{"id":"https://openalex.org/W3186240299","doi":"https://doi.org/10.1007/s10878-021-00783-5","title":"Characterizing slope regions","display_name":"Characterizing slope regions","publication_year":2021,"publication_date":"2021-07-27","ids":{"openalex":"https://openalex.org/W3186240299","doi":"https://doi.org/10.1007/s10878-021-00783-5","mag":"3186240299"},"language":"en","primary_location":{"id":"doi:10.1007/s10878-021-00783-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10878-021-00783-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10878-021-00783-5.pdf","source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10878-021-00783-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078283118","display_name":"Roc\u0131\u0301o Gonz\u00e1lez-D\u0131\u0301az","orcid":"https://orcid.org/0000-0001-9937-0033"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Rocio Gonzalez-Diaz","raw_affiliation_strings":["Department of Applied Math I, University of Seville, Seville, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Applied Math I, University of Seville, Seville, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083304019","display_name":"Darshan Batavia","orcid":null},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Darshan Batavia","raw_affiliation_strings":["Pattern Recognition and Image Processing Group 193/03, TU Wien, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Pattern Recognition and Image Processing Group 193/03, TU Wien, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056404432","display_name":"Roc\u00edo M. Casablanca","orcid":"https://orcid.org/0000-0003-0653-3118"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Rocio M. Casablanca","raw_affiliation_strings":["Department of Applied Math I, University of Seville, Seville, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Applied Math I, University of Seville, Seville, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081777844","display_name":"Walter G. Kropatsch","orcid":"https://orcid.org/0000-0003-4915-4118"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Walter G. Kropatsch","raw_affiliation_strings":["Pattern Recognition and Image Processing Group 193/03, TU Wien, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Pattern Recognition and Image Processing Group 193/03, TU Wien, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5078283118"],"corresponding_institution_ids":["https://openalex.org/I79238269"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.1942,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.48705768,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"44","issue":"4","first_page":"2661","last_page":"2680"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9980000257492065,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9896000027656555,"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/characterization","display_name":"Characterization (materials science)","score":0.7678943872451782},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.7032217383384705},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6702553033828735},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.5088503360748291},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4850586950778961},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4185711145401001},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3268866240978241},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2945295572280884},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27206212282180786},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2011638879776001},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14026308059692383},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11547785997390747}],"concepts":[{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.7678943872451782},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7032217383384705},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6702553033828735},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5088503360748291},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4850586950778961},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4185711145401001},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3268866240978241},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2945295572280884},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27206212282180786},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2011638879776001},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14026308059692383},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11547785997390747},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10878-021-00783-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10878-021-00783-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10878-021-00783-5.pdf","source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Optimization","raw_type":"journal-article"},{"id":"pmh:oai:idus.us.es:11441/126678","is_oa":true,"landing_page_url":"https://idus.us.es/handle//11441/126678","pdf_url":"https://idus.us.es/handle//11441/126678","source":{"id":"https://openalex.org/S4306400333","display_name":"idUS (Universidad de Sevilla)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79238269","host_organization_name":"Universidad de Sevilla","host_organization_lineage":["https://openalex.org/I79238269"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:RePEc:spr:jcomop:v:44:y:2022:i:4:d:10.1007_s10878-021-00783-5","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10878-021-00783-5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10878-021-00783-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10878-021-00783-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10878-021-00783-5.pdf","source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Optimization","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G1419670400","display_name":null,"funder_award_id":"GB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G1650125035","display_name":null,"funder_award_id":"B-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G2309174360","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G300979063","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3690828678","display_name":null,"funder_award_id":"PID2019","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G4126322094","display_name":null,"funder_award_id":"01100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4416040612","display_name":null,"funder_award_id":"PID2019- 107339GB-I00","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G5080475149","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5421974903","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G6582594481","display_name":null,"funder_award_id":"PID2019-107339GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G661330594","display_name":null,"funder_award_id":"00110","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6685425346","display_name":null,"funder_award_id":"0011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7266728691","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7643708868","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G7885150177","display_name":null,"funder_award_id":"PID2019-107339GB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G8055432103","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G8260616629","display_name":null,"funder_award_id":"011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8352492595","display_name":null,"funder_award_id":"0.13039/501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G8638682022","display_name":null,"funder_award_id":"10.13039/50110001103","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8684520763","display_name":null,"funder_award_id":"PID2019","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320310967","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24"},{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3186240299.pdf","grobid_xml":"https://content.openalex.org/works/W3186240299.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W99290536","https://openalex.org/W99824228","https://openalex.org/W105291018","https://openalex.org/W262478894","https://openalex.org/W1238092070","https://openalex.org/W1533522700","https://openalex.org/W1552904969","https://openalex.org/W1971117671","https://openalex.org/W2043154811","https://openalex.org/W2050439505","https://openalex.org/W2068014716","https://openalex.org/W2080391910","https://openalex.org/W2093834886","https://openalex.org/W2136186816","https://openalex.org/W2484464261","https://openalex.org/W2490578157","https://openalex.org/W2499066376","https://openalex.org/W2793167574","https://openalex.org/W2884642675","https://openalex.org/W2906036259","https://openalex.org/W2917992617","https://openalex.org/W2949028644","https://openalex.org/W2969793202","https://openalex.org/W3040586665","https://openalex.org/W3106650910","https://openalex.org/W3153101654","https://openalex.org/W4212803998"],"related_works":["https://openalex.org/W4380682190","https://openalex.org/W3107994849","https://openalex.org/W4315701745","https://openalex.org/W1990290471","https://openalex.org/W2945307361","https://openalex.org/W2102386043","https://openalex.org/W4247143848","https://openalex.org/W2005710836","https://openalex.org/W2003813852","https://openalex.org/W2894130971"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"provides":[3],"a":[4,43,50,56],"theoretical":[5],"characterization":[6,17],"of":[7,27,58],"monotonically":[8],"connected":[9],"image":[10],"surface":[11],"regions,":[12],"called":[13],"slope":[14,51,59],"regions.":[15],"The":[16],"is":[18,62],"given":[19],"by":[20],"several":[21],"topological":[22],"properties":[23],"described":[24],"in":[25,74],"terms":[26],"critical":[28],"points":[29],"relative":[30],"to":[31,46,48],"the":[32,37,69],"region.":[33,52],"We":[34,53],"formally":[35],"prove":[36],"necessary":[38],"and":[39,64,72],"sufficient":[40],"conditions":[41],"that":[42],"region":[44],"needs":[45],"satisfy":[47],"be":[49],"also":[54],"provide":[55],"prototype":[57],"regions":[60],"which":[61],"general":[63],"contains,":[65],"as":[66],"particular":[67],"cases,":[68],"prototypes":[70],"studied":[71],"published":[73],"previous":[75],"conference":[76],"papers.":[77]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}