<italic>L</italic><sub>0</sub> Optimization Using Laplacian Operator for Image Smoothing

Abstract

<p indent=0mm>Image smoothing often leads to the loss of image details and distortion because of over smoothing. An image smoothing method is presented which combines<inline-formula id=inline3><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>optimization and the second-order Laplacian operator. Laplacian operator is used to constrain the color change of the image, and <inline-formula id=inline4><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>optimization is used to minimize the change of the color gradient, so as to achieve the purpose of smooth color transition of the image. In order to keep the edge features of the image better in the process of smoothing, Sobel operator is introduced as the regular term of energy function, and the alternating solution strategy is adopted to solve the energy function. In the experiment, using the classical image in the field of image smoothing and the image obtained through network engine, the proposed method is compared qualitatively and quantitatively with 6 smoothing methods and 7 denoising methods. The experimental results show that the proposed method can reduce the loss of image details while smoothing the image, effectively deal with the phenomenon of stepped edges and color block distribution in the image smoothing, and effectively remove various noises in the image. And the peak signal-to-noise ratio and running time of the proposed method are improved compared with other methods.