Model of data approximation for infrared thermometry

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.