Beyond Staircasing Effect: Robust Image Smoothing via <i>ℓ</i>₀ Gradient Minimization and Novel Gradient Constraints

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.

Keywords

• image smoothing
• detail enhancement
• total variation
• <i>ℓ</i>₀ pseudo-norm
• alternating direction method of multipliers