{"paper":{"title":"A Transport for imaging process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"J\\'er\\^ome Pousin, Martine Picq, Olivier Besson","submitted_at":"2012-06-23T16:27:27Z","abstract_excerpt":"This work originates from a heart's images tracking which is to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one both supposed segmented. Given two images $\\rho_0$ and $\\rho_1$, we calculate an evolution process $\\rho(t,\\cdot)$ which transports $\\rho_0$ to $\\rho_1$ by using the optical flow. In this paper we propose an algorithm based on a fixed point formulation and a space-time least squares formulation of the transport equation for computing a transport problem. Existence results are given for a transport problem with a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5406","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"}