Slow and Fast Diffusion Effects in Image Processing
The real images are reconstructed by new image processing model based on doubly nonlinear degenerate parabolic partial differential equation of porous-medium type. The governed equation
b(u)_t - div ( g( | G * grad (u) | ) grad ( c(u) ) ) = f (u_0 -u)
is the generalization of the 'modified' (in the sense of Catte, Lions, Morel and Coll) Perona-Malik anisotropic diffusion model. The new nonlinearity is added making the image analysis dependent on values of the intensity function.
In Figure 1., we present the reconstruction of Sandro Botticelli's painting Primavera (Uffizi Gallery, Florence) by 'slowed anisotropic diffusion'. The monotone functions b and c are choosen in accordance to keep the details arround the face, which are destroyed by usual anisotropic diffusion during the selective smoothing process. This effect is documented in comparison given in Figure 2. (left - original, middle - reconstruction by anisotropic diffusion, right - reconstruction by 'slowed anisotropic diffusion') and Figure 3. (left up - photography of St.Martin statue of R.Donner (Domus in Bratislava), right up - its destroyed version, next three pictures - three discrete time-scale steps of 'slowed anisotropic diffusion' model, right bottom - reconstruction by Perona-Malik anisotropic diffusion is given for comparison).
Figure 1.
Figure 2.
Figure 3.
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