{"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/accelerated-inference-in-markov-random-fields","title":"Accelerated Inference in Markov Random Fields via Smooth Riemannian Optimization","arxiv_id":"1810.11689","date":"2018-10-27","proceeding":null,"authors":["Siyi Hu","Luca Carlone"],"abstract":"Markov Random Fields (MRFs) are a popular model for several pattern\nrecognition and reconstruction problems in robotics and computer vision.\nInference in MRFs is intractable in general and related work resorts to\napproximation algorithms. Among those techniques, semidefinite programming\n(SDP) relaxations have been shown to provide accurate estimates while scaling\npoorly with the problem size and being typically slow for practical\napplications. Our first contribution is to design a dual ascent method to solve\nstandard SDP relaxations that takes advantage of the geometric structure of the\nproblem to speed up computation. This technique, named Dual Ascent Riemannian\nStaircase (DARS), is able to solve large problem instances in seconds. Our\nsecond contribution is to develop a second and faster approach. The backbone of\nthis second approach is a novel SDP relaxation combined with a fast and\nscalable solver based on smooth Riemannian optimization. We show that this\napproach, named Fast Unconstrained SEmidefinite Solver (FUSES), can solve large\nproblems in milliseconds. Contrarily to local MRF solvers, e.g., loopy belief\npropagation, our approaches do not require an initial guess. Moreover, we\nleverage recent results from optimization theory to provide per-instance\nsub-optimality guarantees. We demonstrate the proposed approaches in\nmulti-class image segmentation problems. Extensive experimental evidence shows\nthat (i) FUSES and DARS produce near-optimal solutions, attaining an objective\nwithin 0.1% of the optimum, (ii) FUSES and DARS are remarkably faster than\ngeneral-purpose SDP solvers, and FUSES is more than two orders of magnitude\nfaster than DARS while attaining similar solution quality, (iii) FUSES is\nfaster than local search methods while being a global solver.","url_abs":"http://arxiv.org/abs/1810.11689v2","url_pdf":"http://arxiv.org/pdf/1810.11689v2.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":"accelerated-inference-in-markov-random-fields","repo_url":"https://github.com/MIT-SPARK/FUSES","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[{"task_slug":"image-segmentation","task_name":"Image Segmentation"},{"task_slug":"riemannian-optimization","task_name":"Riemannian optimization"},{"task_slug":"semantic-segmentation","task_name":"Semantic Segmentation"}],"methods":[{"method_slug":"speed","method_name":"SPEED"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}