Open AccessCorrection of thermographic images based on the minimization method of Tikhonov functional
Author(s) -
Obaida Baaj,
N.V. Chernikova,
Е. Б. Ланеев
Publication year - 2022
Publication title -
yugoslav journal of operations research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.221
H-Index - 21
eISSN - 1820-743X
pISSN - 0354-0243
DOI - 10.2298/yjor211015026b
Subject(s) - tikhonov regularization , smoothing , laplace transform , mathematics , range (aeronautics) , minification , surface (topology) , mathematical analysis , computer science , algorithm , mathematical optimization , inverse problem , computer vision , geometry , materials science , composite material
The paper considers the method of correction of thermographic images (thermograms) obtained by recording in the infrared range of radiation from the surface of the object under study using a thermal imager. A thermogram with a certain degree of reliability transmits an image of the heat-generating structure inside the body. In this paper, the mathematical correction of images on a thermogram is performed based on an analytical continuation of the stationary temperature distribution as a harmonic function from the surface of the object under study towards the heat sources. The continuation is carried out by solving an ill-posed mixed problem for the Laplace equation in a cylindrical region of rectangular cross-section. To construct a stable solution to the problem, the principle of the minimum of the Tikhonov smoothing functional we used.