Gul'manov A.A., Zenovich A.V. Model of data approximation for infrared thermometry

Gul’manov Alеksеy Аtaevich

Master Student in “Applied Mathematics and Informatics”, Volgograd State University
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Prospect Universitetsky, 100, 400062 Volgograd, Russian Federation

Zenovish Andrey Vasilievich

Lecturer, Department of Fundamental Informatics and Optimal Control,
Volgograd State University
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Prospect Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. We consider the problem of data approximation for infrared thermometry and creation of thermal cards for the surface of a human body based on temperature measurements by the infrared thermometer with several sensors. The measuring range is divided into cells of side 1 cm. As the result of measurements we know the values of temperature on the boundary of the square, and it’s required to approximate the temperature inside the squares in order to build a heat map. The proposed approximation method can accurately capture a zone with sharply varying temperatures, and these zones are the most important in the diagnosis of various diseases. We consider two mathematical models of approximation: approximation by harmonic functions and approximation using Coons surfaces. In the first model, the values of harmonic functions in the internal nodes of the grid we found by solving the Dirichlet problem for the Laplace operator. To test the model we used the results of thermometry studies conducted over the past few years in the Volgograd Phlebology Centre of Prof. S. Larin. Computational experiments have shown that the approximation with harmonic functions works well in the case of slowly varying temperatures, but it’s not sufficient for capturing the sharp fluctuations in the temperature. To simulate situations with radical changes in the temperatures is more suitable the approximation of Coons surfaces.

Key words: combined thermometry, infrared thermometry, RTM-diagnostics, Coons surfaces, approximation results.

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Model of data approximation for infrared thermometry by Gul'manov A.A., Zenovich A.V. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №2 (19) 2013 pp. 80-84

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