{"doi":"10.17615/he59-mq69","title":"Continuous medial representations for geometric object modeling in 2D and 3D","abstract":"We describe a novel continuous medial representation for object geometry and a deformable templates method for tting the representation to images. Our representation simultaneously describes the boundary and medial loci of geometrical objects, always maintaining Blum's symmetric axis transform (SAT) relationship. Cubic b-splines de ne the continuous medial locus and the associated thickness eld, which in turn generate the object boundary. We present geometrical properties of the representation and derive a set of constraints on the b-spline parameters. The 2D representation encompasses branching medial loci; the 3D version can model objects with a single medial surface, and the extension to branching medial surfaces is a subject of ongoing research. We present preliminary results of segmenting 2D and 3D medical images. The representation is ultimately intended for use in statistical shape analysis.","journal":"UNC Libraries","year":2021,"id":230416,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":0,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9572,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2021-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":540895,"name":"Stephen M. Pizer","orcid":"0000-0002-4250-6531","position":1,"is_corresponding":false},{"id":598079,"name":"P. Thomas Fletcher","orcid":null,"position":2,"is_corresponding":false},{"id":836873,"name":"Andrew Thall","orcid":null,"position":3,"is_corresponding":false},{"id":389952,"name":"Sarang Joshi","orcid":"0000-0002-3446-4810","position":4,"is_corresponding":false},{"id":259082,"name":"Paul A. Yushkevich","orcid":"0000-0001-8543-4016","position":0,"is_corresponding":true}],"reference_count":0,"raw_metadata":null,"created_at":"2026-07-18T23:55:05.844766Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}