Pankova Alexandra Valerievna

1. INTRODUCTION

For today absence of pregnancy is a urgent problem, which mentions about 10 % of married couples. Now wide circulation for treatment of absence of pregnancy has received application In vitro fertilization (IVF).

For approach of pregnancy are necessary not only good embrions, but also the high qualities of an uterus’s cavity, where will be transferred embrions. The condition of a cavity of uterus can be estimated with the help a x-rayed method of research, ultrasonic research. The ultrasonic method of research has come in medicine considerably after x-ray, but developed even more promptly and became irreplaceable due to the simplicity, absence of contra-indications owing to harmlessness for the patient and large informatization [1].

In given master's work the creation of the specialized computer system (SCS) is planned which will help the doctor on received ultrasound image to reveal sites of a pathology and to put the correct diagnosis.

1.1. Actuality

The actuality of development in the given direction does not cause doubts. The technologies ultrasound diagnostic develop with each year. If ultrasonic scanners was only black-white earlier, now is colour, which allows to receive more the qualitative image. Having received the precise image of ultrasound diagnostic, it is necessary to be able to estimate him correctly , i.e. "to see" a pathology on a snapshot, if it exists. Developed SCS will be a good helper for the doctor of ultrasound diagnostic.

The application of the given development in conditions of the Ukrainian-French centre of the reproduction functions of human "Semya" ("Semya") is supposed.

1.2. Purpose and task of work

The purpose of performance the master's work is the creation of the specialized computer system, which will process the image received at researching and put the preliminary diagnosis. SCS should be easy in use, that the doctor, which has even small skills of work with the computer, could use it without difficulties.

The basic task, which is decided in work, is the processing the image of ultrasound diagnostic with using of Markov's models and statement of the diagnosis with the helping of expert system. SCS analyzes the image received from the device of ultrasound diagnostic Aloka SSD 3500. It is the universal colour diagnostic scanner. The software SCS is developed for processing of the image on the programming language Visual Basic 6.0.

1.3. Scientific novelty and practical value

Despite of a plenty of existing computer systems of processing of the images, the systems for research of the image of an uterus's cavity by preparation to IVF are not developed.

The created specialize computer system "IVF", will pay attention of the doctor on an existing pathology and will help him to carry out more correct treatment and receive good results at realization of treatment of the absence of pregnancy by a method IVF.

2.METHODS OF PROCESSING OF THE IMAGE

Markov Random Fields - metod of processing of the image.

Consider a set of random variables X = { X₁,X₂,...,X_n}defined on the set S, such that, each variable X_i can take a value x_i from the set L ={ l₁,l₂,...,l_n} of all possible values. Then X is said to be a MRF with respect to a neighborhood system N = { N_i| i S} if and only if it satisfies the positivity property P(x)>0, and Markovian property P(x_i|x_S-{i}) = P(x_i|x_Ni ), . Here we refer to Pr(X = x) by P(x), Pr(X_i=x_i) by P(x_i), and the joint event (X₁ = x₁,...,X_n = x_n) as X = x where x = { x_i| i S} is a configuration of X corresponding to a realization of the field.

The MAP-MRF estimation can be formulated as an energy minimization problem where the energy corresponding to the configuration x is the negative log likelihood of the joint posterior probability of the MRF and is defined as

E(x)= - log Pr(x|D).

2.1.MRFs for Image Segmentation

In the context of image segmentation, S corresponds to the set of all image pixels, N is a neighbourhood defined on this set, the set L comprises of labels representing the different image segments, and the random variables in the set X de-note the labelling of the pixels in the image. Note that every configuration x of the MRF defines a segmentation. The im-age segmentation problem can thus be solved by finding the least energy configuration of the MRF. The energy corre-sponding to a configuration x consists of a likelihood and a prior term as:

(1)

where is the log likelihood which imposes individual penalties for assigning label l_i to pixeli and is given by

if xi=lk

(2)

where H_k is the RGB distribution for S_k, the segment denoted by label l_k. Here, Pr( i S_k | H_k )=Pr( I_i | H_k ), where I_i is the colour intensity of the pixel i. The prior (x_i,x_j) takes the form of a Generalized Potts model:

(3)

In MRFs used for image segmentation, a contrast term is added which favours pixels with similar colour having the same label [2, 3, 4]. This is incorporated in the energy function by reducing the cost within the Potts model for two labels being different in proportion to the difference in in-tensities of their corresponding pixels [6].

(4)

where g²(i; j) measures the difference in the RGB values of pixels i and j and dist(i; j) gives the spatial distance between i and j. This term cannot be included in the prior, since the prior cannot include the data, and hence has to be added separately [4]. The energy function of the MRF now becomes

(5)

The contrast term of the energy function is defined as

(6)

2.2.Dynamic Markov Random Fields

Observe that the energy of the MRF defined earlier for image segmentation is dependent on the data (colour intensities of pixels) and the parameters used in the energy function. This also holds true for the MRF modelling the stereo labelling problem, where the label to be estimated for each MRF site (pixel) is the disparity configuration xp. When performing image segmentation on video sequences, the energy function of the MRF changes with every image frame. We refer to such a MRF as being dynamic. The stereo problem in the context of videos can be modelled using dynamic MRFs in a similar fashion [6].

2.3.Solving MRFs using Graph Cuts

The configuration x of the MRF having the least energy cor-responds to the MAP solution of the MRF. The minimization of energies such as the one defined in (5) can be performed by computing graph cuts [5]. Further, a global minima of the energy function can be computed exactly for a pairwise MRF with convex pairwise terms by finding the st-mincut on an equivalent graph. We now describe the equivalent graph construction for the two label case, for the multi-label case, the reader is referred to. Each random variable X_i of the MRF is represented by a vertex v_i in this graph, which is connected by n-edges to the vertices in its neighbourhood set defined as { v_k | X_k N_i}. The cost of the n-edge (i; j) connecting vertices v_i and v_j is given by [6].

Figure 2: The graph representing an MRF with two labels l_x and l_y, and four random variables x_i, x_j, x_k, and x_l. The cost of the t-edge c_xi is and the n-edge c_ij is .

The two labels l_x and l_y are represented by the special vertices, the source s and the sink t. They are connected to all other vertices representing the latent variables in the MRF by t-edges. The cost of a t-edge is given by the likelihood term of the energy function of the MRF. An st-cut in this graph which separates the source and the sink, defines a configuration x of the MRF, and the cost of the cut is the energy of x [5]. From this equivalence, by computing the minimum cost cut we can find the MAP-solution of the MRF [6].

3.RESULTS

Considered Markov model for processing of the images have optimum properties and allow to find out pathologies of an uterus's cavity. On the basis of these models the researches were carried out and the good results are received.

4. CONCLUSION

There is a lot of systems of reception and processing of the image of ultrasound diagnostic, but there is no such system, which would be used particularly for detection of a pathology of an uterus's cavity before a cycle IVF. I hope, that developed SCS will help the doctor to put the maximum correct diagnosis and to nominate the appropriate treatment, for increase of chance of reception of pregnancy after IVF. At the given stage the master's work is in a stage of development. The protection of master's work will has been planned by December, 2007. To address for the additional information to the developer.

E-mail: sachucha@mail.ru, sandra0709@rambler.ru

5. LITERATURE

1.http://doctor-center.ru/diagnostika.html

2. A. Blake, C. Rother, M. Brown, P. Perez, and P. Torr. Interac-tive image segmentation using an adaptive gmmrf model. In ECCV04, pages Vol I: 428–441, 2004.

3. Y. Boykov and M. Jolly. Interactive graph cuts for optimal boundary and region segmentation of objects in n-d images. In ICCV, pages I: 105–112, 2001.

4. M. P. Kumar, P. H. S. Torr, and A. Zisserman. Obj cut. In CVPR05, pages 18–5, 2005.

5. Y. Boykov, O. Veksler, and R. Zabih. Markov random fields with efficient approximations. In CVPR, pages 648–655, 1998.

6. http://cms.brookes.ac.uk/staff/PhilipTorr/Papers/2007/PAMI_submission.pdf