Research On Image Smoothing Based On L₀ Gradient Minimization

Images contain rich and well-structured visual information.while in the course of transmission and acquisition,they are often cottupted by noise and cause errors.These not only have a serious impact on the visual effects of image,but also bring great difficulties to the subsequent image analysis and processing.Therefore,image smoothing as a basic technology in the field of image processing has an important practical significance.Recently,partial differential based image smoothing methods have been widely applied and studied.Specifically,after total variation?TV?modelis proposed,many improved models are derived.L₀ gradient minimization?LGM?has been widely applied successfully in image smoothing.As an improvement of the total variation?TV?model which employs the L₁ norm of the image gradient,the LGM model also suffers from the staircasing effect and is not robust to noise,even though adopts the L₀ norm and performs better when smoothing the piecewise constant images.In order to overcome these drawbacks,this paper proposes two novel methods based on LGM algorithm as follows:Firstly,image smoothing based on the gradient filtering of L₀ gradient minimization?GFLGM?algorithm.When introduce the variables,LGM model ignores the effect of image noise and it's results exist the staircasing.Therefore,this paper proposes an improvement of the LGM model by prefiltering the image gradient.Experimental results have demonstrated that the proposed method not only overcomes the staircasing artifact effectively but also achieves a good image smoothing effect.Secondly,we extend the GFLGM model by replaceing the L₂ fidelity term by L₁ fidelity term and propose the GFLGM-L₁ model.The L₁ fidelity is more robust than the L₂ one when erroneous measurements exist.As a result,the proposed method not only behaves robustly to noise but also improves the ability of edge preserving besides further better improvement of image smoothing.