Issue 21

A. Yu Fedorova et alii, Frattura ed Integrità Strutturale, 21 (2012) 46-53; DOI: 10.3221/IGF-ESIS.21.06 48 Using the discrete Fourier transform we can processed all frames of the film ( , ) exp( ( )) ( , )          t x y x y t T k k i k x k y T x y dydx , (1) where x, y – spatial coordinates, t – number of frame, T t (x, y) – temperature at t-th infrared frame, i 1   . To find the relative motion value we used arbitrary selected fragment of first frame of the film (“flag”). One of the variants of “flag” is presented in Fig. 2. Using the Fourier image of first frame     1 1 , exp( ( )) ,         x y x y T k k i k x k y T x y dydx , (2) we can define the position of the chosen fragment in the subsequent frames of the film as follows         1 2 , exp( ( ) 1 ) , , 2      t x y t x y x y x y T x y i k x k y T k k T k k dk dk , (3) The dependence of the "flag" coordinates versus time determines the absolute value of the displacement of each pixel in the image and allows us to compensate for the relative motion. Figure 2 : Implementation of the motion compensation algorithm for the temperature contour images. Spatially fixed temperature signal of the specimen was processed by the two-dimensional discrete Fourier transform with the standard Gaussian kernel to increase data accuracy and eliminate the influence of random temperature fluctuations. The expression for determining the temperature had the form         2 , exp( ( )) , , 2 1        x y x y x y x y T x y i k x k y T k k f k k dk dk , (4) where 2 2 2 2 ( , ) exp ( ( ))       f x y x y - Gaussian kernel,   ,  x y f k k - direct Fourier transform of the standard Gaussian kernel,