Fast and Effective L0 Gradient Minimization by Region Fusion

Abstract

L0 gradient minimization can be applied to an input signal to control the number of non-zero gradients. This is useful in reducing small gradients generally associated with signal noise, while preserving important signal features. In computer vision, L0 gradient minimization has found applications in image denoising, 3D mesh denoising, and image enhancement. Minimizing the L0 norm, however, is an NP-hard problem because of its non-convex property. As a result, existing methods rely on approximation strategies to perform the minimization. In this paper, we present a new method to perform L0 gradient minimization that is fast and effective. Our method uses a descent approach based on region fusion that converges faster than other methods while providing a better approximation of the optimal L0 norm. In addition, our method can be applied to both 2D images and 3D mesh topologies. The effectiveness of our approach is demonstrated on a number of examples.