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

In this paper, we propose robust image-smoothing methods based on l(0) gradient minimization with novel gradient constraints to effectively suppress pseudo-edges. Simultaneously minimizing the l(0) 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 l(0) 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 l(0) gradient minimization demonstrate the advantages of our proposed methods compared to existing l(0) gradient-based approaches.