While establishing diagnosis doctors usually rely on medical images to which we refer x-ray diagram, MRI images, CT images, PET tomography etc. Using of medical images is growing every year due to the introduction of modern medical technologies in clinics and medical centers. Objects in the medical images have very complex and multifactor leading to high requirements for reliability, accuracy and reliability of research results. The rapid development of digital and analog technologies in recent years opened new opportunities for developers. For example, increasing the speed of computers allows the use of complex, time-critical algorithms, and thanks to the emergence of color television with high-resolution sensors we can receive and process images.

     To date, a very large volume of medical information is contained in all kinds of medical images. Images have different complexity and multifactor [2], there is always the problem accurately find objects and boundaries of objects in images presented for accurate diagnosis. This problem can be solved using the methods of digital image analysis. Segmentation is a difficult task, methods for solving the problem each time is different, it all depends on the characteristics and properties of an image.

     The algorithm of ant colonies (ACO) - used in many optimization problems, and shows good results. When applied to the segmentation problem we get the efficiency. To date, these developments take place, but the practical implementation still requires additional research and results.

Image 1 - Common view of ACO

In order to construct a suitable ant algorithm for solving any problem, it is necessary [4]:

1. Present the problem as a set of components and conversions, or a set of undirected weighted graph on which the ants can build solutions.

2. Determine the value of pheromone trail.

3. Heuristics to determine the behavior of an ant when building a solution.

4. If possible, implement an effective local search.

5. Choose a specific ACO algorithm and apply the solution.

6. Configure the ACO algorithm.

Also, determine are:

• number of ants;
• balance between study and use;
• combination with greedy heuristics or local search;
• when the pheromone is updated.

Image 2 - Finding by ants path from nest to food source

     The algorithm of ant colonies will be used in conjunction with the clustering method k-means, to increase the efficiency of image segmentation [2]. The developed hybrid algorithm will start with the choice of the number of clusters and randomly initialize their centers. Now, according to the clustering algorithm k-means we must identify the affiliation of each pixel of the image a certain cluster. At this stage the most important role is played by an algorithm of ant colonies, he defines the relationship of each pixel of the image clusters. This is done according to the probability which is inversely proportional to the distance between the , which represents i pixel and the center of the cluster and variable t the level of pheromone. The level of pheromone proportional to determine the minimum distance between each pair of cluster centers and inversely proportional to the distance between each pixel and each of its center. Thus, the value of the pheromone level increases with the distance between the centers of the clusters and more compact pixel klastere. Pri these conditions increases the probability of joining a pixel to a cluster [5].
     Pheromone evaporation is calculated in order to mitigate the impact of the previously selected solutions, which are lower priority. Similarly, k-means algorithm, the distribution of the states are updated cluster centers by applying the average value of pixels in each cluster and this continues as long as the change in the value of the cluster center does not change significantly. Unlike k-means algorithm, developed the method does not stop at this point. The clustering process continues to execute m ants, each of which eventually finds a solution. Criterion for finding the best solutions and new levels of pheromone, respectively, for the next group of m ants are leading to the next group. The criterion breakpoint clustering is completed this way, the best solution found.
     The algorithm starts with determining the level of pheromone t and set h heuristic information for each pixel. Then, each ant determines the membership of the pixel cluster with probability P, which is calculated from the expression (3.1):

(3.1)

where - the probability that a pixel cluster i, and - information on pheromones and heuristic variable supplies the pixel cluster i, respectively, - the constant parameters that determine the relative influence of pheromone and heuristic information, K - the number of clusters. Heuristic information is calculated according to expression (3.2):

(3.2)

where - pixel number n, - i-th spectral clustering center and i-th spatial center of the cluster. - according to the distance between pixel and color characteristics - Euclidean distance between , according to the pixel's place on the image. , according to the arrangement of a pixel in the image. The constant k is used to balance the values of n with t. Significance level of pheromone in the initial phase is set to 1, so the first iteration, it does not affect the probability of a transition.

     Suppose m - number of ants selected for the clustering of images. Each ant finds its individual solution. After m ants segmented image, select the best solution for the current iteration, for it is incremented, and the pheromone level is updated all the cluster centers according to the best solution. On the next iteration of the initialization of ants occurs according to previous experience. At each iteration, each of m ants find an individual solution, which adjusts its own heuristic knowledge, the best overall solution found by all ants. This is repeated until a solution is found that satisfies all the specified conditions. The general solution of the m individual solutions is chosen according to 2 parameters:

1. Euclidean distance between cluster centers based on the color characteristics (isolated clusters).

2. The sum of Euclidean distance between the center of the cluster and each of its pixels according to color and spatial characteristics (similarities and compactness of clusters).

To select the best solution of all local necessary to satisfy the following conditions:

1. Euclidean distance between clusters in terms of color characteristics must be large, respectively, the clusters are different from each other.

2. The sum of Euclidian distances between the center of the cluster and each of its pixels according to color characteristics should be small, respectively, the cluster is more homogeneous.

3. The sum of Euclidian distances between the center of the cluster and each of its pixels according to the spatial characteristics should be small, respectively, clusters are more compact.

Image 3 - Segmentation using k-means algorithm

     In order to fulfill the first condition, we look forward to each ant distances between each pair of cluster centers and sort them. Then we choose the minimum among all the ants and compare them, choosing the maximum [MinMax (k)].
     For the implementation of paragraphs 2 and 3 to calculate the sum of distances between cluster centers and their pixels, and then sort them. Select the maximum for each ant and the minimum of these values. Each time the selected value gets added priority. The highest priority is the best. Once you select the best solution is updated according to the value of the level of pheromone expression (3.3):

(3.3)

where the rate of evaporation , which acts on a previously established level of pheromone. Due to this factor increases the effect of later decisions and priorities is weakened earlier. Parameter in expression (3.3) - the difference is the level of pheromone, which is added to the previous successful ant. It is calculated according to [3]:

(3.4)

where Q - is a positive constant, which is associated with the value added by ants pheromone - a minimum of the color distances between each pair of cluster centers found by ant k '(the most successful ant). AvgCDist (k ', i) - the average Euclidian distance of the color and AvgPDist (k ', i) - the average of the spatial Euclidean distance between each pixel and the centers (color and spatial) for the most successful ant. Min (k ') - a cause of increased pheromone at a great distance clusters. AvgCDist (k ', i) and AvgPDist (k', i) - the reasons for increasing the level of pheromone with greater homogeneity and compactness of the cluster.      A mixed algorithm of ant colonies, and to-medium on a step by step [5]:

1. Initialize the basic parameters of the algorithm: the importance of the level of pheromone in the first phase is set equal to 1, the number of clusters K, the number of ant m.

2. Initialize the m ants for K sluchaymo selected cluster centers.

3. .Let each ant associates each pixel with one of the clusters i, at random, the probability of expression (3.1).

4. Compute the new centers of the clusters. If the new center coincides with the previous, then proceed to the next step, if not, proceed to Step 3.

5. Save the best solution of all found m ants.

6. Update the pheromone level for each pixel according to 3.3 and 3.4

7. Adjust the overall best solution on the basis of the found individual solutions for each ant.

8. If the stopping criterion, then proceed to the next step. Otherwise, proceed to Step 3.

9. We found the overall best solution.

Image 4 - Example of image segmentation

Conclusion

     Although the image processing algorithms can provide accurate quantitative indicators (eg, measurement of left ventricular ejection fraction heart of a dynamic image sequence) or likely to solve certain problems that are not feasible for manual processing (eg, the precise registration of multimodal images), reliability issues and responsibilities remain the main obstacles to widespread use of these algorithms. Validation of the algorithm is often difficult due to lack of theory capable of quantitatively compare the results of treatment.

Literature

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2. L. Lucchese and S.K. Mitra “Color Image Segmentation: A State-of-the-Art Survey”, 2001

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Important notice

     When writing this abstract the master’s qualification work is not completed. Date of final completion of work: December, 1, 2011. Full text of the work and materials on a work theme can be received from the author or his scientific supervisor after that date.