A Novel Algorithm for Bi-Level Image Coding and Lossless Compression
based on Virtual Ant Colonies
Matthew Mouring
1
, Khaldoon Dhou
2
and Mirsad Hadzikadic
3
1
KPIT Extended PLM, Raleigh, NC, U.S.A.
2
Department of Mathematics and Computer Science, University of Missouri, St. Louis, U.S.A.
3
Department of Software and Information Systems, University of North Carolina at Charlotte, U.S.A.
Keywords:
Ant Colonies, Pheromone, Proximity, Binary Images, Arithmetic Coding.
Abstract:
Ant colonies emerged as a topic of research and they are applied in different fields. In this paper, we develop an
algorithm based on the concept of ant colonies and we utilize it for image coding and compression. To apply
the algorithm on images, we represent each image as a virtual world which contains food and routes for ants
to walk and search for it. Ants in the algorithm have certain type of movements depending on when and where
they find food. When an ant finds food, it releases a pheromone, which allows other ants to follow the source
of food. This increases the likelihood that food areas are covered. The chemical evaporates after a certain
amount of time, which in turn helps ants move to cover another food area. In addition to the pheromone, ants
use proximity awareness to detect other ants in the surrounding, which can help ants cover more food areas.
When an ant finds food, it moves to that location and the movement and coordinates are recorded. If there is
no food, an ant moves randomly to a location in the neighborhood and starts searching. We ran our algorithm
on a set of 8 images and the empirical results showed that we could outperform many techniques in image
compression including JBIG2.
1 INTRODUCTION
In reality, ants are good at identifying the nearest path
to the food and readjust to variations in their sur-
roundings (Beckers et al., 1992). It is well known
that an ant drops a chemical while searching and
ants choose to follow a route which has a high con-
centration of the chemical. This nature of move-
ment and communication in an ant colony explains
how ants search and identify the sources of food in a
short amount of time. This behavior of ants helped
researchers solve many real-life problems and has
been explored by scientists from different perspec-
tives. Mullen et al. (2009) reviewed the literature of
ant colony algorithms and their applications. A clas-
sical example is applying the structure of ant colonies
to the traveling salesman problem (Maniezzo, 1992).
This work was subject to further exploration and de-
velopment in many fields of research (Gambardella
and Dorigo, 2015; Dorigo and Gambardella, 2016;
Neto and Godinho Filho, 2013). For example, chem-
icals released by ants when they find a source of food
were helpful in finding out the optimum routes for
evacuation during a tsunami (Forcael et al., 2014).
Similarly, Li et al. (2008) used an ant colony algo-
rithm to shorten the time of coding, which reduced
the amount of searching. In the same vein, Jaferzadeh
et al. (2009) developed a method for fractal image
compression which forces ants to move to certain re-
gions in the image, the purpose of which is to expedite
the encoding process.
Although there has been a tremendous amount of
work which utilizes ant colonies in different applica-
tions, our vast research did not find any work in ap-
plying ant colonies in lossless image compression for
binary images. The contribution of this paper is to de-
sign an ant colony algorithm derived from the behav-
ior of real ants; to design ant movement rules which
are fed into the algorithm; to utilize the power of arith-
metic encoding algorithm in ant movement to provide
a higher compression ratio; and to apply it on images
simulated as virtual environments which contain ants,
food and routes for ants to move and search for food.
The algorithm in this research is meant to provide a
new approach on how ant colonies can be used in bi-
nary image coding and compression.
This paper is organized as follows: Section 2 re-
views related work in ant colonies, image compres-
72
Mouring, M., Dhou, K. and Hadzikadic, M.
A Novel Algorithm for Bi-Level Image Coding and Lossless Compression based on Virtual Ant Colonies.
DOI: 10.5220/0006688400720078
In Proceedings of the 3rd International Conference on Complexity, Future Information Systems and Risk (COMPLEXIS 2018), pages 72-78
ISBN: 978-989-758-297-4
Copyright
c
2019 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
sion and coding; section 3 overviews the proposed al-
gorithm, which is based on the rules in an ant colony
and how that is applied in image compression; in sec-
tion 4, we present our results and compare our scheme
with other algorithms in the image processing com-
munity such as JBIG1, JBIG2; section 5 provides
summary and conclusions.
2 RELATED WORK
In this section, we review related literature in agent-
based modeling and ant colonies. Furthermore, we
overview related work which exists in image coding
and compression domain.
2.1 Agent based Modeling
Agent based modeling has attracted much attention
in the research community. It allows scientists build
simulations to gain an understanding of real life sce-
narios. A remarkable achievement in the agent-based
modeling domain is the development of Netlogo, a
programming environment developed in Northwest-
ern University (Wilensky, 1999). Netlogo offers many
agent-based models and it has been extensively used
as a simulation tool in research. For example, Hodzic
et al. (2016) developed parameters for an ecological
model of predator and prey as allowed by Netlogo.
In their work, predator and prey agents have certain
movements the main goal of which is to simulate a
mathematical formula.
One of the models offered by Netlogo is the bio-
logical model of ants (Wilensky, 1997). In this model,
ants have certain rules of movement while walking
to search for food. This particular set of movement
rules was a basis for many research projects in var-
ious domains. For example, Onan et al. (2017) pre-
sented an enhanced algorithm for ant clustering that
uses heuristic methods. In another study, Lin et al.
(2017) utilized Ant Colony Optimization in solving
problems of test construction heuristics. With a sim-
ilar objective, Jacknoon and Abido (2017) used Ant
Colony Optimization for tuning certain parameters
the purpose of which is to preserve the vertical stand
of the Inverted Pendulum in specific circumstances.
Ant colonies were also utilized in solving traffic prob-
lems (Kponyo et al., 2016; Jabbarpour et al., 2014).
The concept of ant colonies have been applied in
various image processing applications (Baterina and
Oppus, 2010; Dorrani and Mahmoodi, 2016; Han and
Shi, 2007; Kaur and Kaur, 2016; Liu and Fang, 2015;
Nayak and Dash, 2016; Pruthi and Gupta, 2017; Ran-
jan et al., 2014; Sharma and Chopra, 2016; Tian et al.,
2008; Zhang and Peng, 2016). For instance, Tian et al.
(2008) utilized the concept of pheromone in an ant
colony to represent the corner information based on
the movements of ants in an image. In addition, Shen
et al. (2016) used the concept of ant colonies cou-
pled with a genetic algorithm to reduce noise in im-
ages. Although ant movements have been widely
used in image processing research, the extensive lit-
erature review revealed very few studies on utilizing
ant colonies in image compression. An example is
by Li et al. (2008) who used ant colony algorithm to
minimize the amount of search and their algorithm
provides higher compression ratio than other block-
based partition methods. Similarly, Yan et al. (2007)
proposed a hybrid ant colony algorithm that relies on
scale compression. A major advantage of our research
is the design af ant colony algorithm for the purpose
of binary image compression, which is a new research
direction as the extensive literature review revealed.
2.2 Coding and Compression
Similar movements to ants have their grounds in im-
age processing. This began by the chain coding de-
veloped by Freeman (1961), which is an encoding
strategy that utilizes the directions between pixels in
an image. This strategy is expressed by a combina-
tion of eight possible directions from 0 to 7, where
each direction is represented by 3 bits. This method
was subjected to extensive enhancement and explo-
ration over the years. For example, Bons and Kegel
(1977) developed the Differential Chain Code which
uses Huffman coding on the differences between the
consecutive codes obtained via Freeman chain code.
Further development of DCC included further reduc-
tion of the scope of the outcomes by 50% via taking
the modulus of eight (Hwang et al., 2001). Bribiesca
(1999) developed the vertical chain code (VCC) for
shape encoding. Their method utilizes three numbers
to represent the boundaries of a shape: 1 for the out-
side edges, 3 for inside edges and 2 otherwise. The
previous methods can be used for image compression
via encoding the shapes or binary contours and us-
ing the code as a representation. Later, Liu and
ˇ
Zalik
(2005) developed a chain code based on the relative
angles between elements in the chain and used Huff-
man code to compress the final string. Although their
method showed an improvement, its limitation is to
use the Huffman coding, which does not always gen-
erate the highest compression ratio. Zahir and Dhou
(2007) developed a new chain code for binary image
compression which depends on the relative directions
between the adjacent chain codes and the grouping
of certain codes. Recently, Zhao et al. (2017) intro-
A Novel Algorithm for Bi-Level Image Coding and Lossless Compression based on Virtual Ant Colonies
73
duced a new method to get the connected components
in bi-level images which retrieves the chain code and
identify the boundaries. They concluded that the algo-
rithm enhances the complexity and the usage of mem-
ory. Along with improvements, the subject of chain
code has been the basis of many applications. For ex-
ample, Decker et al. 2017 introduced a new tracking
mechanism to be used in endoscopy which overcomes
many obstacles in soft surgery. Additionally, Ngan et
al. 2017 utilized 3D chain codes in symbolizing the
routes of human movement.
Advanced techniques of image compression have
been explored by researchers in image processing do-
main. A notable achievement that has drawn much
attention in lossless data compression is arithmetic
encoding (Sayood, 2012). It uses small number of
bits to encode symbols of higher frequency and more
bits to encode symbols that exist less. This, in turn,
reduces the number of bits that represent the whole
string. This method is extensively used in image pro-
cessing research. For example, Saarinen (2017) used
arithmetic coding, coupled with blinding countermea-
sures in cryptography to reduce the size of the sig-
natures. Similarly, Mondal and Sarkar (2017) used
arithmetic coding to compress a set of vowels. More-
over, Shahriyar et al. (2016) proposed a lossless depth
coding scheme based on a binary tree and created
blocks that were coded using context based arithmetic
coding.
3 METHOD
One way to envision how the algorithm works on
bi-level images is to represent an image as a virtual
world which contains ants, food and routes where
ants can walk and collect food. Since we have binary
images, we assume that the 1 pixels represent cells
that contain food, while 0 pixels represent the routes
where ants can walk and collect food. The coordi-
nates of the first location and the movement of ants
for the purpose of food collection are recorded and
can be used to reconstruct an image back. The algo-
rithm consists of the following steps:
Step 1: Convert the image to a food-route represen-
tation where pixels with the value 1 are replaced with
food and pixels with value 0 are replaced with routes.
An example is provided in Figure 1.
Step 2: Determine the coordinates of the image, so
that ants move within the image boundaries and their
movements are recorded.
Step 3: Drop ants randomly within the boundaries of
the image. Each time an ant is dropped onto the im-
age, the algorithm checks that it does not land on top
of another ant. If it lands, it is picked back up, and
dropped to a new random location on the image until
it is stays in a location where it is not dropped over
another ant.
Step 4: After all ants are properly dropped on an im-
age, each ant checks to see if it was dropped over a
food cell or not. If an ant is not dropped over a food
location, it starts searching for a food cell. If an ant
is dropped over a food cell, or if it reaches a food
cell, it records the location and looks in the neighbor-
hood for a cell that contains food. If an ant finds a
neighboring location with food, it moves to that loca-
tion and records the movement according to ‘normal
movement’ (See Figure 2). Normal movement con-
sists of four possible directions: top, down, right and
left. An ant will choose the normal movement in two
cases:
If an ant was dropped over a food cell and finds a
cell in the neighborhood which contains food
If an ant moves from a route location to a food
location and is there is a neighborhood cell which
contains food
Only moves to collect food were recorded because
they allow reconstructing the image back.
Step 5: Besides recording coordinate locations when
an ant is over a food cell, an ant also sets off a
pheromone so that other ants in the area may be drawn
to that smell. Over time the smell will lessen until it
is gone completely. Figure 3 shows an example of
pheromone density released by two ants over cells of
food. Each ant releases pheromone in its cell and the
eight cells around it. Some cells in the virtual world
have a higher pheromone density because they are lo-
cated in the neighborhood of two ants.
Pheromone dissipates after the second movement
of an ant. Figure 4 provides an example pheromone
dissipation. An ant is moving to collect food cells
while the movement was recorded. Figure 4 (a)
shows the initial location of an ant, where it sets the
pheromone level around it. Figure 4 (b) shows the first
movement, where the ant sets a new pheromone level
in the surrounding, while the pheromone level that
was set in the previous movement (Figure 4 (a)) starts
to diminish. Figure 4 (c) shows a new pheromone
density in the surrounding cells while some cells with
pheromone levels from previous movements have less
or no pheromone levels.
Step 6: After the first normal movement, an ant
searches the neighborhood looking for a cell which
has food. If found, the ant chooses to move us-
ing a ‘related movement’. A related movement de-
pends on the previous movement and can have five
possibilities: Advance’, Advance Left’, Advance
COMPLEXIS 2018 - 3rd International Conference on Complexity, Future Information Systems and Risk
74
1 0 0 0 0
0
0
0
0
1 1 1 0
0 0 1 0
0 1 0 0
0 0 1 1
1 0 0 0 0
0
0
0
0
1 1 1 0
0 0 1 0
0 1 0 0
0 0 1 1
route
food
Figure 1: An image segment converted to a food-route reresentation. 1 pixels are converted to food and 0 pixels are converted
to routes.
1 0 0 0 0
0
0
0
0
1 1 1 0
0 0 1 0
0 1 0 0
0 0 1 1
Right
Left
TopDown
(b)(a)
Figure 2: Normal ant movement.
1 0 0 0 0
0
0
0
0
1 1 1 0
0 0 1 0
0 1 0 0
0 0 1 1
route
food
X
X
X
XXX
XX
X
X X
X
X X
XX
X
pheromone density
ant
Figure 3: Example of pheromone density. Some cells have a
higher concentration of pheromone because they are within
the neighborhood of two ants.
Right’, ‘Right’and ‘Left’ (Figure 5). For example, if
the movement is similar to the previous movement,
the direction will be recorded as Advance’. If the
movement is to the right, the direction is recorded as
‘Right’ and so on. Figure 6 shows an example of ant
movement. An ant starts from a cell which has food
and there is food in a cell in the 8-cell neighborhood.
Thus, ant decides to have a ‘normal movement’. After
that, ant decides to choose ‘related movement’ in the
subsequent food cells utilizing five directions: Ad-
vance’, Advance Right’, ‘Advance Left’, ‘Right’ and
‘Left’.
Ants make a decision to move to a neighboring
cell based on five factors:
If a neighboring cell has food
If a pheromone exists in the neighboring cell
If the cell has not been explored by an ant before.
An ant only chooses to move over an explored lo-
cation, if necessary
If the location has less ant density. Ants use prox-
imity awareness to detect the density of ants in
the neighborhood. Figure 7 shows that some cells
have a higher density because they are located in
a shared neighborhood.
In a ‘related movement’, an ant chooses Ad-
vance’ direction to move to a new food location,
if possible. Otherwise, it chooses a random loca-
tion which has food.
Step 7: During an ant movement, the algorithm
records each 10 consecutive Advance’ movements as
one movement called ‘Huge Advance’. In case the al-
gorithm detects less than 10 and more than 4 consecu-
tive ‘Advance’ movements, it encodes the first ve as
one movement called ‘Intermediate Advance’ move-
ment. The reason why we chose to have these two
extra movements is to obtain a higher compression
ratio when we use the arithmetic coding algorithm to
compress the string resulting from the movement of
ants.
Step 8: Arithmetic coding (Sayood, 2012) was used
to compress the string where variables which have a
higher frequency are represented by less bits to save
space.
4 RESULTS AND DISCUSSION
To evaluate our method, we applied our algorithm on
8 images obtained from Zhou (2007). Then, we com-
pared the results with other standard algorithms: G3,
G4, JBIG1 and JBIG2. To this end, we looked at the
number of bits generated by our algorithm to repre-
sent the chain of ant movements after the arithmetic
coding is applied as described in the method section
and compared that with the number of bits resulting
from other algorithms as shown by Zhou (2007). Ta-
ble 1 shows the results on the eight images we used
A Novel Algorithm for Bi-Level Image Coding and Lossless Compression based on Virtual Ant Colonies
75
1 0 0 0 0
0 1 1 1 0
1 0
0 0 0
1 1
1 0 0 0 0
1 0
1 0
0 0 0
1 1
1 0
0
0
0 0 0
1 1
(a)
(b) (c)
1
0 0
1 1
(d)
Figure 4: An example of changing pheromone density. Darker cells indicate a higher density of pheromone.
1 0 0 0 0
0
0
0
0
1 1 1 0
0 0 1 0
0 1 0 0
0 0 1 1
Advance Right
Advance
Advance Left
Right
Left
(b)(a)
Figure 5: Related ant movement.
1 2
3
4
5
6 7
8
1
2
3
4
5
6
7
Right
Advance
Left
Advance Right
8
Advance
Advance Left
Right
Advance Right
Figure 6: Example of ant movement, which is a mixture of
normal and related movements. Initially, since the begin-
ning is from a food cell, the ant decides to utilize ‘normal
movement’. After that, ant starts to apply a ‘related move-
ment’.
for testing. For each algorithm, the compression ratio
of the images was computed as the following:
Compression Ratio =
Size before compression
Size after compression
(1)
The compression ratio of the eight images in the
ant colony algorithm is 15.85 while it was 4.65, 7.64,
9.83 and 10.18 for G3, G4, JBIG1 and JBIG2, respec-
tively.
X X X
X
X
X
X XX X
XX X X
X X
Figure 7: Example of proximity awareness used by ants as
part of their decision to make a movement. An ant prefers
to move to a location with less density of ants. Some cells
in the figure have more density than others because they are
in the neighborhood of two ants.
5 SUMMARY AND CONCLUSION
In this paper, we have presented a new method for
image coding and lossless compression. Our method
works for bi-level images and allows the image to be
reconstructed back. The method utilizes ant colony
rules, coupled with arithmetic encoding in bi-level
compression. The experimental results show that the
proposed method is superior to many existing meth-
ods in the literature and produces a higher compres-
sion ratio than many methods such as JBIG1 and
JBIG2. Additionally, the advantage of our method is
that it is simpler to implement compared to the family
of JBIG.
Future work can be utilizing the rules in ant
colonies in different image processing applications.
One application might be designing new algorithms
that help researchers classify images based on their
components via the movement rules of ants. Further-
more, this research can be expanded to investigate
other applications on imaging such as retrieval and
indexing.
COMPLEXIS 2018 - 3rd International Conference on Complexity, Future Information Systems and Risk
76
Table 1: Number of bits in the string representing the compressed movements of virtual ants used in the algorithm as compared
to the number of bits resulting from other methods existing in the literature (Bhaskaran and Konstantinides, 1997; Ono et al.,
2000; Zhou, 2007).
Image Original G3 G4 JBIG1 JBIG2 Ours
Image 1 65280 26048 19488 15176 15064 8556
Image 2 202320 29856 12208 8648 8616 4892
Image 3 187880 26000 11184 8088 8072 4342
Image 4 81524 14176 6256 5080 5064 2591
Image 5 40000 11712 5552 5424 5208 2314
Image 6 96472 21872 9104 7336 7328 3935
Image 7 414720 102208 81424 62208 58728 43966
Image 8 83600 20064 8192 7200 6984 3319
Total 1171796 251936 153408 119160 115064 73915
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