{"paper":{"title":"Improving PSF calibration in confocal microscopic imaging---estimating and exploiting bilateral symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.AP","authors_text":"Hajo Holzmann, Miros{\\l}aw Pawlak, Nicolai Bissantz","submitted_at":"2011-02-03T09:30:58Z","abstract_excerpt":"A method for estimating the axis of reflectional symmetry of an image $f(x,y)$ on the unit disc $D=\\{(x,y):x^2+y^2\\leq1\\}$ is proposed, given that noisy data of $f(x,y)$ are observed on a discrete grid of edge width $\\Delta$. Our estimation procedure is based on minimizing over $\\beta\\in[0,\\pi)$ the $L_2$ distance between empirical versions of $f$ and $\\tau_{\\beta}f$, the image of $f$ after reflection at the axis along $(\\cos\\beta,\\sin\\beta)$. Here, $f$ and $\\tau_{\\beta}f$ are estimated using truncated radial series of the Zernike type. The inherent symmetry properties of the Zernike functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0630","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"}