{"paper":{"title":"Estimating perimeter using graph cuts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Dejan Slep\\v{c}ev, James von Brecht, Nicol\\'as Garc\\'ia Trillos","submitted_at":"2016-02-12T16:20:23Z","abstract_excerpt":"We investigate the estimation of the perimeter of a set by a graph cut of a random geometric graph. For $\\Omega \\subset D = (0,1)^d$, with $d \\geq 2$, we are given $n$ random i.i.d. points on $D$ whose membership in $\\Omega$ is known. We consider the sample as a random geometric graph with connection distance $\\varepsilon>0$. We estimate the perimeter of $\\Omega$ (relative to $D$) by the, appropriately rescaled, graph cut between the vertices in $\\Omega$ and the vertices in $D \\backslash \\Omega$. We obtain bias and variance estimates on the error, which are optimal in scaling with respect to $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04102","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}