A Novel Algorithm for Bi-Level Image Coding and Lossless Compression

based on Virtual Ant Colonies

Matthew Mouring

, Khaldoon Dhou

and Mirsad Hadzikadic

KPIT Extended PLM, Raleigh, NC, U.S.A.

Department of Mathematics and Computer Science, University of Missouri, St. Louis, U.S.A.

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-

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

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

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

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

1 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

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

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

1 1 1 0

0 0 1 0

0 1 0 0

0 0 1 1

route

food

XXX

X 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 ﬁve 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

1 0 0 0 0

0 1 1 1 0

1 0

0 0 0

1 1

1 0 0 0 0

1 0

0 0 0

1 1

1 0

0 0 0

1 1

(a)

(b) (c)

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

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

6 7

Right

Advance

Left

Advance Right

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 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

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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