{"id":"https://openalex.org/W17148550","doi":"https://doi.org/10.1007/3-540-51815-0_60","title":"Adapting multi-grid-methods to the class of elliptic partial differential equation appearing in the estimation of displacement vector fields","display_name":"Adapting multi-grid-methods to the class of elliptic partial differential equation appearing in the estimation of displacement vector fields","publication_year":1989,"publication_date":"1989-01-01","ids":{"openalex":"https://openalex.org/W17148550","doi":"https://doi.org/10.1007/3-540-51815-0_60","mag":"17148550"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-51815-0_60","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-51815-0_60","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5033306513","display_name":"Markus A. Schmidt","orcid":"https://orcid.org/0000-0002-5324-6405"},"institutions":[{"id":"https://openalex.org/I127251866","display_name":"Alfred-Wegener-Institut Helmholtz-Zentrum f\u00fcr Polar- und Meeresforschung","ror":"https://ror.org/032e6b942","country_code":"DE","type":"facility","lineage":["https://openalex.org/I127251866","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Markus Schmidt","raw_affiliation_strings":["Dept. ZDV, Alfred-Wegener-Institute for Polar Research, Am Handelhafen 12, D-2850, Bremerhaven","Dept. ZDV, Alfred-Wegener-Institute for Polar Research, Bremerhaven,"],"affiliations":[{"raw_affiliation_string":"Dept. ZDV, Alfred-Wegener-Institute for Polar Research, Am Handelhafen 12, D-2850, Bremerhaven","institution_ids":["https://openalex.org/I127251866"]},{"raw_affiliation_string":"Dept. ZDV, Alfred-Wegener-Institute for Polar Research, Bremerhaven,","institution_ids":["https://openalex.org/I127251866"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009501148","display_name":"J. Dengler","orcid":"https://orcid.org/0000-0002-0739-081X"},"institutions":[{"id":"https://openalex.org/I17937529","display_name":"German Cancer Research Center","ror":"https://ror.org/04cdgtt98","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I17937529"]},{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Joachim Dengler","raw_affiliation_strings":["Dept. Medical and Biological Informatics, German Cancer Research Center, Im Neuenheimer Feld 280, D-6900, Heidelberg","Dept. Medical and Biological Informatics, German Cancer Research Center, Heidelberg,"],"affiliations":[{"raw_affiliation_string":"Dept. Medical and Biological Informatics, German Cancer Research Center, Im Neuenheimer Feld 280, D-6900, Heidelberg","institution_ids":["https://openalex.org/I17937529","https://openalex.org/I223822909"]},{"raw_affiliation_string":"Dept. Medical and Biological Informatics, German Cancer Research Center, Heidelberg,","institution_ids":["https://openalex.org/I17937529","https://openalex.org/I223822909"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5033306513"],"corresponding_institution_ids":["https://openalex.org/I127251866"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.01111111,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"266","last_page":"274"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","score":0.9973999857902527,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9973999857902527,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9840999841690063,"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/computer-science","display_name":"Computer science","score":0.6627112030982971},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6531012058258057},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.6462092995643616},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5527235865592957},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.539202868938446},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5285364985466003},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.49216097593307495},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.47011294960975647},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.46207669377326965},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45878201723098755},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.44066742062568665},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43057310581207275},{"id":"https://openalex.org/keywords/vector-operator","display_name":"Vector operator","score":0.4300106167793274},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.4241045117378235},{"id":"https://openalex.org/keywords/displacement-field","display_name":"Displacement field","score":0.42203304171562195},{"id":"https://openalex.org/keywords/vector-laplacian","display_name":"Vector Laplacian","score":0.4184945225715637},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3679540157318115},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3208944499492645},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3168799877166748},{"id":"https://openalex.org/keywords/vector-potential","display_name":"Vector potential","score":0.2610175311565399},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14486119151115417},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.10954612493515015},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07006025314331055}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6627112030982971},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6531012058258057},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.6462092995643616},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5527235865592957},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.539202868938446},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5285364985466003},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.49216097593307495},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.47011294960975647},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.46207669377326965},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45878201723098755},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.44066742062568665},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43057310581207275},{"id":"https://openalex.org/C148221864","wikidata":"https://www.wikidata.org/wiki/Q7917838","display_name":"Vector operator","level":4,"score":0.4300106167793274},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4241045117378235},{"id":"https://openalex.org/C29660869","wikidata":"https://www.wikidata.org/wiki/Q5282615","display_name":"Displacement field","level":3,"score":0.42203304171562195},{"id":"https://openalex.org/C37312099","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Vector Laplacian","level":4,"score":0.4184945225715637},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3679540157318115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3208944499492645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3168799877166748},{"id":"https://openalex.org/C2027888","wikidata":"https://www.wikidata.org/wiki/Q521126","display_name":"Vector potential","level":3,"score":0.2610175311565399},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14486119151115417},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.10954612493515015},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07006025314331055},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C7451433","wikidata":"https://www.wikidata.org/wiki/Q1265039","display_name":"Solenoidal vector field","level":3,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.0},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-51815-0_60","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-51815-0_60","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5199999809265137,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W972853512","https://openalex.org/W1601442889","https://openalex.org/W1972584972","https://openalex.org/W2022140147","https://openalex.org/W2083851951","https://openalex.org/W2127981460","https://openalex.org/W2501171808","https://openalex.org/W4230055019"],"related_works":["https://openalex.org/W4237871234","https://openalex.org/W2490966737","https://openalex.org/W2954193812","https://openalex.org/W4210331724","https://openalex.org/W4366307899","https://openalex.org/W1979970769","https://openalex.org/W2052448522","https://openalex.org/W3004975566","https://openalex.org/W4302327562","https://openalex.org/W3168011518"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
