{"id":"https://openalex.org/W2036733586","doi":"https://doi.org/10.1137/s105262349935726x","title":"Approximating Binary Images from Discrete X-Rays","display_name":"Approximating Binary Images from Discrete X-Rays","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2036733586","doi":"https://doi.org/10.1137/s105262349935726x","mag":"2036733586"},"language":"en","primary_location":{"id":"doi:10.1137/s105262349935726x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s105262349935726x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009407877","display_name":"Peter Gritzmann","orcid":"https://orcid.org/0000-0003-0157-6880"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peter Gritzmann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102921808","display_name":"Sven de Vries","orcid":"https://orcid.org/0000-0002-2440-4937"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sven de Vries","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045021069","display_name":"Markus Wiegelmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Markus Wiegelmann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0142,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.94180842,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"11","issue":"2","first_page":"522","last_page":"546"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":1.0,"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":1.0,"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":0.9973000288009644,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9908999800682068,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/mathematics","display_name":"Mathematics","score":0.8350830078125},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.7175639867782593},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.5649558305740356},{"id":"https://openalex.org/keywords/set-packing","display_name":"Set packing","score":0.523483395576477},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5150384902954102},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5142931342124939},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5036692023277283},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.45500892400741577},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4499439299106598},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.41519176959991455},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4107816815376282},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3956083655357361},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3370581865310669},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32019203901290894},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11521419882774353},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1064276397228241},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09671926498413086},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06804847717285156}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8350830078125},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.7175639867782593},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.5649558305740356},{"id":"https://openalex.org/C134516590","wikidata":"https://www.wikidata.org/wiki/Q475603","display_name":"Set packing","level":3,"score":0.523483395576477},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5150384902954102},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5142931342124939},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5036692023277283},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.45500892400741577},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4499439299106598},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41519176959991455},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4107816815376282},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3956083655357361},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3370581865310669},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32019203901290894},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11521419882774353},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1064276397228241},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09671926498413086},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06804847717285156},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s105262349935726x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s105262349935726x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1509620596","https://openalex.org/W1536142435","https://openalex.org/W1963547452","https://openalex.org/W1980328919","https://openalex.org/W2011039300","https://openalex.org/W2021903957","https://openalex.org/W2027906720","https://openalex.org/W2044291212","https://openalex.org/W2053359891","https://openalex.org/W2076146651","https://openalex.org/W2078587369","https://openalex.org/W2083070454","https://openalex.org/W2086397287","https://openalex.org/W2091299439","https://openalex.org/W2140118062","https://openalex.org/W2156873112","https://openalex.org/W2334568949","https://openalex.org/W4246168648","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4230581126","https://openalex.org/W4378765297","https://openalex.org/W2761548024","https://openalex.org/W2016521071","https://openalex.org/W2001367988","https://openalex.org/W2069384021","https://openalex.org/W1990308498","https://openalex.org/W1986629578","https://openalex.org/W2149075715","https://openalex.org/W1968241640"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,81],"problem":[3,33],"of":[4,15,38,76],"approximating":[5],"binary":[6,97],"images":[7],"that":[8],"are":[9,85],"accessible":[10],"only":[11,88],"through":[12,21],"few":[13],"evaluations":[14],"their":[16,22,64],"discrete":[17,32],"X-ray":[18],"transform,":[19],"i.e.,":[20],"projections":[23],"counted":[24],"with":[25,87],"multiplicity":[26],"along":[27],"some":[28],"lines.":[29],"This":[30],"inverse":[31],"belongs":[34],"to":[35,95],"a":[36],"class":[37],"generalized":[39],"set":[40],"partitioning":[41],"problems":[42,54],"and":[43,47,60],"allows":[44],"natural":[45],"packing":[46],"covering":[48],"relaxations.":[49],"For":[50],"these":[51,77],"($\\mathbb{NP}$-hard)":[52],"optimization":[53],"we":[55,68],"present":[56],"various":[57,74],"approximation":[58],"algorithms":[59],"provide":[61],"estimates":[62],"for":[63,73,92],"worst-case":[65],"performance.":[66],"Further,":[67],"report":[69],"on":[70],"computational":[71],"results":[72],"variants":[75],"algorithms.":[78],"In":[79],"particular,":[80],"corresponding":[82],"integer":[83],"programs":[84],"solved":[86],"small":[89],"absolute":[90],"error":[91],"instances":[93],"up":[94],"$250,000$":[96],"variables.":[98]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
