{"id":"https://openalex.org/W2160616608","doi":"https://doi.org/10.1109/icip.2005.1530592","title":"Hexagonal versus orthogonal lattices: a new comparison using approximation theory","display_name":"Hexagonal versus orthogonal lattices: a new comparison using approximation theory","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2160616608","doi":"https://doi.org/10.1109/icip.2005.1530592","mag":"2160616608"},"language":"en","primary_location":{"id":"doi:10.1109/icip.2005.1530592","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2005.1530592","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE International Conference on Image Processing 2005","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/211359","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/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":false,"raw_author_name":"L. Condat","raw_affiliation_strings":["Laboratoire LIS-F\u00e9d\u00e9ration ELESA, Grenoble, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire LIS-F\u00e9d\u00e9ration ELESA, Grenoble, France","institution_ids":["https://openalex.org/I4210114274"]}]},{"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":"D. Van De Ville","raw_affiliation_strings":["Biomedical Imaging Group, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017511611","display_name":"Thierry Blu","orcid":"https://orcid.org/0000-0001-5759-0011"},"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":"T. Blu","raw_affiliation_strings":["Biomedical Imaging Group, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7694,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.73041875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"III","last_page":"1116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9972000122070312,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9972000122070312,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9824000000953674,"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":0.9695000052452087,"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/hexagonal-lattice","display_name":"Hexagonal lattice","score":0.6342334151268005},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6082330346107483},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.538544774055481},{"id":"https://openalex.org/keywords/hexagonal-tiling","display_name":"Hexagonal tiling","score":0.5345145463943481},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.4759906530380249},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.45552241802215576},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.430675745010376},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.3793115019798279},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2955244779586792},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20252513885498047},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1726773977279663},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12825608253479004},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11969581246376038}],"concepts":[{"id":"https://openalex.org/C90626534","wikidata":"https://www.wikidata.org/wiki/Q4523381","display_name":"Hexagonal lattice","level":3,"score":0.6342334151268005},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6082330346107483},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.538544774055481},{"id":"https://openalex.org/C35908053","wikidata":"https://www.wikidata.org/wiki/Q3063631","display_name":"Hexagonal tiling","level":3,"score":0.5345145463943481},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.4759906530380249},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.45552241802215576},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.430675745010376},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.3793115019798279},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2955244779586792},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20252513885498047},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1726773977279663},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12825608253479004},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11969581246376038},{"id":"https://openalex.org/C155355069","wikidata":"https://www.wikidata.org/wiki/Q575224","display_name":"Antiferromagnetism","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/icip.2005.1530592","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2005.1530592","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE International Conference on Image Processing 2005","raw_type":"proceedings-article"},{"id":"pmh:oai:infoscience.epfl.ch:211359","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/211359","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:211359","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/118108","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:211359","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/211359","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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320915","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W2003410902","https://openalex.org/W2060968961","https://openalex.org/W2079003264","https://openalex.org/W2113524221","https://openalex.org/W2144166513","https://openalex.org/W2153608957","https://openalex.org/W2163889321","https://openalex.org/W2165066371","https://openalex.org/W2222833901","https://openalex.org/W6689361306"],"related_works":["https://openalex.org/W1594480161","https://openalex.org/W3153287478","https://openalex.org/W2131662362","https://openalex.org/W1983561394","https://openalex.org/W2138531454","https://openalex.org/W960802878","https://openalex.org/W2280965958","https://openalex.org/W3100111582","https://openalex.org/W2081883258","https://openalex.org/W4391494363"],"abstract_inverted_index":{"We":[0,74],"provide":[1],"a":[2,29,50,66,141],"new":[3],"comparison":[4],"between":[5],"hexagonal":[6,47,82,126,150],"and":[7,41],"orthogonal":[8,39],"lattices,":[9,18],"based":[10],"on":[11,80,155],"approximation":[12,72,78,110],"theory.":[13],"For":[14,49,128],"each":[15],"of":[16,53,60,70,109,111,149],"the":[17,21,34,38,42,46,57,61,71,77,81,91,107,112,125,131,147],"we":[19,55],"select":[20],"\"natural\"":[22],"spline":[23],"basis":[24,113],"function":[25,31],"as":[26,140],"generator":[27],"for":[28,37,45],"shift-invariant":[30],"space;":[32],"i.e.,":[33],"tensor-product":[35],"B-splines":[36],"lattice":[40,83],"non-separable":[43],"hex-splines":[44],"lattice.":[48],"given":[51],"order":[52,108],"approximation,":[54],"compare":[56],"asymptotic":[58,102],"constants":[59,103],"error":[62],"kernels,":[63],"which":[64],"give":[65],"very":[67],"good":[68],"indication":[69],"quality.":[73],"find":[75],"that":[76],"quality":[79],"is":[84],"consistently":[85],"better,":[86],"when":[87,106,152],"choosing":[88],"lattices":[89,151],"with":[90],"same":[92],"sampling":[93,97],"density.":[94],"The":[95],"area":[96],"gain":[98],"related":[99],"to":[100,122,145],"these":[101],"quickly":[104],"converges":[105],"functions":[114],"increases.":[115],"Surprisingly,":[116],"nearest-neighbor":[117],"interpolation":[118],"does":[119],"not":[120],"allow":[121],"profit":[123],"from":[124],"grid.":[127],"practical":[129],"purposes,":[130],"second-order":[132],"hex-spline":[133],"(i.e.,":[134],"constituted":[135],"by":[136],"linear":[137],"patches)":[138],"appears":[139],"particularly":[142],"useful":[143],"candidate":[144],"exploit":[146],"advantages":[148],"representing":[153],"images":[154],"them.":[156]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
