Beyond Staircasing Effect: Robust Image Smoothing via ℓ0 Gradient Minimization and Novel Gradient Constraints

Signals Pub Date : 2023-09-26 DOI:10.3390/signals4040037
Ryo Matsuoka, Masahiro Okuda
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Abstract

In this paper, we propose robust image-smoothing methods based on ℓ0 gradient minimization with novel gradient constraints to effectively suppress pseudo-edges. Simultaneously minimizing the ℓ0 gradient, i.e., the number of nonzero gradients in an image, and the ℓ2 data fidelity results in a smooth image. However, this optimization often leads to undesirable artifacts, such as pseudo-edges, known as the “staircasing effect”, and halos, which become more visible in image enhancement tasks, like detail enhancement and tone mapping. To address these issues, we introduce two types of gradient constraints: box and ball. These constraints are applied using a reference image (e.g., the input image is used as a reference for image smoothing) to suppress pseudo-edges in homogeneous regions and the blurring effect around strong edges. We also present an ℓ0 gradient minimization problem based on the box-/ball-type gradient constraints using an alternating direction method of multipliers (ADMM). Experimental results on important applications of ℓ0 gradient minimization demonstrate the advantages of our proposed methods compared to existing ℓ0 gradient-based approaches.
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超越阶梯效应:通过l0梯度最小化和新的梯度约束实现鲁棒图像平滑
本文提出了一种基于梯度最小化的鲁棒图像平滑方法,该方法具有新颖的梯度约束,可以有效地抑制伪边缘。同时最小化l0梯度,即图像中非零梯度的数量,并保证l2的数据保真度,得到光滑的图像。然而,这种优化通常会导致不受欢迎的工件,例如伪边缘,称为“阶梯效应”,以及光晕,这在图像增强任务中变得更加明显,如细节增强和色调映射。为了解决这些问题,我们引入了两种类型的梯度约束:盒子和球。这些约束使用参考图像(例如,输入图像用作图像平滑的参考)来抑制均匀区域中的伪边缘和强边缘周围的模糊效果。我们还利用交替方向乘法器(ADMM)提出了一个基于盒/球型梯度约束的梯度最小化问题。在一些重要应用上的实验结果表明,与现有的基于梯度的方法相比,我们提出的方法具有优势。
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CiteScore
3.20
自引率
0.00%
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0
审稿时长
11 weeks
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