Improved L(0) Gradient Minimization with L(1) Fidelity for Image Smoothing

Edge-preserving image smoothing is one of the fundamental tasks in the field of computer graphics and computer vision. Recently, L(0) gradient minimization (LGM) has been proposed for this purpose. In contrast to the total variation (TV) model which employs the L(1) norm of the image gradient, the LGM model adopts the L(0) norm and yields much better results for the piecewise constant image. However, as an improvement of the total variation (TV) model, the LGM model also suffers, even more seriously, 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 L(1) fidelity. The proposed improved LGM (ILGM) behaves robustly to noise and overcomes the staircasing artifact effectively. Experimental results show that the ILGM is promising as compared with the existing methods.