Image Smoothing Based On Nonlinear Partial Diffe-Rencial Equation

With the popularization of various kinds of digital instruments and products, digital image processing has become a new crossing field of mathematics method and computer technique, in which the image smoothing is a study hotspot all the while. The contradiction of eliminating noise and keeping edges can not be solved by the traditional filtering methods. In order to solve this problem, people have tried kinds of ways. Fortunately, this problem has been solved by the models based on nonlinear partial differential equation. The anisotropic equation is adopted by this kind of technique, and the image is smoothed selectively. This technique based on nonlinear partial differential equation is a kind of promising image smoothing method.In this paper, the forms and the mechanisms of controlling smoothing speed of the five models based on nonlinear partial differential equation are introduced in detail. The derivation course and the discrete scheme of the first model-Perona-Malik model have been expatiated on emphasis. One item of the P-M model is omitted in the P-M's discrete scheme, and the gradient magnitude is replaced by the absolute value of difference quotient. The impacts of these simplifications on the processing time and effect is analyzed. A new semi-implicit scheme is proposed by discreting the original model directly. This scheme is divergent being validated, and it is not limited by the time step length. The experimental result demonstrates that the processing time-cost is reduced and the effect of processing result is improved by the discrete scheme of this paper.The five models based on nonlinear partial differential equation mentioned above can only eliminate Gaussian noise. The Catte model, Alvarez model and the two improved schemes of Alvarez model can also eliminate salt and pepper noise of image with simple content, but their processing results of salt and pepper noise of image with complicated content are not very well. In this paper, a method eliminating mixed noise based on waveletshrikage and forward-and-backward diffusion is proposed by combining the nonlinear partial differentialequation with waveletshrikage and adding a judging function to the forward-and-backward diffusion. This method can not only eliminate Gaussian and salt-and-pepper noise separately but also eliminate the mixed noise parallely.