold value on the compression ratio (CR) and on the
peak signal to noise ratio (PSNR), in Figure 7 (a), the CR is plotted versus the threshold value. Also, in Figure
7 (b), the PSNR is plotted versus the threshold value. This has been done for the Lena image. It can be easily
figured out that the CR increases with the increase of the threshold value as shown by Figure 7 (a). While, the
quality of the image decreases as the threshold is increased as shown by Figure 7 (b).
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
4 6 8 10 12 14 16 18 20 22
Compression
Ratio
Threshold
D = 1
D = 2
D = 5
(a)
28
30
32
34
36
38
40
42
44
46
4 6 8 10 12 14 16 18 20 22
PSNR
Threshold
D = 1
D = 2
D = 5
(b)
Figure 7. Threshold vs. compression ratio and PSNR for depth one, two, and five: (a) threshold vs.
compression ratio, (b) threshold vs. PSNR
4. CONCLUSION
A spatial lossy compression technique that is based on inter-pixel and psych-visual redundancies has
been proposed. The approach in the proposed technique is to find paths between neighboring pixels that have
close values within some threshold. Paths are constructed by investigating the neighborhood of the current
pixel for a certain depth. In the nearest depth, the next level neighborhood is investigate. While, in next higher
depth neighborhood of the neighborhood is investigate and son. In order to determine the direction of the path,
the value of the current pixel is compared with the values of all unvisited pixels in its neighborhood. This is
repeated for a number of times that is basted on the chosen depth. Three different depths have been tested and
the compression ratio versus the image quality results have been reported for five different threshold values.
Increasing the search depth from (D=1) to (D=2) would improve the compression ration with a loss in the
image quality. On the other hand, very minor changes, on the compression ration and the image quality, arise
when moving from search depth (D=2) to (D=5). The techniques have been implemented using MATLAB.
Promising compression results have been achieved.
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BIOGRAPHIES OF AUTHORS
Abdel Rahman Idrais (Student Member, IEEE) received the B.Sc. and M.Sc. degrees in Computer
Engineering from Jordan University of Science and Technology, Irbid, Jordan, in 2011 and 2015,
respectively. He is currently working toward the Ph.D. degree in Electrical and Computer Engineering
with Concordia University, Montreal, QC, Canada, under supervision of Dr. M. Omair Ahmad and
Dr. M.N.S. Swamy. His research interests include machine and deep learning, image processing,
computer vision.
Inad Aljarrah is an Associate Professor at the Department of Computer Engineering at Jordan Uni-
versity of Science and Technology. He received his B.S. in Electrical Engineering from Jordan Uni-
versity of Science and Technology in 1999. He received his Masters and Ph.D. degrees in Electrical
and Computer Engineering from Ohio University, Athens, Ohio, USA in the years 2002 and 2006
respectively. His research interests are Computer Vision, Image Processing and Analysis, and Artifi-
cial Intelligent systems. Currently he is a visiting scholar at the Electrical and Computer engineering
department at North Carolina State University Raleigh, NC.
Osama Al-Khaleel is an associate professor of Computer Engineering in the Department of Com-
puter Engineering at Jordan University of Science and Technology (Irbid, Jordan), received his B.S in
Electrical Engineering from Jordan University of Science and Technology in 1999, M.Sc. and Ph.D.
in Computer Engineering from Case Western Reserve University, Cleveland, OH, USA in 2003 and
2006, respectively. Currently, his main research interests are in embedded systems design, reconfig-
urable computing, computer arithmetic, and logic design.

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