Semi-Global Weighted Least Squares in Image Filtering
Wei Liu, Xiaogang Chen, Chuanhua Shen, Zhi Liu, Jie Yang
Abstract
Solving the global method of Weighted Least Squares (WLS) model in image filtering is both time- and memory-consuming. In this paper, we present an alternative approximation in a time- and memory- efficient manner which is denoted as Semi-Global Weighed Least Squares (SG-WLS). Instead of solving a large linear system, we propose to iteratively solve a sequence of subsystems which are one-dimensional WLS models. Although each subsystem is one-dimensional, it can take two-dimensional neighborhood information into account due to the proposed special neighborhood construction. We show such a desirable property makes our SG-WLS achieve close performance to the original two-dimensional WLS model but with much less time and memory cost. While previous related methods mainly focus on the 4-connected/8-connected neighborhood system, our SG-WLS can handle a more general and larger neighborhood system thanks to the proposed fast solution. We show such a generalization can achieve better performance than the 4-connected/8-connected neighborhood system in some applications. Our SG-WLS is ~20 times faster than the WLS model. For an image of MxN, the memory cost of SG-WLS is at most at the magnitude of max\ 1 / M, 1 / N\ of that of the WLS model. We show the effectiveness and efficiency of our SG-WLS in a range of applications.
BibTeX
@inproceedings{iccv2017_semiglobalweight,
title = {Semi-Global Weighted Least Squares in Image Filtering},
author = {Wei Liu and Xiaogang Chen and Chuanhua Shen and Zhi Liu and Jie Yang},
booktitle = {ICCV 2017},
year = {2017}
}