Improved L0 Gradient Minimization with L1 Fidelity for Image Smoothing.

Xueshun Pang,Junhua Gu,Lingling Li,Huaibin Wang,Suqi Zhang,Boying Liu,Li Zeng

doi:10.1371/journal.pone.0138682

Xueshun Pang, Junhua Gu + Show 5 more

Open Access

https://doi.org/10.1371/journal.pone.0138682

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Abstract

Edge-preserving image smoothing is one of the fundamental tasks in the field of computer graphics and computer vision. Recently, L0 gradient minimization (LGM) has been proposed for this purpose. In contrast to the total variation (TV) model which employs the L1 norm of the image gradient, the LGM model adopts the L0 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 L1 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.

Highlights

Image smoothing aims at removing the insignificant details and preserving salient structure such as edges, there are many applications of image smoothing in computer graphics and image processing
Xu et al proposed an improvement of the total variation (TV) model by replacing the L1 norm of the image gradient with the L0 norm, i.e., the L0 gradient minimization (LGM)[34]
We will demonstrate the performance of the proposed method and make a comparison with several state-of-the-art methods including Bilateral filtering(BLF) [1], Weighted least square method(WLS)[33], Total variation (TV)[21]

Summary

Introduction

Image smoothing aims at removing the insignificant details and preserving salient structure such as edges, there are many applications of image smoothing in computer graphics and image processing. Xu et al proposed an improvement of the TV model by replacing the L1 norm of the image gradient with the L0 norm, i.e., the L0 gradient minimization (LGM)[34]. Since the LGM model counts the number of non-zero gradients in the result, it is not robust to noise. Similar to LGM [34], the alternating minimization (AM) algorithm [37] is employed for the ILGM model by introducing auxiliary variables; the AM algorithm yields global optimal result for the ILGM model.

Results

Conclusion