A cooperative multi-agent platform is a massively parallel and distributed virtual machine where the mobile agents which represent the Processing Elements (PEs) are involved in the execution of the parallel programs on different structures (SIMD, SPMD, MIMD…) and topologies (2D Mesh, 3D Mesh, hierarchical…) according to the parallel problem to resolve.

In this work we implement the well known algorithm for big data image segmentation which is the c-means algorithm as a distributed program on this model by using SPMD structure. The main components which are engaged to perform the execution of this program are the host agent and the team worker agents that are designed to play the roles introduced in Figure 1.

This model is based on an intelligent grid computing organized as a bidimensional 2D mesh topology (Figure 2) of size m × n, in which each mobile agent MPE (Mobile Processing Element) is localized in row i and column j and has an AID (Agent Identifier). Figure 2 shows an example of (2 × 2) workers machines hosted by M0. All the agents (i, j) in the mesh execute their tasks autonomously and maintain asynchronous communication by exchanging ACL (Agent Communication Language) Messages between each other over the grid computing. In order to achieve a high performance computing of the big data image segmentation, it is important to deploy the large amount of skills of these agents, as:

1) Autonomy: each mobile agent can perform, image classification autonomously. It can extend its activities to make the diagnostic on images and generates reports and data for eventual decisions.

2) Adaptability: it can execute its tasks in different environments with the same performance as in the environment where it was created.

3) Mobility: it can move from one machine to another and resume its tasks if some parallel computing challenges happen.

4) Asynchronous communication ability: it can exchange data, tasks and knowledge using ACL message in remote or local communication.

The c-means algorithm as defined in [13] , is an image segmentation algorithm which consists on a partitioned groups of set S of n attribute vectors into c classes (clusters C_i i = 1, ・・・, c). In this algorithm [13] authors used the pixel gray level as the main classification attribute. The finale goal is to find the class centers (centroïd) that minimize the cost function J defined by the following equation:. To do so, we have to execute the different equations, given in Table 1.

The c-means classification is achieved using the following algorithm stages which are summarized in Figure 3.

In this section, we present our distributed implementation of the c-means algorithm on a cooperative multi-agent platform using the 2D mesh architecture of the same size as the input image (MRI cerebral image of 256 gray levels). MRI images are stored on a cooperative multi-agent platform one pixel per agent. In order to perform the distributed c-means classification of the image in this model we need to perform the following three global stages as shown in Figure 4.

1) Host agent initialization: when our segmentation platform goes on. The host agent is the first one created, and initialized by the size of the data image which is in our case (m × n).

2) Grid construction: just after the initialization, the host agent splits the input image into (m × n) elementary images and then deploys a list of the classification agents which each of them encapsulates an elementary image and moves to a specific destination where it supposes to execute it tasks.

3) C-means classification: to start the data segmentation, the classification agents process, the classification tasks and the initial class centers which are sent by their host agent, and execute the local class determination task in order to compute the membership matrix. Then they replay the message with the results to their host agent which assembles the elementary results from all the classification agents and performs the global class determination and computes the cost function J and test the condition. If it is not achieved, it sends a new class centers to the classification agents to repeat the classification until it is achieved. Finally the host agent sends a request to the classification agents in order to send the output elementary images which will be assembled in order to display the c output segmented images for the classification.

This cooperative and intelligent platform is a distributed and parallel virtual machine on which we implemented the image segmentation algorithm according to the model of Figure 5. It is based especially on the JADE middleware [14] and on the mobile agent skills.

Thanks to the JADE middleware, we prepare the platform where we run the parallel and distributed c-means program. The main components of this model are:

・ The main container: it is the first container which starts in the platform and which is different from the others by its two special agents (the AMS agent and the DF agent). It connects all the performed containers in the platform.

・ The host container: is the second container that is started in the platform where the host agent is created in order to manage the required infrastructure and computational inside in the physical grid computing.

・ The agent containers: the free containers are started in the platform to receive groups of the classification agents so that each group can execute its classification tasks.

In a multi-agent system, we distinguish the mobile agents that have interesting and additional skill from the other agents which is the ability to migrate between nodes. It is considered the one key of the high performance computing and it fit well with our main goal.

The mobile agents are considered as Processing Elements (PEs) which encapsulate tasks and data in order to achieve the parallel programs execution. So they are independent inside their containers, where they are deployed, in order to stay or move to the most suitable environment to achieve perfectly their tasks. They have the ability to communicate between each other asynchronously by exchanging ACL messages. Thanks to the high performance of the mobile agent we can take strong control about all the parallel computing challenges: load balancing, fault tolerance and communication cost. This allows us to constitute a cooperative and intelligent grid for high performance computing.

This part presents the implementation of the proposed distributed c-means program in our cooperative platform according to the organization chart presented in Figure 4 using the MRI cerebral image. We obtain the following results: the Figure 6(a) corresponds to a human cerebral cut; it is the original input image of the program which is split into (m × n) elementary images as in Figure 6(b). And the Figures 6(c)-(e), are the segmented

output images where each of them corresponds to a specific class: the gray matter, the cerebrospinal fluid and the white matter.

The effectiveness features of this distributed method for data image classification is shown under these three cases of studies for dynamic convergence analysis and time classification analysis under the fourth case.

1) (c₁, c₂, c₃) = (1, 2, 3) where we see clearly in Table 2 the convergence of the algorithm after 15 iterations to the final class centers (c₁, c₂, c₃) = (28.60, 101.60, 146.03) and which are illustrated in Figure 7.

2) (c₁, c₂, c₃) = (1, 30, 255) where the algorithm converges to the same final class centers of the case 1 (c₁, c₂, c₃) = (28.60, 101.60, 146.03) after 5 iterations as shown in Table 3 and which are illustrated in Figure 8.

3) (c₁, c₂, c₃) = (140, 149, 255) where the algorithm converges to the final class centers (c₁, c₂, c₃) = (33.37, 103.50, 146.03) after 10 iterations as shown in Table 4 which are illustrated in Figure 9.

In Figure 10, we present the variation of the classification time according to the number of agents involved in the computing using the initial class centers (1, 2, 3).

In this experience, the used distributed system is composed by 8 CPUs. We notice that the execution time is decreasing according to the number of classification agents. From 8 agents, the classification time saved become very small. This is due to the fact that the distributed system is composed of 8 CPUs.