{"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/estimating-the-convex-hull-of-the-image-of-a","title":"Estimating the Convex Hull of the Image of a Set with Smooth Boundary: Error Bounds and Applications","arxiv_id":"2302.13970","date":"2023-02-27","proceeding":null,"authors":["Thomas Lew","Riccardo Bonalli","Lucas Janson","Marco Pavone"],"abstract":"We study the problem of estimating the convex hull of the image $f(X)\\subset\\mathbb{R}^n$ of a compact set $X\\subset\\mathbb{R}^m$ with smooth boundary through a smooth function $f:\\mathbb{R}^m\\to\\mathbb{R}^n$. Assuming that $f$ is a submersion, we derive a new bound on the Hausdorff distance between the convex hull of $f(X)$ and the convex hull of the images $f(x_i)$ of $M$ sampled inputs $x_i$ on the boundary of $X$. When applied to the problem of geometric inference from a random sample, our results give error bounds that are tighter and more general than in previous work. We present applications to the problems of robust optimization, of reachability analysis of dynamical systems, and of robust trajectory optimization under bounded uncertainty.","url_abs":"https://arxiv.org/abs/2302.13970v3","url_pdf":"https://arxiv.org/pdf/2302.13970v3.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":"estimating-the-convex-hull-of-the-image-of-a","repo_url":"https://github.com/stanfordasl/convex-hull-estimation","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","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}