Improved L0 Gradient Minimization with L1 Fidelity for Image Smoothing

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.

Image smoothing via truncated gradient regularisation

“…For the sake of reproducibility, we have chosen representatives of the state-of-the-art for which either source code or executables are readily available. The comparison methods include the BLF filterbased scheme (BLF) [4], the guided image filter-based scheme (guided filter) [11], the relative TV measure scheme (RTV) [16], the gradient-based ℓ 0 -regularised scheme (L0) [17], the improved ℓ 0 scheme by prefiltering the image gradient and employing the ℓ 1 fidelity (IL0) [18], the five-directional partial derivatives-based approach (D5D) [21]. Besides the ℓ 0 scheme, two more sophisticated approaches IL0 and D5D are considered to obtain the initial guesses, and the corresponding proposed two-stage smoothing algorithms are designated by L0-TL0, IL0-TL0 and D5D-TL0, respectively.…”

“…Cheng et al [19] developed an efficient approximation algorithm based on a fused coordinate descent framework for the non-convex ℓ 0 optimisation problem, which can obtain a solution with good gradient sparsity and sufficiently close to the original input. Pang et al [18] proposed an improved ℓ 0 regularised model by prefiltering the image gradient and employing the ℓ 1 fidelity. It behaves robustly to the noise and overcome the drawbacks of staircase artefacts effectively.…”

Accurate Extraction Method for Structural Features of Building Facades Through Texture Fusion

“…The total variation (TV) model, which is frequently used in the image noise processing field, has long been introduced to image texture fusion research [35], [36]. As the norm of image gradient, TV can effectively represent and separate textural elements and structural features [37]- [39]. On the basis of TV, Xu et al developed the relative total variation (RTV) model [38].…”

Smoothing of Mammogram Using an Improved Gradient based Technique

“…The non-local mean (NLM) lter [9,10] compares the gray value at one point, as well as the spatial structure in the whole neighborhood. Pang et al [11] proposed improved L 0 gradient minimization to overcome stair casing artifacts. Feihang and Lifeng [12] proposed a gradient minimization for Chinese calligraphy works on steles to remove the noise.…”