Method for clarifying the boundaries of inhomogeneity on a dynamic image for EIT

. This article proposes an algorithmic solution to refine the boundaries of heterogeneity in a dynamic image for EIT. The essence of the method is to calculate the rate of change of the color value of each pixel p(i,j) Gn for a given research area. Next, the received data array is processed and the initial image of the heterogeneity region Gn is scaled. Software has been developed that implements the proposed algorithmic solutions. The method of automatic control of the parameters of the EIT examination is implemented, which consists in the automatic mode of operation without operator intervention from the moment of setting the parameters of the examination to the receipt of the final result. The operation of the method for refining the boundaries of inhomogeneity has been tested on computer models. According to the results of the study, the error in determining γ was reduced by 1.44 times. Thus, it seems possible to reduce it when transmitting and digitizing measurement data.


Introduction
Solving the problems of improving the correctness of the results of EIT research [1][2][3][4][5] is one of the main directions of its development. This direction is a wide range of tasks aimed at improving the quality of rendered dynamic images. Of particular importance is information about the boundaries of the internal structures of the object under study. This is due to the fact that the acquisition of measurement data is not ideal, but is associated with certain errors that occur during transmission and their digitization. Also, the incorrectness of the solution of the inverse problem is of great importance on the result of the reconstruction. In this regard, the development of methods and algorithms aimed at clarifying the boundaries of the visualized structures is relevant.
The practical implementation of the method requires the development of an algorithm for clarifying the boundaries of heterogeneity in the EIT-image, software, as well as a method for automatically controlling the EIT-study process. Given the above, the tasks that need to be solved in the course of this work are defined: -to develop in the form of an algorithm a method for clarifying the boundaries of heterogeneity on a dynamic image for EIT; -to develop in the form of an algorithm a method for automatic control of the process of EIT-research -develop software that implements the developed algorithms; -check the operation of the algorithm on computer models of inhomogeneities.

Development of a method for clarifying the boundaries of inhomogeneity in an EIT image
The implementation of the method in practice requires the creation of hardware and software solutions for measuring, reconstructing and analyzing the data obtained [6][7][8].
In general terms, the process of obtaining and processing the results of an EIT study is shown in figure 1. At the same time, the processing of results is one of the most important stages of an effective EIT study. In this regard, the implementation of this block requires the development and creation of new methods and algorithms that can generally improve the quality of the results obtained.
One of the proposed approaches is the construction of this block in the form of sequential execution of the following algorithms: -measurement of potential differences between measuring electrodes ("Measurement"); -reconstruction of the conduction field ("Reconstruction"); -calculation of the linear dimensions of the found inhomogeneity ("Calculation of linear dimensions"); -making decisions based on the received data ("Decision Making"). Thus, the circuit shown in Figure 1 can be represented as the following circuit shown in Figure 2. The method for refining the boundaries of heterogeneity in the reconstructed EIT image consists in calculating the rate of change of the color value of each pixel p(i,j) in the region of heterogeneity Gn, which lies in the horizontal and vertical planes relative to 〖p(i〗 _0,j_0)∈Gn, and processing obtained array of derivatives in order to obtain extrema corresponding to the refined boundaries of the studied inhomogeneity, and subsequent scaling of the preliminary binarized region, taking into account the obtained data on the dimensions Gn, in order to preserve information about its shape. The method for refining the dimensions of the heterogeneity is to analyze the derived values in each pixel of the deri image. A schematic representation of the method for generating the deri array and finding the refined boundaries Gn is shown in Figure 3 and has the following form: The algorithm that implements the proposed method uses the investigated array of pixels M'. The color values p col are read at the points i_0, j, i, j_0, which are then stored in an array. The block diagram of the algorithm for reading col in a column and row is shown in Figure 4.   The derivative of the pixel value is calculated as the modulus of the difference between the col values of the current and previous p(i): To find the boundaries of the inhomogeneity, the array , is analyzed, starting from the element iG0 with coordinates 0 , 0 , towards = 1 и = , in order to find the elements iG1 and iG2, that satisfy the condition where bord -given threshold , chosen as the arithmetic mean of all elements of the array of derivatives der: Thus, as a result of determining the boundaries Gn iG1 and iG2 we get the corrected value dx': To refine the boundaries of Gn coefficient Cx is used: In a similar way, one finds dy' and Cy. Next, the found coefficients Cx and Cy re used to scale the original image Gn horizontally and vertically, respectively, as shown in figure 6. As a result of applying the developed method, we obtain the image Gn'.

An application that implements an algorithm for refining the boundaries of inhomogeneity in a reconstructed EIT image
The proposed methods and algorithms for calculating and refining the sizes and boundaries of the inhomogeneity are implemented in the form of software that performs the functions of filtering the reconstructed image I, calculating and refining its linear dimensions and the boundaries of the existing inhomogeneities Gn.
The developed program is a window with a button for selecting a reconstructed image file. When the button is pressed, the user is prompted to select a file containing I, as shown in figure 7.   As a result, the proposed method for calculating linear dimensions and a method for refining the boundaries of inhomogeneity in the reconstructed EIT image are proposed and implemented in the form of algorithms and software.

Development of an algorithm for automatic control of the EIT study process
The automatic control algorithm for the EIT study process implements a method for automatic control of the EIT study parameters, and consists in automatic operation without operator intervention from the moment the study parameters are set to the final result. Implemented automatic control of switching of individual injection and measurement channels IC, GND, M1, M2, njection current parameters Fcs and Acs, as well as the gain of the kMPGA measuring amplifier.
The automatic control method is implemented as an automatic control function P: P = f(Fcs, Acs, t, kMPGA, Δφi, IC, GND, M1, M2), When starting the measurement process, the initial parameters are set Fcs, Acs. For automatic control of electrode switching, the following algorithm is used, which is a private implementation of the P function (the block diagram of the algorithm is shown in figure 11). The switching algorithm of the injection electrodes IC, GND is as follows: the current source СIS is connected to the electrode Ei, i=1. After that, a test measurement of Δφi is performed on each pair of Ei+1, Ei+2, at which kMPGA = 1, as a result, the maximum value of kMPGA is selected-the gain of the MPGA measuring signal so that the output signal of the circuit does not exceed the measurement limit of the analog-to-digital converter Umax: kMPGA Δφi ≤ Umax.
Thus, the gain of the MPGA measurement signal is a function kMPGA = f(Δφi).
Next, the measurement of Δφi is performed using the selected kMPGA.  Next, the CIS source is connected to the next electrode (i=2) and the process is repeated until all Ei are used as injectors (i=N). Thus, an array of measurement data of length i2 is formed.

Conclusion
As a result of the work performed, a method was proposed and implemented in the form of an algorithm for refining the boundaries of inhomogeneity in the reconstructed EIT image, which consists in calculating the rate of change in the color value of each pixel of the selected area, which lies in the horizontal and vertical planes relative to the center of inhomogeneity, and processing the resulting array of derivatives to obtain extrema , corresponding to the refined boundaries of the studied inhomogeneity, and subsequent scaling of the preliminary binarized region, taking into account the obtained data on the sizes of the inhomogeneity dx' and dy'.
Also proposed and implemented in the form of an algorithm is a method of automatic control of the EIT-study process, which consists in the automatic operation of the complex without operator intervention from the moment of setting the parameters of the study to obtaining the final result. Automatic control of switching of individual injection and measurement channels, the shape, frequency and amplitude of the injection current, as well as the gain of the measuring amplifier as a function P = f(Fcs, Acs, t, kMPGA, Δφi, IC, GND, M1, M2).