{"id":"https://openalex.org/W2281322045","doi":"https://doi.org/10.1007/978-3-642-36062-6_37","title":"Note on Level Set Functions","display_name":"Note on Level Set Functions","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2281322045","doi":"https://doi.org/10.1007/978-3-642-36062-6_37","mag":"2281322045"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-36062-6_37","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-36062-6_37","pdf_url":null,"source":{"id":"https://openalex.org/S4210175514","display_name":"IFIP International Federation for Information Processing/IFIP","issn_l":"1571-5736","issn":["1571-5736","1861-2288"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP Advances in Information and Communication Technology","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://inria.hal.science/hal-01347558","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058396980","display_name":"Piotr Fulma\u0144ski","orcid":"https://orcid.org/0000-0003-4939-0882"},"institutions":[{"id":"https://openalex.org/I34250744","display_name":"University of \u0141\u00f3d\u017a","ror":"https://ror.org/05cq64r17","country_code":"PL","type":"education","lineage":["https://openalex.org/I34250744"]},{"id":"https://openalex.org/I188884621","display_name":"Lodz University of Technology","ror":"https://ror.org/00s8fpf52","country_code":"PL","type":"education","lineage":["https://openalex.org/I188884621"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Piotr Fulma\u0144ski","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, University of \u0141\u00f3d\u017a, Banacha 22, 90-238, \u0141\u00f3d\u017a, Poland","\u0141\u00f3d\u017a University of Technology (116 \u017beromskiego Street\r\n90-924 Lodz - Poland)"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, University of \u0141\u00f3d\u017a, Banacha 22, 90-238, \u0141\u00f3d\u017a, Poland","institution_ids":["https://openalex.org/I34250744"]},{"raw_affiliation_string":"\u0141\u00f3d\u017a University of Technology (116 \u017beromskiego Street\r\n90-924 Lodz - Poland)","institution_ids":["https://openalex.org/I188884621"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059636240","display_name":"Alicja Miniak-G\u00f3recka","orcid":"https://orcid.org/0000-0002-1860-8853"},"institutions":[{"id":"https://openalex.org/I34250744","display_name":"University of \u0141\u00f3d\u017a","ror":"https://ror.org/05cq64r17","country_code":"PL","type":"education","lineage":["https://openalex.org/I34250744"]},{"id":"https://openalex.org/I188884621","display_name":"Lodz University of Technology","ror":"https://ror.org/00s8fpf52","country_code":"PL","type":"education","lineage":["https://openalex.org/I188884621"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Alicja Miniak-G\u00f3recka","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, University of \u0141\u00f3d\u017a, Banacha 22, 90-238, \u0141\u00f3d\u017a, Poland","\u0141\u00f3d\u017a University of Technology (116 \u017beromskiego Street\r\n90-924 Lodz - Poland)"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, University of \u0141\u00f3d\u017a, Banacha 22, 90-238, \u0141\u00f3d\u017a, Poland","institution_ids":["https://openalex.org/I34250744"]},{"raw_affiliation_string":"\u0141\u00f3d\u017a University of Technology (116 \u017beromskiego Street\r\n90-924 Lodz - Poland)","institution_ids":["https://openalex.org/I188884621"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058396980"],"corresponding_institution_ids":["https://openalex.org/I188884621","https://openalex.org/I34250744"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.25970149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"368","last_page":"377"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.7893999814987183,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.7893999814987183,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.7498999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.7224000096321106,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.7063180208206177},{"id":"https://openalex.org/keywords/set-function","display_name":"Set function","score":0.6920018196105957},{"id":"https://openalex.org/keywords/level-set","display_name":"Level set (data structures)","score":0.6774904727935791},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6675321459770203},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6458944082260132},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5739624500274658},{"id":"https://openalex.org/keywords/level-set-method","display_name":"Level set method","score":0.46650761365890503},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4330657422542572},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41746559739112854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1997811496257782},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06413418054580688},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.04589653015136719}],"concepts":[{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.7063180208206177},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.6920018196105957},{"id":"https://openalex.org/C153008295","wikidata":"https://www.wikidata.org/wiki/Q6535093","display_name":"Level set (data structures)","level":2,"score":0.6774904727935791},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6675321459770203},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6458944082260132},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5739624500274658},{"id":"https://openalex.org/C125269122","wikidata":"https://www.wikidata.org/wiki/Q1751397","display_name":"Level set method","level":4,"score":0.46650761365890503},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4330657422542572},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41746559739112854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1997811496257782},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06413418054580688},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.04589653015136719},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-642-36062-6_37","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-36062-6_37","pdf_url":null,"source":{"id":"https://openalex.org/S4210175514","display_name":"IFIP International Federation for Information Processing/IFIP","issn_l":"1571-5736","issn":["1571-5736","1861-2288"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP Advances in Information and Communication Technology","raw_type":"book-chapter"},{"id":"pmh:oai:HAL:hal-01347558v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01347558","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. pp.368-377, ⟨10.1007/978-3-642-36062-6_37⟩","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01347558v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01347558","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. pp.368-377, ⟨10.1007/978-3-642-36062-6_37⟩","raw_type":"Conference papers"},"sustainable_development_goals":[{"score":0.5699999928474426,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1499032414","https://openalex.org/W1985388964","https://openalex.org/W1994875376"],"related_works":["https://openalex.org/W2104958086","https://openalex.org/W2223158884","https://openalex.org/W2006108232","https://openalex.org/W2061028002","https://openalex.org/W1979393293","https://openalex.org/W2144751639","https://openalex.org/W2171493617","https://openalex.org/W3157737852","https://openalex.org/W744483630","https://openalex.org/W3032209860"],"abstract_inverted_index":{"In":[0],"this":[1],"note":[2],"a":[3,12,16,41],"concept":[4],"of":[5,31,44,56],"\u03b5-level":[6,37,58],"set":[7,18,38,47,59],"function":[8,13,19,48],"is":[9,35,49],"introduced,":[10],"i.e.":[11,51],"which":[14],"approximates":[15],"level":[17,46],"satisfying":[20],"the":[21,32,45,54],"Hamilton-Jacobi":[22,33],"inequality.":[23],"We":[24],"prove":[25],"that":[26],"each":[27],"Lipschitz":[28],"continuous":[29],"solution":[30],"inequality":[34],"an":[36,57],"function.":[39,60],"Next,":[40],"numerical":[42],"approximation":[43],"presented,":[50],"method":[52],"for":[53],"construction":[55]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}