{"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/gpu-based-computation-of-2d-least-median-of","title":"GPU-Based Computation of 2D Least Median of Squares with Applications to Fast and Robust Line Detection","arxiv_id":"1510.01041","date":"2015-10-05","proceeding":null,"authors":["Gil Shapira","Tal Hassner"],"abstract":"The 2D Least Median of Squares (LMS) is a popular tool in robust regression\nbecause of its high breakdown point: up to half of the input data can be\ncontaminated with outliers without affecting the accuracy of the LMS estimator.\nThe complexity of 2D LMS estimation has been shown to be $\\Omega(n^2)$ where\n$n$ is the total number of points. This high theoretical complexity along with\nthe availability of graphics processing units (GPU) motivates the development\nof a fast, parallel, GPU-based algorithm for LMS computation. We present a CUDA\nbased algorithm for LMS computation and show it to be much faster than the\noptimal state of the art single threaded CPU algorithm. We begin by describing\nthe proposed method and analyzing its performance. We then demonstrate how it\ncan be used to modify the well-known Hough Transform (HT) in order to\nefficiently detect image lines in noisy images. Our method is compared with\nstandard HT-based line detection methods and shown to overcome their\nshortcomings in terms of both efficiency and accuracy.","url_abs":"http://arxiv.org/abs/1510.01041v1","url_pdf":"http://arxiv.org/pdf/1510.01041v1.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":"abstracts"},"code_links":[{"paper_slug":"gpu-based-computation-of-2d-least-median-of","repo_url":"https://github.com/ligaripash/CudaLMS2D","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":null,"task_name":"CPU"},{"task_slug":null,"task_name":"GPU"},{"task_slug":"line-detection","task_name":"Line Detection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}