{"id":"https://openalex.org/W7138089402","doi":"https://doi.org/10.48550/arxiv.2603.13503","title":"A Discrete Radon Transform Based on the Area of Cube-Plane Intersection","display_name":"A Discrete Radon Transform Based on the Area of Cube-Plane Intersection","publication_year":2026,"publication_date":"2026-03-13","ids":{"openalex":"https://openalex.org/W7138089402","doi":"https://doi.org/10.48550/arxiv.2603.13503"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.13503","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13503","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.13503","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091764895","display_name":"Robert Beinert","orcid":"https://orcid.org/0000-0002-7813-2762"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Beinert, Robert","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092513065","display_name":"Jonas Bresch","orcid":"https://orcid.org/0009-0009-3855-0933"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bresch, Jonas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054449081","display_name":"Michael Quellmalz","orcid":"https://orcid.org/0000-0001-6206-5705"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Quellmalz, Michael","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.725600004196167,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.725600004196167,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12549","display_name":"Image and Object Detection Techniques","score":0.10639999806880951,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.05290000140666962,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/radon-transform","display_name":"Radon transform","score":0.7236999869346619},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6980999708175659},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6480000019073486},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.6320000290870667},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5856999754905701},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5633000135421753},{"id":"https://openalex.org/keywords/unit-cube","display_name":"Unit cube","score":0.49399998784065247},{"id":"https://openalex.org/keywords/marching-cubes","display_name":"Marching cubes","score":0.4797999858856201}],"concepts":[{"id":"https://openalex.org/C197231052","wikidata":"https://www.wikidata.org/wiki/Q979829","display_name":"Radon transform","level":2,"score":0.7236999869346619},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6980999708175659},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6480000019073486},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.6320000290870667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6144999861717224},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5856999754905701},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5633000135421753},{"id":"https://openalex.org/C60432849","wikidata":"https://www.wikidata.org/wiki/Q2072112","display_name":"Unit cube","level":2,"score":0.49399998784065247},{"id":"https://openalex.org/C42087268","wikidata":"https://www.wikidata.org/wiki/Q1886184","display_name":"Marching cubes","level":3,"score":0.4797999858856201},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44749999046325684},{"id":"https://openalex.org/C545943180","wikidata":"https://www.wikidata.org/wiki/Q1133","display_name":"Radon","level":2,"score":0.4113999903202057},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.37290000915527344},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.34869998693466187},{"id":"https://openalex.org/C78168278","wikidata":"https://www.wikidata.org/wiki/Q5227269","display_name":"Data cube","level":2,"score":0.3325999975204468},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.31119999289512634},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29739999771118164},{"id":"https://openalex.org/C113740112","wikidata":"https://www.wikidata.org/wiki/Q5904738","display_name":"Slab","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26989999413490295},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25929999351501465},{"id":"https://openalex.org/C97742081","wikidata":"https://www.wikidata.org/wiki/Q7820109","display_name":"Tomographic reconstruction","level":3,"score":0.258899986743927},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.13503","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13503","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.13503","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13503","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,141],"Radon":[1,41,59,85],"transform":[2,42,60,86],"is":[3,64,147],"a":[4,34,57,80,88,101,114,150],"fundamental":[5],"tool":[6],"for":[7,39,68],"analyzing":[8],"data":[9,70],"in":[10,47,61,129,144],"tomographic":[11],"imaging,":[12],"optimal":[13],"transport,":[14],"crystallography,":[15],"and":[16,30,71,100,113,137],"geometric":[17],"analysis.":[18],"Numerical":[19,120],"computations":[20],"require":[21],"an":[22,44],"accurate":[23],"discretization.":[24],"To":[25],"deal":[26],"with":[27,152],"voxelized":[28,69],"images":[29],"objects,":[31],"we":[32,55,78],"derive":[33],"closed-form,":[35],"piecewise":[36],"polynomial":[37],"expression":[38],"the":[40,84,91,95,104,108,111,118,123,126],"of":[43,87,94,107,125],"axis-aligned":[45],"cube":[46,99,112],"arbitrary":[48],"dimension":[49],"$d$.":[50],"Building":[51],"on":[52],"this":[53],"formula,":[54],"propose":[56],"discrete":[58],"$\\mathbb{R}^d$":[62],"that":[63,98],"both":[65],"analytically":[66],"exact":[67],"computationally":[72],"efficient.":[73],"For":[74],"improved":[75],"numerical":[76],"stability,":[77],"introduce":[79],"regularized":[81],"variant":[82],"replacing":[83],"cube,":[89],"i.e.\\":[90],"$(d-1)$-dimensional":[92],"area":[93],"intersection":[96,109],"between":[97,110],"hyperplane,":[102],"by":[103,149],"$d$-dimensional":[105],"volume":[106],"thin":[115],"slab":[116],"around":[117],"hyperplane.":[119],"experiments":[121],"demonstrate":[122],"effectiveness":[124],"proposed":[127],"approach":[128],"several":[130],"applications":[131],"including":[132],"3D":[133],"shape":[134],"matching,":[135],"classification,":[136],"sliced":[138],"Wasserstein":[139],"barycenters.":[140],"computational":[142],"efficiency":[143],"higher":[145],"dimensions":[146],"verified":[148],"comparison":[151],"Monte":[153],"Carlo":[154],"integration.":[155]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-18T00:00:00"}
