{"paper":{"title":"A projection algorithm on measures sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OC"],"primary_cat":"math.NA","authors_text":"IMT), Jonas Kahn, Nicolas Chauffert (PARIETAL), PARIETAL), Philippe Ciuciu (NEUROSPIN, Pierre Weiss (ITAV","submitted_at":"2015-09-01T11:17:52Z","abstract_excerpt":"We consider the problem of projecting a probability measure $\\pi$ on a set $\\mathcal{M}\\_N$ of Radon measures. The projection is defined as a solution of the following variational problem:\\begin{equation*}\\inf\\_{\\mu\\in \\mathcal{M}\\_N} \\|h\\star (\\mu - \\pi)\\|\\_2^2,\\end{equation*}where $h\\in L^2(\\Omega)$ is a kernel, $\\Omega\\subset \\R^d$ and $\\star$ denotes the convolution operator.To motivate and illustrate our study, we show that this problem arises naturally in various practical image rendering problems such as stippling (representing an image with $N$ dots) or continuous line drawing (represe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00229","kind":"arxiv","version":1},"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"}