{"id":"https://openalex.org/W2138556535","doi":"https://doi.org/10.1109/icip.2006.312430","title":"Efficient Reconstruction of Hexagonally Sampled Data using Three-Directional Box-Splines","display_name":"Efficient Reconstruction of Hexagonally Sampled Data using Three-Directional Box-Splines","publication_year":2006,"publication_date":"2006-10-01","ids":{"openalex":"https://openalex.org/W2138556535","doi":"https://doi.org/10.1109/icip.2006.312430","mag":"2138556535"},"language":"en","primary_location":{"id":"doi:10.1109/icip.2006.312430","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2006.312430","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 International Conference on Image Processing","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/211382","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024254029","display_name":"Laurent Condat","orcid":"https://orcid.org/0000-0001-7087-1002"},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I4210114274","display_name":"Laboratoire d\u2019Informatique et Syst\u00e8mes","ror":"https://ror.org/0257sgk90","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I143002897","https://openalex.org/I21491767","https://openalex.org/I4210114274"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Laurent Condat","raw_affiliation_strings":["Laboratory of Images and Signals (LIS), Institut National Polytechnique de Grenoble, Grenoble, France","Laboratory of Images and Signals (LIS), Institut National Polytechnique de Grenoble, 38031 Grenoble, France. E-mail: laurent.condat@lis.inpg.fr"],"affiliations":[{"raw_affiliation_string":"Laboratory of Images and Signals (LIS), Institut National Polytechnique de Grenoble, Grenoble, France","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I4210114274"]},{"raw_affiliation_string":"Laboratory of Images and Signals (LIS), Institut National Polytechnique de Grenoble, 38031 Grenoble, France. E-mail: laurent.condat@lis.inpg.fr","institution_ids":["https://openalex.org/I4210114274","https://openalex.org/I106785703"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003693672","display_name":"Dimitri Van De Ville","orcid":"https://orcid.org/0000-0002-2879-3861"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Dimitri Van De Ville","raw_affiliation_strings":["Biomedical Imaging Group (BIG), Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","Biomedical Imaging Group (BIG), Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group (BIG), Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Biomedical Imaging Group (BIG), Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne, Switzerland","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027830035","display_name":"Micha\u00ebl Unser","orcid":"https://orcid.org/0000-0003-1248-2513"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Michael Unser","raw_affiliation_strings":["Biomedical Imaging Group (BIG), Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","Biomedical Imaging Group (BIG), Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group (BIG), Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Biomedical Imaging Group (BIG), Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne, Switzerland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5024254029"],"corresponding_institution_ids":["https://openalex.org/I106785703","https://openalex.org/I4210114274"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.18655779,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"38","issue":null,"first_page":"697","last_page":"700"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9951000213623047,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9922999739646912,"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/spline","display_name":"Spline (mechanical)","score":0.7146177291870117},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7035784721374512},{"id":"https://openalex.org/keywords/finite-impulse-response","display_name":"Finite impulse response","score":0.6717807650566101},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6585281491279602},{"id":"https://openalex.org/keywords/box-spline","display_name":"Box spline","score":0.6199464201927185},{"id":"https://openalex.org/keywords/thin-plate-spline","display_name":"Thin plate spline","score":0.5973027944564819},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5698152184486389},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4402121603488922},{"id":"https://openalex.org/keywords/impulse","display_name":"Impulse (physics)","score":0.4321862459182739},{"id":"https://openalex.org/keywords/impulse-response","display_name":"Impulse response","score":0.41658756136894226},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.388286828994751},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26384347677230835},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2598881721496582},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.24573829770088196},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.12162983417510986},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09214484691619873}],"concepts":[{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.7146177291870117},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7035784721374512},{"id":"https://openalex.org/C198386975","wikidata":"https://www.wikidata.org/wiki/Q117785","display_name":"Finite impulse response","level":2,"score":0.6717807650566101},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6585281491279602},{"id":"https://openalex.org/C78383375","wikidata":"https://www.wikidata.org/wiki/Q4951620","display_name":"Box spline","level":4,"score":0.6199464201927185},{"id":"https://openalex.org/C93132110","wikidata":"https://www.wikidata.org/wiki/Q7784288","display_name":"Thin plate spline","level":4,"score":0.5973027944564819},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5698152184486389},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4402121603488922},{"id":"https://openalex.org/C70836080","wikidata":"https://www.wikidata.org/wiki/Q837940","display_name":"Impulse (physics)","level":2,"score":0.4321862459182739},{"id":"https://openalex.org/C72279823","wikidata":"https://www.wikidata.org/wiki/Q1139726","display_name":"Impulse response","level":2,"score":0.41658756136894226},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.388286828994751},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26384347677230835},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2598881721496582},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.24573829770088196},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.12162983417510986},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09214484691619873},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/icip.2006.312430","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2006.312430","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 International Conference on Image Processing","raw_type":"proceedings-article"},{"id":"pmh:oai:infoscience.epfl.ch:211382","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/211382","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:infoscience.tind.io:211382","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/118130","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"conference proceedings"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:211382","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/211382","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.4699999988079071}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1482711749","https://openalex.org/W1981937069","https://openalex.org/W2002422940","https://openalex.org/W2003410902","https://openalex.org/W2060968961","https://openalex.org/W2062636705","https://openalex.org/W2122776646","https://openalex.org/W2138584164","https://openalex.org/W2160616608","https://openalex.org/W2163889321","https://openalex.org/W2612706235","https://openalex.org/W4252664964","https://openalex.org/W6624167275"],"related_works":["https://openalex.org/W2154654948","https://openalex.org/W1999269698","https://openalex.org/W1557433619","https://openalex.org/W1963635401","https://openalex.org/W2091284938","https://openalex.org/W2741608222","https://openalex.org/W2062768614","https://openalex.org/W1975728046","https://openalex.org/W2006420318","https://openalex.org/W2555832222"],"abstract_inverted_index":{"Three-directional":[0],"box-splines":[1,50],"are":[2,73],"particularly":[3],"well-suited":[4],"to":[5,56,76],"interpolate":[6],"and":[7,71,94],"approximate":[8],"hexagonally":[9],"sampled":[10],"data.":[11],"In":[12],"this":[13],"paper,":[14],"we":[15,24,42,89,95],"propose":[16],"a":[17,26,33,44,57],"computationally":[18],"efficient":[19],"end-to-end":[20],"reconstruction":[21],"process.":[22],"First,":[23],"introduce":[25],"prefiltering":[27],"step":[28],"that":[29,54],"is":[30],"based":[31],"on":[32,68],"quasi-interpolation":[34],"scheme":[35],"using":[36],"low-complexity":[37],"finite-impulse-response":[38],"(FIR)":[39],"filters.":[40],"Second,":[41],"derive":[43],"closed":[45],"analytical":[46],"expression":[47],"for":[48],"three-directional":[49],"of":[51,60,86],"any":[52],"order":[53],"leads":[55],"fast":[58],"evaluation":[59],"the":[61,69,84,91],"spline":[62],"surface.":[63],"All":[64],"operations":[65],"act":[66],"locally":[67],"data,":[70],"thus":[72],"well":[74],"adapted":[75],"applications":[77],"dealing":[78],"with":[79],"large":[80],"images.":[81],"To":[82],"demonstrate":[83],"feasibility":[85],"our":[87],"method,":[88],"implemented":[90],"complete":[92],"procedure":[93],"present":[96],"experimental":[97],"results.":[98]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}