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Survey of mathematical methods of adoption of medical solutions taking into account specificity of pulmonary diseases

Methods which are based on an estimation and transformation of a bar graph of digital pictures, the roentgenology, the analysis of images in polygraphy and preparation before printing [151] have gained a wide circulation in the various areas connected with machining schedules, for example, of system of a pattern recognition.

The given methods are realised in software means on work with digital images which allow to define on a bar graph of the digital image distribution svetlot in it tonovom a range. Such analysis is operative and allows to choose correctly

Strategy of correction of the image. Except distribution svetlot on a bar graph there is a possibility of the control and structural properties of the image, for example, noise, presence of contours in a picture, but these methods are not passed round in the software because of necessity to resort to the statistical analysis of a bar graph for reception of the most authentic results [151]. The bar graph also allows to change luminance of the image, its contrast and the square with which occupy light, dark and others jarkostnye elements, and, at last, to define, where on an image plane there are the separate areas (installations) matching to those or other ranges of values of luminance. Gistogrammnymi picture transformations name transformation of two-dimensional functions of luminance which are presented by the formula:

Where, fр - function of representation of luminance which does not depend on a pixel rule (h,). For example, the elementary gistogrammnym picture transformation is linear transformation of luminance, function of which representation of luminance will look like:

Where a - factor which defines change of contrast of a picture, b - factor which defines change of average luminance of a picture, I - directly luminance in an observed point of a picture. Β a case of discrete digital images function of representation of luminance becomes the so-called table of representation jarkostigistogrammnaja

Machining of the image by means of this table is carried out as follows:

Where, - pixel of the image with koordinatamia LUT -

Integral-valued file a size of 256 elements of the 8-bit image and long 65536 elements for the 16-bit image.

The analysis of projections. A projection of a picture to an axis is the intensity integral pikselov images which are taken in a direction, perpendicular the given axis. The elementary case of a projection of the two-dimensional image are a vertical projection on a X-axis which represents the sum intensivnostej pikselov on picture columns:

And also a horizontal projection on a Y-axis counted in lines of a picture:

Β the general case the projection of the image to any axis is observed.

Let the axis direction is set by unit vector with koordinatamitogda

Projection of the image to axis E:

After formation of a file of a projection, its analysis is carried out by standard means and allows to gate out singular points of function the projections matching to vertical or horizontal contours of various installations which are present in a picture.

Transformation Hafa - algorithm which allows to find the plane curves belonging to the defined on the monochrome image
To the class-room of figures on the basis of a voting procedure. The given procedure is applied to space in parametre from which there are installations of figures on a local maximum in memory space. Transformation appointment - to solve a problem of a group of boundary points by application of a concrete voting procedure to a set parametrizovannyh installations of the image. Let the group of curves on a plane which is set by a parametric equation is given:

Where F-function, a1, a2..., an - parametres of a family of curves, x, at - co-ordinates on a plane. Parametres of curves form, so-called, a phase space, which each point (certain values of parametres α1, a2..., an) belongs to some curve. Because of discrete computer representation and an input information (picture), it is necessary to convert a continuous phase space to the discrete. For this purpose in a phase space the grid which breaks it into meshes is inducted, each of which matches to a set of curves with close values of parametres. Each mesh of space the number (counter) which specifies quantity of points of interest in a picture, belonging at least is put by one of the curves matching to the given mesh in conformity. The analysis of counters of meshes allows to find curves to which posess the greatest quantity of points of interest in a picture.

Textural segmentation, in particular method of textural descriptors. The structure analysis is comparable with the analysis of structure of solids. Physicists in the field of solids should be able to define repeating structure and distribution of atoms in lattice cell. The structure analysis is complicated by that, as structures, and periodic repetition can manifest essential random fluctuations. One of the methods applied to the description of a structure, use of statistical characteristics which are defined on is
To bar graph of luminance of all image and its area. Let z - a random quantity which matches to luminance of a section of a picture, and

Bar graph, where Lозначает quantity of various levels of luminance. Then the central moment of an order nслучайной magnitudes zравен:

Where m - a mean z (average luminance of the image):

From (8) and (9) it is obvious, that μϋ =1 and μ = 0. For the structure description especially important that dispersijakotoraja is a brightness contrast measure.

It was possiblly to use for construction of descriptors of relative smooth finish. For example:

To equally null for areas with constant luminance, that is there where a dispersion also it is equal to null and it is aimed to 1 for great values

One more characteristic is asymmetry:

Uniformity:

And average entropy:

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For a picture uniformity u =1тогда when all its elements have equal luminance and decrease in process of growth jarkostnyh differences. Entropy characterises variability of luminance of the image. It is equal 0 there where luminance is constant and maximum in case of increment z.

Classification problems also was possiblly to solve by means of methods of the discriminant analysis, including methods of classical statistics. The section of mathematical statistics which is engaged in working out of methods for a discrimination problem solving to concrete signs is called as the discriminant analysis [23, 91, 92]. The basic parametre with which help it is possible to size up efficiency of a method of the discriminant analysis nazyyovajut accuracy of classification. It is defined on the basis of a share of truly classified installations on a basis prognosticheskogo the equations. [93].

Β a case if sample of installations is numerous the approach in which the researcher analyses a part of data is applied to classification of observations, and for the others it is applied prognosticheskoe uravyonenie. Speaking in other words, cross verification is carried out. Β the discriminant analysis there are methods of stage-by-stage sampling of variables which help to make sampling of predicted variables [24].

Β theories of the analysis of multidimensional data are present methods, which reyoalizujut construction of linear discriminant functions which help to support a minimum of criterion of an average probability of erroneous classification in opredeljnnyh cases.

For example, when exists two class-rooms ω1и®2 construction methods linejyonyh discriminant functions should lean against two assumptions [4].

As to the first assumption, areas D1и D2 in which konyotsentrirujutsja installations jn two class-rooms, can be divided (r - І)-dimensional giperyoploskostju:

Equation factors ωiмогут to be interpreted in the capacity of parametres which specify a hyperplane inclination in relation to co-ordinate axes, and factors ω0называются a threshold which specify distance from a hyperplane prior to the beginning of co-ordinates.

In the second the criteriaon of performance of delimitation of areas D1и D2 by a hyperplane at () + w0 = 0 is sized up.

To count a vector of optimum weight numbers w it is possible by formula:

Where mi - it is a vector of average values of signs for the class-room ω ·

In a case when installations of each of class-rooms have multidimensional normal distribution with identical kovariatsionnoj matrix S and equal vectors of a mean mi then the threshold value ω0, the minimising criterion of an average probability of an error, will pay off under the following formula:

Artificial neural networks (INS) are widely used in a science and technics and applied in various areas of chemistry, physics and biology. They

Are an excellent method of a problem solving of detection of images with problems in which investigated data do not contain great volumes of data, and existing data have loud noise [20, 97, 98, 99, 100].

Thanks to considerable plasticity of an input information, INS have appeared useful at the analysis of samples of blood and urine of patients with a diabetes (Catalogna et

al. 2012, Fernandez de Canete et al. 2012), tuberculosis diagnostic (Er et al. 2008, Elveren and Yumusak 2011), classification lejkozov (Dey et al. 2012), the analysis difficult vypotnyh samples (Barwad et al. 2012) and the analysis of images on roentgenograms or even a living tissue (Barbosa et al. 2012, Saghiri et al. 2012).

INS is a mathematical representation of neural architecture of the person, reflecting its abilities to instruction and generalisation [101, 102, 138]. For this reason INS refer to to artificial intellect area. INS are widely applied in researches because they can model strongly nonlinear systems in which communication between variables is unknown or very difficult.

Mathematical substantiation. The neural network is formed by a series of "nerve cells" (or "knots") which are organised in layers. Each nerve cell in a layer is connected with each nerve cell in a following layer through the weighed joint. Value of weight

w. Specifies in a bonding force between i-м nerve cell in a layer and j-м nerve cell in the following. The structure of a neural network consists of the "entrance" layer, one or several "latent" layers and a "target" layer [21]. The quantity of nerve cells in a layer and quantity of layers strongly depends on complexity of investigated system. Hence, the optimum architecture of a network should be defined. The general circuit design of typical three-layer architecture of a neural network is resulted in drawing 1.2 [29, 30].

Drawing 1.2 - the General structure of a neural network with two latent layers. w. - weight

AT

Communications between 1st and j-м in knot.

Nerve cells in an entrance layer are obtained by data and transfer to their nerve cells in the first latent layer through the weighed communications. Here data matematicheski are processed, and the result is transferred to nerve cells in a following layer. In the final reckoning, nerve cells in last layer provide a network exit. J-й the nerve cell in the latent layer processes entering data () means (i) scalings of the weighed sum and addition of a member of displacement (#.) according to the equation 17:

Peobrazovanie netjчерез suitable mathematical "transfer function" and transfer of result to nerve cells in a following layer. Are accessible various peradatochnye to function (Zupan and Gastelger, 1999); nevertheless, it is used sigmovidnaja more often:

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Instruction. Mathematical process by means of which the network attains "instruction", can be ignored in the core by the end user [22]. Thus, the network can be observed as «a black container» which gains a vector with m entries and gives a vector with n exits (drawing 1.3) [31, 32].

Drawing of 1.3-details of elements of the input and output, referring to to diagnostic on the basis of neural city (the architecture is often hidden and it is marked out as a black container).

The network is trained on series of "instances" which form «educational baseline

Drawing 1.4 - the Instance of structure of an educational database. Each line refers to to other patient marked with a numeric code. The element datak, i refers to to i-м to medical data (a symptom, laboratory findings etc.) k th patient.

It is attained by iterative change of values of scales of joints (w) according to the suitable mathematical rule named At

Algorithm of instruction. Values of scales change with use of method of steepest descent to minimise the suitable function used in the capacity of of criterion of a stop of training. One of most often used functions is the discrepancy of the sum of the squares, set by the equation 20:

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Where - actual and network j-й a leading-out matching і

To entrance vector accordingly. Current change of weight on the given layer is given by the formula 21:

Where η - the positive constant named in the speed of instruction. To achieve faster instruction and to avoid local minima, the additional term and the equation 21 is used becomes:

Where μ - a member of "pulse", and - change of weight thive of a cycle

Instruction. Speed of instruction controls speed of updating of weight according to new change of weight, and the pulse acts as the stabilizer, realising the previous change of weight.

The function set by the equation 20 also is used in the capacity of criterion for optimisation of architecture of a network as it depends on quantity of the latent layers and quantity of nerve cells in them. To find optimum architecture, the most widespread approach is construction of the schedule of value E (the equation 20), as functions from quantity of knots in the latent layer (q). The instance of such schedule is resulted in drawing 1.5.

Drawing 1.5 - the Instance of the schedule used for sampling of optimum quantity of knots in the given latent layer. It is specified, that too the considerable quantity of knots can lead to conversion training.

With increase q - E decreases. However after optimum value q martempering weak enough. Usually optimum value q is from an intersection point of two branches of the schedule. After the optimum architecture of a neural network is found, instruction process is carried out until appropriate minimum value E will be attained. After that the network is mustered on instances which were not used earlier at a grade level. This process is called as check. At last, the network can be used for forecasting of exits for new entrance vectors [33, 34].

Structure of an educational database. As it is specified above, the network should be trained with use of a suitable database. The database represents the table (or a matrix) the data concerning patients, for which diagnosis

(Positive or negative) about certain disease it is already known. Each number of a matrix refers to to one patient. First m elements of a line are medical data, and last n elements an output information (diagnosis) represents. The term «medical data» specifies in a biochemical, nuclear magnetic resonance (nuclear magnetic resonance), laboratory findings, and also symptoms and other information given by the medical specialist. The instance of such training matrix from one target variable (n = 1) which can accept two possible values (positive or negative), is resulted in drawing 1.4.

Survey of neural networks in medical diagnostic. Neural networks were applied at diagnostic: kolorektalnogo a cancer (Spelled et al. 2012), multiple sclerosis defeats (Mortazavi et al. 2012a, b), a cancer of a thick gut (Ahmed 2005), (iv) pancreas disease (Bartosch-Harlid et al. 2008), (v)

Gynecologic diseases (Siristatidis et al. 2010) and an early diabetes

(Shankaracharya et al. 2010). Besides, neural networks also were applied at the analysis of data and diagnostic classification of patients with not investigated dispepsiej in gastroenterology (Pace and Savarlno 2007) and by search of biolabels (Bradley 2012). The new, general, sweeping and adaptive system of diagnostic of diseases has been developed on the basis of INS quantizations of vectors of instruction. This algorithm is the first offered adaptive algorithm and can be applied to absolutely different diseases that proves to be true the accuracy of classification of 99,5 % attained at a cancer a mammary gland and a thyroid gland. The cancer, a diabetes and cardiovascular diseases are among the most serious and various diseases. The volume of the data arriving from the instrumental and clinical analysis of these diseases, is great enough, and consequently working out of tools is of great importance for simplification of diagnostic.

Iskustvennye neural networks represent the powerful tool helping doctors to carry out diagnostic and other forced measures. In this respect INS have a number of advantages, including:

- Ability to process great volume of data;

- Decrease in probability of the dropping of the matching information;

- Abbreviation of a time of diagnostic. INS have appeared suitable for satisfactory diagnostic of various diseases.

Besides, their use does diagnostic of more reliable and, hence, raises satisfaction of patients. However, despite their wide application in modern diagnostic, they should be observed only as the tool promoting adoption of the definitive solution by the clinical physician which finally is responsible for a critical estimation of an exit nejronnnoj networks. Methods of generalisation and refinement of informative and intellectual data are constantly improved and can promote largely to effective, exact and sweeping medical diagnostic.

For computer implementation of diagnostic model system Matlab with integration into medium M§sgozoj Visual C # by means of the library comprising the trained neural network [35] has been chosen. The model of differential diagnostic of diseases of lungs which with certain accuracy can refer to the individual to certain group of the presented has been as a result builted.

1.3

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Scientific source Vasilchenko Vladislav Alekseevich. INTELLECTUALIZATION of PROCESSES of ADOPTION of MEDICAL SOLUTIONS Within the limits of a bioengineering system of DIAGNOSTIC And TREATMENT of PULMONOLOGICHESKY DISEASES. The dissertation on competition of a scientific degree of a Cand.Tech.Sci. Voronezh - 2019. 2019

Other medical related information Survey of mathematical methods of adoption of medical solutions taking into account specificity of pulmonary diseases:

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