Image smoothing via L ₀ gradient minimization

Abstract

We present a new image editing method, particularly effective for sharpening major edges by increasing the steepness of transition while eliminating a manageable degree of low-amplitude structures. The seemingly contradictive effect is achieved in an optimization framework making use of L 0 gradient minimization, which can globally control how many non-zero gradients are resulted in to approximate prominent structure in a sparsity-control manner. Unlike other edge-preserving smoothing approaches, our method does not depend on local features, but instead globally locates important edges. It, as a fundamental tool, finds many applications and is particularly beneficial to edge extraction, clip-art JPEG artifact removal, and non-photorealistic effect generation.

Fast Edge-Aware Processing via First Order Proximal Approximation

“…(a) Input (b) BLF [1] (c) NCF [11] (d) TV [20] (e) Extrema [27] (f) GF [28] (g) WLS [16] (h) L0 [21] (i) Proposed [21]). The proposed method produces high-quality smoothing while being flexible and computationally efficient.…”

“…GPU processing can be used instead of the CPU for real-(a) Input (b) BLF [13] (c) NC [11] (d) WLS [16] (e) Extrema [27] (f) GF [28] (g) L0 [21] (h) Proposed method Fig. 15: Edge simplification example (picture from [21]). The proposed method permits to extract relevant edge structures while being computationally efficient.…”

“…The approach has shown to produce improved smoothing results and was successfully used in detail manipulation applications. Xu et al make use of the l 0 -minimization framework [21] to progressively suppress details. The l 0 quasi-norm is a non-convex and non-differentiable function that highly promotes sparsity.…”

“…In order to preserve sharp edges, the regularization term should promote sparsity in the gradient domain. Minimization results in solving large inhomogeneous linear systems in the case of the WLS method or a large iteration number of gradient shrinkage/reconstruction such as the case of the method in [21]. We provide in Figure 1 some smoothing results on synthetic data to compare local filtering methods such as the bilateral filter and optimization methods such as WLS and the proposed method.…”

A generalized relative total variation method for image smoothing

“…Unfortunately, feature-preserving filtering is inherently challenging, because it is difficult to distinguish features from noise. There exist some different feature-preserving filtering methods, which can be roughly classified into two categories, i.e., spatial filters [6,9,13,18,25] and variational models [10,23,27,28]. They differ from each other in how they define edges and how this prior information guides smoothing.…”