Efficient Splitting-based Method for Global Image Smoothing

TL;DR

This paper presents a highly efficient splitting-based global image smoothing method that minimizes an ${l_2}$ objective function in linear time, outperforming traditional methods in speed while maintaining high quality.

Contribution

Introduces a novel splitting-based approach that solves a constrained optimization problem for global EPS, enabling linear time solutions for complex smoothing tasks.

Findings

Achieves linear time complexity for global image smoothing.

Converges quickly and is comparable in runtime to local methods.

Demonstrates effectiveness across various vision and image processing tasks.

Abstract

Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and prior terms. This global EPS approach shows better smoothing performance than a local one that typically has a form of weighted averaging, at the price of high computational cost. In this paper, we introduce a highly efficient splitting-based method for global EPS that minimizes the objective function of ${l_2}$ data and prior terms (possibly non-smooth and non-convex) in linear time. Different from previous splitting-based methods that require solving a large linear system, our approach solves an equivalent constrained optimization problem, resulting in a sequence of 1D sub-problems. This enables linear time solvers for weighted-least squares and -total variation problems. Our solver converges quickly, and its runtime is even comparable to state-of-the-art local EPS approaches. We also propose a family of fast iteratively re-weighted algorithms using a non-convex prior term. Experimental results demonstrate the effectiveness and flexibility of our approach in a range of computer vision and image processing tasks.