基于改进的L_0梯度最小化的图像平滑

Improved L_0 gradient minimization for image smoothing

计算机图像和视觉领域中的一项基本任务是图像平滑,而L0梯度最小化模型(LGM)作为一个最基本的数学工具已被广泛应用于图像平滑领域.作为总变差模型(TV)的改进版本,L0梯度最小化模型采用L0范数来约束图像的梯度并且对分段常数的图像有更好的平滑效果.然而,如同总变差模型一样,L0梯度最小化模型处理的结果图中也存在着严重的阶梯效应并且其对噪声也缺乏鲁棒性.为了克服这些缺点,本文提出了采用L1范数作保真项并且预滤波处理图像梯度的模型,即改进的L0梯度最小化模型.该模型不仅能够克服阶梯效应并且对噪声有较强的鲁棒性.大量的实验结果表明:与现有的方法相比,改进的L0梯度最小化模型能够获得更好的平滑效果.

Edge-preserving image smoothing is one of the fundamental tasks in the field of computer vision and computer graphics and the L0 gradient minimization（LGM）method has been proposed for this purpose very recently. As an improvement of the total variation（TV）model,the LGM model adopts L0 norm and yields much better results for the piecewise constant image. However,like as the TV model,the LGM model also suffers from the staircasing effect and is not robust to noise. In order to overcome these drawbacks,in this paper,we propose an improvement of the LGM model by prefiltering the image gradient and employing the L1 fidelity. The proposed improved LGM（ILGM） behaves robustly to noise and overcomes the staircases effectively. Experimental results show that the ILGM is promising as compared with the existing methods.