Agent-Based Model for Image Segmentation Fazel Keshtkar 800 King Edward Ave University of Ottawa, SITE Tel: +1-613-562-5800. Ex: 6248 Email: [email protected] ABSTRACT

Anthony White 5354 Herzberg Carleton University, Ottawa, Canada Tel: +1 (613) 520-2600 x2208 Email: [email protected]

One of the major difficulties met in image segmentation lies in the varying degrees of homogeneousness of the different regions in a given image. Hence, it is more efficient to adopt adaptive threshold type methodologies to identify the regions in the image. In this project, a number of agent-based image segmentation models, based on swarm intelligence techniques, are developed for this purpose. In this paper, we present a swarm-based image segmentation approach. In this approach we consider a digital image as a two-dimensional cellular automata environment in which agent looking for homogenous-segment pixels.

Categories and Subject Descriptors Swarm Intelligence, Agent-based, Image processing.

General Terms Autonomous agents, reactive behavior, evolutionary computation, homogeneous-segment searching, adaptive image segmentation, and agent dynamics.

Keywords Image Processing, Segmentation, Agent, Homogenous pixels, Hidden Markov Model .

1. INTRODUCTION In this paper we explore and present an agent-based approach to image segmentation. In image segmentation, one of the difficulties in a given image is that regions may be homogeneous at various degrees. In those cases, to solve the problems it is not a sophisticate task to define a single threshold on the whole image. To overcome this kind of difficulty, one solution would be to apply different operators to different regions [1], catering to the specific changes in the average region intensity gradients, and to do so in an agent-based approach that each agent is triggered only by a desirable homogeneous segment of the image. Our

present work on agent-based image segmentation has been motivated by such an idea.

1.1 Agent-Based Approach In real-world applications, autonomous agents are often used to solve specific tasks in a distributed fashion [2], [6]. The agents interact with their environments in the course of problem-solving. They received different local properties to responding to their task environments. Agents can select and exhibit different behavioral patterns. In their environments agents to different patterns behavior. In the case of search to move from current state to next state, they make decision randomly. In such case agents move and find their direction base of Hidden Mrkov Chain. Behavioral patterns of the agents may be reflected in their decisions on in which direction and how much localized search would be necessary. By the time agents may be they activate by certain conditions from their environment. In this work, we will focus on autonomous agents with a pre-defined behavioral for the task of image segmentation. In general in AgentBase Approach there are three basic subjects: agents, an environment or space, and rules [4]. In the future section we will describe briefly in order to our work. 1.1.1 Agents Each agent has internal states of behavior rules. Some states are fixed for the agent’s life, while others change through interaction with other agents or with the external environment [4]. These movements, interactions, changes of state all depend on rules of behavior for the agent and space.

1.1.2 Environment The environment, the medium over which agents interact, can be a more abstract structure, such as a communication networks, digital Image. The point is

that the “environment” is a medium separate from the agents, on which the agents operate, and interact.

1.1.3 Rules And finally there are some behavioral rules for the agents and for environments. The some simple rules for agents that can be list as bellow: Look around as far as possible, find the homogenous pixels, and label the pixels. And also it depends on agent’s environment that we send or agent active there.

1.2 An Outline of the Paper The rest of the paper is organized as follows: Section 2 defines some notions as well as the main problem in agent-based image segmentation model. Section 3 presents an overview of the Markov Chain Model, as well as Hidden Markov Chain, and using this model in our agent-based model. Section 4 we observe our model, including agent behavior, agent movement,, and labeling pixels in image environment. Section 5 we illustrates the proposed approach with a real imagesegmentation example. Section 6 discusses the main characteristics of the agent-based approach. Finally, Section 6 concludes the paper by summarizing the contributions and some extensions and future work.

tosses, the outcomes being heads or tails. People use Markov models to analyze a wide variety of stochastic processes, from daily stock prices to the positions of genes in a chromosome [3]. Markov models can construct very easily using state diagrams, such as the one shown in Figure 1. The rectangles in the diagram represent the possible states of the process that is trying to model, and the arrows represent transitions between states. The label on each arrow represents the probability of that transition, which depends on the process that is modeling. At each step of the process, the model generates an output, or emission, depending on which state it is in, and then makes a transition to another state. For example, if you are modeling a sequence of coin tosses, the two states are heads and tails. The most recent coin toss determines the current state of the model and each subsequent toss determines the transition to the next state. If the coin is fair, the transition probabilities are all 1/2. In this simple example, the emission at any moment in time is simply the current state. However, in more complicated models, the states themselves can contain random processes that affect their emissions. For example, after each flip of the coin, you could roll a die to determine the emission at that step .

2. SECTIONS In this approach we aim to show how imagesegmentation tasks may be handled by agents that are produced in response to the local conditions of an image environment. To describe our approach, we first formulate our problem as follows: Suppose that S is a digital image, i.e., two-dimensional array of size U x V that contains a number of pixels that includes a specific homogeneous segment. We characterize the homogeneous segment to represent and tested base of some mathematically criteria. The goal of agents are to visit S and label the pixels in homogeneous segment. Here, our search space, S, can be viewed as an environment in which the agents inhabit and recognize.

3. Hidden Markov Model 3.1 Introduction Markov models are mathematical models of stochastic processes — processes that generate random sequences of outcomes according to certain probabilities. A simple example of a stochastic process is a sequence of coin

Figure 1. A State Diagram for a Markov Model

3.2 Hidden Markov Chain A hidden Markov model is one in which we observe a sequence of emissions, but we do not know the sequence of states the model went through to generate the emissions [3]. In this case, our goal is to recover the state information from the observed data.

There are five Statistics functions for analyzing hidden Markov models: • Calculates the posterior state probabilities of a sequence • Generates a sequence for a hidden Markov model • Estimates the parameters for a Markov Model • Calculates the maximum likelihood estimate of hidden Markov model parameters • Calculates the most likely state path for a hidden Markov model sequence

3.3 Markov Chain This section defines Markov chains, which are the mathematical descriptions of Markov models. A Markov chain contains the following elements: • A set of states {1, 2, ..., M} • An M-by-M transition matrix T whose i, j entry is the probability of a transition from state i to state j. The matrix corresponds to a state diagram like the one shown in the Figure 1. , a State Diagram for a Markov Model. The sum of the entries in each row of T must be 1, because this is the sum of the probabilities of making a transition from a given state to each of the other states. • A set of possible outputs, or emissions, {s1, s2, ... , sN}. By default, the set of emissions is {1, 2, ... , N}, where N is the number of possible emissions, but you can choose a different set of numbers or symbols. • An M-by-N emission matrix E whose i,k entry gives the probability of emitting symbol s k given that the model is in state i. When the model is in state i1 , it emits an output s k1 with probability E i1k 1 . The model then makes a transition to state

In this implementation, the initial state is 1 with probability 1, and all other states have probability 0 of being the initial state. At times, if it might need to change the probabilities of the initial states. You can do so by adding a new artificial state 1 that has transitions to the other states with any probabilities you want, but that never occurs after step 0.

3.4 Applying Hidden Markov Chain to Agent-Based Approach As we describe in section 3.2, most important part of Hidden Markov Model is to Generates Random Sequences of state by using transmission matrix T. For our model we consider for state as following. When agent wants to move from one stage to another state, they have four choices that may can be decided to move: 1. stay in the current state 2. go to the North 3. go to the East 4. and finally go to the West Agents make those decisions by random base of Markov Chain Model. Figure 2. shows the state transmissions and their probabilities of movement base of Markov Model.

N W

E

C

i2 with probability Ti k 1 , and emits 1

another symbol. The model then makes a transition to state i1 with probability T1i1 , and emits an output sk 1 with probability Ei1k 1. Consequently, the probability of observing the sequence of states i1 i2 … ir and the sequence of emissions s k1 s k 2 … s kr in the first r steps, is [3]:

T1i1 Ei1k 1 Ti2i1 2 Ei 2k 2 … Tir !1ir Ei1r k r

(1)

Figure 2. A State Transmission Diagram for Agent-based Approach, base of Markov Chain; C(Current), N(North), E(East), W(West).

As we mentioned in our model, agents move from current state to next state base of Markov Chain Model, so as we explained in previous section when the model is in state i1 , it emits an output s k1 with probability

Ei1k 1 . The model then makes a transition to state i2 with probability Ti1k 1 , and emits another symbol. For our model we consider the following possible emission: State C Transmission roll: When agent is in state C: • Moves to state N with probability C N . •

Moves to state E with probability C E .

•

Moves to state W with probability CW .

• Moves to state C with probability C C . State N Transmission roll: When agent is in state N: • Moves to state N with probability N N . •

Moves to state E with probability N E .

•

Moves to state W with probability N W .

• Moves to state C with probability N C . State E Transmission roll: When agent is in state E: • Moves to state N with probability C N .

CE .

•

Moves to state E with probability

•

Moves to state W with probability CW .

• Moves to state C with probability C C . State W Transmission roll: When agent is in state W: • Moves to state N with probability C N . •

Moves to state E with probability C E .

•

Moves to state W with probability CW .

• Moves to state C with probability C C . There for base of above emission rolls our Transmission Matrix is:

&C N $ $N N T= $E N $ $%W N

C N C E CW # ! N N N N CN ! E N E E EW ! ! W N WE WW !"

by the time we ca determine our emission matrix as below:

&1 / 4# $1 / 4! ! E= $ $1 / 4! $ ! %1 / 4" In this case we consider the possibility for all the state as the same probability, since we have 4 state transmission so we suppose in each random time one state randomly chosen, so they have equal probability and it is ¼ for each of state. So base of Markov Chain, the sequence of emissions of states, i.e., in the first step, is:

C N 1/4 N N 1/4 E N 1/4 W N 1/4

Note that if the function returns a generated sequence of states, the first state in the sequence is i1 : the initial state,

i0 , is not included.

3.5 Creating popularities sequences As we mentioned in section 3.4, the sum of each row in matrix T must be equal to 1 for the all the state. It means sum of the emission that comes out from state (probabilities) and goes to another states are equal to 1,base of Markov Chain Model. In our model, to make sure that emission in Matrix T always works properly and follow Markov Chain Model, we define a function that creates probabilities for our Model. Before we formulate this function we need to notice following condition: let agents i are in sate s i ; they can move to next state with probability

According to Markov Model all probabilities the emit from state are equal to 1. So we have:

if

E N + E N + E E + EW = 1 W N + W N + WE + WW = 1

pi

:

n

"p

k

!1

(4)

k =1

C N + C N + C E + CW = 1 N N + N N + N E + NW = 1

(3)

(2)

(n: # state;

pk

refers to previous missions)

so according to (4) our function that creates emissions for Matrix T can be formulated as below:

i "1

pi = rand (0,1 " # pk !1) (5) k =1

we should notice that rand function can be consider any function that creates random variable under equation (4) and (5) conditions. 4.

Agent-Based Model Approach

In the proposed agent-based approach, agents are designed in such a way that they operate directly on the individual pixels of a digital image by continuously sensing their neighboring regions and checking the homogeneity criteria of relative contrast, regional mean, and/or regional standard deviation. Based on the sensory feedback from their neighboring regions, the agents will accordingly select and execute their behaviors[1]. In our approach agents may stay in current coordinate or, move to adjacent pixels, or destroy in the image. In this condition, we consider the behavior of the agents as being reactive, by the local environment of the agents.

DEFINITION 4.1: (The neighboring region of an agent). The neighboring region of an agent at location (i, j) is a circular region centered at location (i, j) with radius R(i,j)_region [1]. The pixels falling inside this region are called the neighbors of the agent, as illustrated in Figure 3. Having defined the neighboring region of an agent, we can now give the expressions of regional mean and regional standard deviation, as follows:

An agent

4.1 Local Behavior to Agents Before we declare our local behavior in image environment, here we define our environment as a Digital Image, that agent can sense the adjacent pixels of pixels in their areas of act ivies. Here we define our Image as tow-dimension environment i.e.: Image A = ( I x , I y ), that

I x and I y are intensity of

relative pixel at (x, y). In this approach we cluster our image in several regions, that we call region criteria. We assume that a homogeneous segment can be mathematically specified. We use three criteria to show our region situation in Image Segmentation: regional mean, and regional standard deviation of the gray-level intensity. These criteria are observe as follows: For each region criteria we consider regional mean, and regional standard deviation of the gray-level of image. mean -criteria:

std _ r( i , j ) in (d1 , d2)

mean _ r( i , j )

(7)

that n1, n2, d1, and d2 are predefine constant. It means agents in each region interacts base of their response in their criteria variables.

1 = N

n

! I (k , l )

(8)

( i , j ) #( k ,l ) " R( i , j ) _ R

and

std _ r(i , j ) =

1 N •

• •

mean _ r( i , j ) in(n1, n 2) (6)

standard deviation-criteria:

Figure 3. The local neighboring region of an agent at location ( i, j). R: the radius of agent neighboring region centered at (i, j).

n

" I (k , l ) ! mean _ r

(i , j )

( i , j ) !( k ,l ) # R( i , j ) _ R

R:

the radius of agent neighboring region centered at (i, j), I(i, j): the gray-level intensity value at (i, j), and N: the number of pixels within a neighboring region of R(i,j)_region

Our work for agent-based model to find homogenous image segmentation that using Hidden Markov Chain Model divide in different phase: Computing statistical variable for homogenous region/image, Making Hidden

Markov Sequence, Searching for homogenous pixels within environment, and Labeling homogenous pixels. In Figure 4. The preceding descriptions are summarized in the form of a schematic diagram that outlines the behavioral reactions of the agents to their local image conditions. Import Image

Computing Local Variable

Making Markov Chain

•

std _ r(i , j ) of the image/region: we also need for our model to calculate standard derivation of image/region.

After calculation of above local variable for image, we need to procure following variable: Percentage of homogeneous pixel in image/region; to do so, we count number of homogenous pixel base of mean _ r( i , j ) . If pixels meet this variable we consider that as a homogenous pixel. we are able to formulate this behavior by represented with the following expression. If there are any pixel >

mean _ r( i , j ) then (9)

Increase HmgPixels by one Searching

Labeling

After we attain HmgPixels we are able to recognize how much percentage of pixels is under/above of homogenous pixels. So we need to calculate this percentage amount by following equation:

Figure4. Summarized the preceding descriptions of behavioral reactions

4.1.1 Computing Local Variable In this section we propose computing local variable that we explained briefly in section 4. After importing image, that image lies in our environment. In this environment pixels stored as a two-dimension patch, that agent are bale to scene and access to the pixels at any time that they meet local region or area of activity. As we briefly explore in section 4. the most important local variable for our model is to compute local stimulus in appreciate image. as we said local variable for our model are:

mean _ r( i , j ) , and std _ r(i , j ) .

Before we move to next phase we must to compute these variables base of our image and how homogenous pixel lies in the image. •

mean _ r( i , j ) Of the image/region: depends on how we wish to cluster our image, so base of that clustering we are able to calculate mean _ r( i , j ) value for whole the image or particular region. This variable is Mean of intensity of gray-level in image.

( HmgPixels / total pixels ) * 100

(10)

HmgPixels variable plays important role in our model, and we mention on the crucial aspect of this variable as following: •

we use HmgPixels to estimate at least number of agents to use in our image during searching, and labeling homogenous pixels.

Obtaining number of agents in our Model: By (10) we know how much percentage of pixels in our image exceed to homogenous area, hence we use this variable to create number of agents that we need in our model. We can describe this behavior by following expression: - Set HmgPixels to NoAgent - Sprout randomly NoAgent in Environment

(11)

by having NoAgent that we attain from percentage of homogenous pixel we meet remarkable result: -

By using NoAgent, we will have at least number of agents in our model to searching and labeling homogenous pixels.

-

While we creating NoAgent as amount of agent, this variable is not costly in our model.

-

By NoAgent we are able to recognize mostly of homogenous pixels in whole the environment.

-

While we increase the amount of agents, there is no much different by recognizing homogenous pixels in regions. Except in edge area, that does not seem too important, in our goal.

In our implementation we declare agents with red-color in our environment 4.1.2 Making Hidden Markov Sequence As we explained briefly in section 3 we define Hidden Markov Chain, we after we implied Markov Model in agent-based behavior. Here we don’t go through deeply, but we mention while agents start to interact in environment they need to choose their direction to move from current state to next state. Agents choose their direction base of Hidden Markov Chain sequence that we created in section 3. They have four choices to move to next state, base of probabilities of Markov sequence: North, East, West, and Current state.

4.1.4 Labeling homogenous pixels In this phase agents that have found homogenous pixels will label them. Here during upon agents found homogeneous pixels that meet by local variable of environment base of capacities of homogenous pixels agents create an agent neighboring that we defined in section 4. The radius of circle depends on amount of homogenous pixels in appreciate location that agents explore the pixels. Agents compare these pixels that falling into agent neighboring with local stimulus of image/region parameters, if they meet these properties agents will label them. We can formulate this behavior by following expression: LABEL: If local stimuli meets criteria of agents THEN

agent ( R ) ( i , j ) ( sk ) => L( i , j ) (13) where R: is

radius of agent neighbor

L( i , j ) : Pixels that labeling by agents 4.1.5 The Agent Computation Algorithm A complete algorithm for agent-based image segmentation is given in Figure 5.

U ! V digital image.

4.1.3 Searching in Environment

Input: A

After creating Markov sequence, agents are able to move by choosing the direction that apply Markov chain to them. As we mention before agents assume to obtain on of four directions for moving from current stat to next state. We may describe this behavior by following expression:

Output: Labeled homogenous region.

SEARCH:

Begin Import: appreciate digital image into environment Setup: calculate local stimulus parameters of

If agent is in current state

si and wish to

Move to next state THEN

agent ( i , j ) ( sk ) => sl ,! (12) where (i, j): current location of agent.

sk : current state that agent located. sl ,! : next state ! : Direction of next state: N, E, W, and C.

Image: mean, std Compute: percentage of HmgPixels variable of image Sprout agents to environment; base of HmgPixels Do while stoptime < clocktime Do search Choose direction of ! from Markov sequence list {N, E, W, C} by random

Go to

s( k ,! )

IF find homogenous pixels THEN

L( i , j )

Label ELSE

Choose direction of ! from Markov sequence list {N, E, W, C} by random Move to next State

s( l ,! )

End IF End search

developing over time. Modelers can give instructions to hundreds or thousands of independent "agents" all operating concurrently. This makes it possible to explore the connection between the micro-level behavior of individuals and the macro-level patterns that emerge from the interaction of many individuals [5]. The preceding section has provided a computational our model, covering reactive behaviors agents as well as behavioral evolution and control algorithm. As a validation of the proposed approach, in this section we will present an illustrative example. This example examines the use of agents in the detection of significant homogeneous segments.

agent ( i , j ) ( sk ) => sk IF

agent ( i , j ) ( sk ) exceed from region THEN Inactive

agent ( i , j ) ( sk )

End do while End begin.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

Figure5. The algorithm for reactive agent-based

Here we should mention that we use decay for our model. As we describe in previous sections we do not consider a life cycle for each agent during their reactive in the environment, but we consider a global decay for all agents. We not allowed agents comes back to environment while they leaving the area of image or regions. We inactive the agents when they exceed the edge of image during the search. We also may consider a simple expression for agent’s life cycle in our model. DECAY: IF

agent ( i , j ) ( sk ) exceed the edge of Image THEN Inactive

(15)

agent ( i , j ) ( sk )

5. An Illustrative Example We used Netlogo as programming environment for our Model, as we know Netlogo is not strong for al type of image, but we use a sufficient image to do not miss many pixel during the import phase. NetLogo is a programmable modeling environment for simulating natural and social phenomena. It is particularly well suited for modeling complex systems

(l)

Figure6. Snapshots of agents-based at different timesteps in searching and labeling various homogeneous regions in a brainscan image. (a) t = 0. (b) t = 3. (c) t = 4. (d) t = 5. (e) t = 10. (f) t = 20. (g) t= 70. (h) t= 90. (i) t= 100. (j) t=120. (k) t= 150. (l) t=200.

A separate view of the identified outlines and homogeneous regions is given in Figure 6

(a)

(b)

(c)

Figure7. Snapshots of agents-based at different timesteps in a brain-scan image. (a) t = 200. (b) t = 200. (c) t = 200.

we executed our model by several times, and we observe here only snapshot of image that we took at end of evolution time, that is t=200. at it clearly showed, the homogeneous area in all three image nicely distinguished , and they do not have much different. As mentioned, the most different in homogenous region only depends on distribution of agents that we sprout in the image while we start to search in environment. Figure 8. proposes another property of our model.

120 100

Test1

80

Test2 Test3

60 40 20

0

0

Time

15

10

70

10

4

0

0

interested in is whether or not the proposed behaviorbased reactive agents can demonstrate the desired adaptability during distributed image segmentation Initially, 120 agents from each of the test were randomly distributed over the given image. As may be observed in Figure 6., after a number of behavioral evolution steps, the active agents belonging to the homogeneous-segment-searching gradually vanish, by the time all the homogeneous segments are identified.

Time/Agents 140

Agents

Specifically, we have defined a complex image of size 80x110, as shown in Figure 6. The searching and labeling behaviors of an agent will be triggered by its local stimuli that satisfy certain criteria of homogeneity. in view of the general requirement for the biased search; the greater the life span, the greater the positional mutation of an agent would be. As mentioned earlier, here we do not address the issue of how to best represent a homogeneous segment. Here , what we are.

Figure 8. Plot the numbers of agents in image base on time

as it observe while evolution timelabeling is increasing the evolution stoptime during searching and the homogenous number of pixels agents that searching and labeling the homogenous pixels in the image are decreasing. The interesting result that we would wish to get, is showed while time evolution done, or on the other hand life cycle for environment finish we see almost all the image labeling by activated agent during the active behavior of agents. In Figure 8. as we see, number of agent steadily decreasing to 80 while time evolution is around 70, but after time evolution exceeds 70 the number of agent extremely decrease around 20. but at the end we see there no too much remarkable different between homogenous pixels that agent recognize during activation time. The main reason that above matter happen is, because of our distribution agent while e were distributed in image before the model starts to run.

6. Related Works Ramos [6] has explored the idea of using a digital image as an environment for an artificial ant colony. He observed that artificial ant colonies could react and adapt appropriately to any type of digital habitat. Ramos [7] has also investigated ant colony based data clustering and developed an ant colony clustering algorithm referred to as ACLUSTER which he applied to a digital image retrieval problem. In doing so, Ramos [7] was able to perform retrieval and classification successfully on images of marble samples. Liu and Tang [8] have conducted similar work and have presented an algorithm for gray scale image segmentation using behavior-based agents that self-reproduce in areas of interest. They applied it to gray scale images of a brain scan and found the algorithm to be reliable, easy to represent and implement, and adaptive with respect to the local distribution of agents.

7. CONCLUSION AND FUTURE WORK In this paper, we have described an agent-based approach to distinguished image segmentation. We assumed that homogeneous segments to be searched could be mathematically modeled. We used Hidden Markov Chain sequence to create direction to apply in agents while they wish to move from local state to next state of environment, they directly operate in the given image environment and execute a number of reactive behavioral responses. The proposed approach our model to image segmentation with active agent’s exhibits several features; In our model we have used several behavior activities for agent as following:

[2] Del Rey, Calif., 5-8 Feb. 1997. ACM Press, 1997. W.L. Johnson, ed., Proc. First Int’l Conf. Autonomous Agents, Marina [3] Statistics Toolbox For use with MATLAB. P. 315 [4] http://ccl.northwestern.edu/netlogo/ [5] V. Ramos and F. Almeida, “Artificial Ant Colonies in Digital Image Habitats - A Mass Behavior Effect Study on ACM Press, 1998. Pattern Recognition,” ,” Proceedings of ANTS'2000 - 2nd International Workshop on Ant Algorithms (From Ant Colonies to Artificial Ants), Marco Dorigo, Martin Middendorf & Thomas Stüzle (Eds.), pp. 113-116, Brussels, Belgium, 7-9 Sep. 2000.

1. SEARCHING: agents looking for homogenous pixels in image, and they easily recognize those pixels by comparer to mathematical parameters that we define for our image. And the agents adopt to respect to local environment of image and connectively represent the homogenous pixels

[6] V. Ramos, F. Muge, P. Pina, “Self-Organized Data and Image Retrieval as a Consequence of Inter-Dynamic Synergistic Relationships in Artificial Ant Colonies,” in Javier Ruiz-del-Solar, Ajith Abraham and Mario Köppen (Eds.), Frontiers in Artificial Intelligence and Applications, Soft Computing Systems - Design, Management and Applications, 2nd Int. Conf. on Hybrid Intelligent Systems, IOS Press, Vol. 87, ISBN 1 5860 32976, pp. 500-509, IOS Press, Vol. 87, ISBN 1 5860 32976, pp. 500-509, Santiago, Chile, Dec. 2002.

2.

[7] J. Liu, Y. Y. Tang, “Adaptive Image Segmentation With

LABELING: Another behavior of our model is labeling the homogenous pixels in image. We define a agent neighboring that they were able to recognize adjacent pixels in image

3. Our model easy to represent and implement. 4. we have used Hidden Markov Chain Model to choose agent direction while they wish to Move form current state to next state There remain some open problems that are to be addressed in our future research. For instance, it would be interesting to find out a optimal threshold that could distinguished homogenous pixels from non-homogenous pixels. The way that we wish is to each agent able to carry out own local threshold, while meet the homogenous pixels. Second is to find out optimal solution for behavior of agent while they move from each state to others state; our goal is use ACO(Ant Colony System) to apply in our model. So we would like to use ant colony parameters that our agent mimic from ACO and be able to moving base of pheromone that ants using in Marko Dorigo Model.

8. REFERENCES [1] Adoptive Image Segmentation With Distributed Behavior-Based Agents Jiming Liu, Senior Member, IEEE, and Yuan Y. Tang, Senior Member, IEEE

Distributed Behavior-Based Agents,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 6, pp. 544-551, June 1999.