A Method For Image Staircasing Effect And Over-Smoothing Based On PDEs

Nowadays, images are often mixed with a lot of noise. Image noise not only seriouslyaffects the image of visual effects, but also brings certain difficulties to the subsequent imageanalysis and understanding in the image processing. So image smoothing is a very importantstep for the follow-up treatment.Traditional image smoothing algorithms such as mean filter, median filter and Gaussfilter belong to the isotropic diffusion. They remove the noise of the image while underminethe character of the image. The image smoothing technology based on partial differentialequations can solve this problem. They remove the noise while enhance the edge of image.Smoothing image should balance the removing noises and preserving features. Imagesmoothing technology based on PDE is an adaptive smoothing method. During the course ofsmoothing, image features and their directions are extracted. There are less smoothes in thelocations with strong image features, more smoothes in the locations with weak image feature;There are minimal smoothes in the directions across the image features, and maximalsmoothes in the directions along the image features. The smoothing can make noises removedwhile preserve edge well. And it is a quite well smoothing method. Perona-Malik modelsrepresented by such models are already widely applied in marginal detection, imageenhancement and so on. However, when researches are going deeply, people find that thereare staircasing effects as image smoothing using 2-order diffusion equation. For dealing withthe problem, people mainly use higher order method, for example 4-order method, directioncurvature method and complex diffusion method; In addition, when image denosing used byPDE, over-smoothing is also a common problem. For avoiding this problem, we can choosethe appropriate iterative time and improve the diffusion coefficient.In this paper, we improve the diffusion coefficient to avoid the over-smoothing effect,then combine the improved diffusion coefficient with complex diffusion model, bring out anew image smoothing method. This method can integrativly deal with staircasing effect andover-smoothing, the experimental results show the effective performance of the integrativemethod.