{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/semi-global-weighted-least-squares-in-image-1","title":"Semi-Global Weighted Least Squares in Image Filtering","arxiv_id":"1705.01674","date":"2017-05-04","proceeding":null,"authors":["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 $\\sim20$ times faster than the WLS model. For an image of $M\\times N$, the memory cost of SG-WLS is at most at the magnitude of $max\\{\\frac{1}{M}, \\frac{1}{N}\\}$ of that of the WLS model. We show the effectiveness and efficiency of our SG-WLS in a range of applications. The code is publicly available at: https://github.com/wliusjtu/Semi-Global-Weighted-Least-Squares-in-Image-Filtering.","url_abs":"http://arxiv.org/abs/1705.01674v4","url_pdf":"http://arxiv.org/pdf/1705.01674v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"semi-global-weighted-least-squares-in-image-1","repo_url":"https://github.com/wliusjtu/Semi-Global-Weighted-Least-Squares-in-Image-Filtering","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}