{"paper":{"title":"Illusory Shapes via Phase Transition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","q-bio.NC"],"primary_cat":"math.OC","authors_text":"Jianhong Jackie Shen, Yoon Mo Jung","submitted_at":"2014-06-05T04:40:31Z","abstract_excerpt":"We propose a new variational illusory shape (VIS) model via phase fields and phase transitions. It is inspired by the first-order variational illusory contour (VIC) model proposed by Jung and Shen [{\\em J. Visual Comm. Image Repres.}, {\\bf 19}:42-55, 2008]. Under the new VIS model, illusory shapes are represented by phase values close to 1 while the rest by values close to 0. The 0-1 transition is achieved by an elliptic energy with a double-well potential, as in the theory of $\\Gamma$-convergence. The VIS model is non-convex, with the zero field as its trivial global optimum. To seek visually"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1265","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"}