{"id":"https://openalex.org/W2011532560","doi":"https://doi.org/10.1137/080722758","title":"Scale-Space Analysis of Discrete Filtering over Arbitrary Triangulated Surfaces","display_name":"Scale-Space Analysis of Discrete Filtering over Arbitrary Triangulated Surfaces","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2011532560","doi":"https://doi.org/10.1137/080722758","mag":"2011532560"},"language":"en","primary_location":{"id":"doi:10.1137/080722758","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080722758","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},"type":"article","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/A5010997999","display_name":"Chunlin Wu","orcid":"https://orcid.org/0000-0003-1932-7997"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chunlin Wu","raw_affiliation_strings":["clwu@ntu.edu.sg#TAB#"],"affiliations":[{"raw_affiliation_string":"clwu@ntu.edu.sg#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100604592","display_name":"Jiansong Deng","orcid":"https://orcid.org/0000-0003-4093-373X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiansong Deng","raw_affiliation_strings":["dengjs@ustc.edu.cn and chenfl@ustc.edu.cn#TAB#"],"affiliations":[{"raw_affiliation_string":"dengjs@ustc.edu.cn and chenfl@ustc.edu.cn#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032285268","display_name":"Falai Chen","orcid":"https://orcid.org/0000-0002-9898-5922"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Falai Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101951979","display_name":"Xue\u2010Cheng Tai","orcid":"https://orcid.org/0000-0003-3359-9104"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xuecheng Tai","raw_affiliation_strings":["tai@math.uib.no#TAB#"],"affiliations":[{"raw_affiliation_string":"tai@math.uib.no#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5010997999"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1142,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.86429037,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2","issue":"2","first_page":"670","last_page":"709"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9926000237464905,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9926000237464905,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9836999773979187,"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/mathematics","display_name":"Mathematics","score":0.6342037916183472},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.597438395023346},{"id":"https://openalex.org/keywords/anisotropic-diffusion","display_name":"Anisotropic diffusion","score":0.5324243903160095},{"id":"https://openalex.org/keywords/discrete-space","display_name":"Discrete space","score":0.4988093376159668},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.4786178469657898},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.44556158781051636},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3969741463661194},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39633578062057495},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35152626037597656},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3438558280467987},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2889692783355713},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.22645872831344604},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13408327102661133},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1064511239528656}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6342037916183472},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.597438395023346},{"id":"https://openalex.org/C203504353","wikidata":"https://www.wikidata.org/wiki/Q4765461","display_name":"Anisotropic diffusion","level":3,"score":0.5324243903160095},{"id":"https://openalex.org/C153782549","wikidata":"https://www.wikidata.org/wiki/Q175116","display_name":"Discrete space","level":2,"score":0.4988093376159668},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4786178469657898},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.44556158781051636},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3969741463661194},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39633578062057495},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35152626037597656},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3438558280467987},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2889692783355713},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.22645872831344604},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13408327102661133},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1064511239528656},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/080722758","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080722758","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.217.4655","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.4655","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mi.uib.no/~tai/papers/chunlin.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","score":0.550000011920929,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W19793066","https://openalex.org/W106081075","https://openalex.org/W1480546554","https://openalex.org/W1484228140","https://openalex.org/W1490713447","https://openalex.org/W1496099826","https://openalex.org/W1499695691","https://openalex.org/W1527702568","https://openalex.org/W1559466911","https://openalex.org/W1589429287","https://openalex.org/W1589604081","https://openalex.org/W1597705134","https://openalex.org/W1598868422","https://openalex.org/W1626653188","https://openalex.org/W1963743024","https://openalex.org/W1973976434","https://openalex.org/W1987519781","https://openalex.org/W2000214666","https://openalex.org/W2002312729","https://openalex.org/W2006714486","https://openalex.org/W2009262561","https://openalex.org/W2013549980","https://openalex.org/W2021528463","https://openalex.org/W2022735534","https://openalex.org/W2031178395","https://openalex.org/W2032325716","https://openalex.org/W2042280704","https://openalex.org/W2048427115","https://openalex.org/W2054965818","https://openalex.org/W2055339315","https://openalex.org/W2063291805","https://openalex.org/W2071447530","https://openalex.org/W2087309680","https://openalex.org/W2103559027","https://openalex.org/W2109200236","https://openalex.org/W2109863423","https://openalex.org/W2111165106","https://openalex.org/W2112328181","https://openalex.org/W2113834179","https://openalex.org/W2117612778","https://openalex.org/W2119057036","https://openalex.org/W2120103450","https://openalex.org/W2122661899","https://openalex.org/W2128738317","https://openalex.org/W2134448913","https://openalex.org/W2146052399","https://openalex.org/W2150134853","https://openalex.org/W2151103935","https://openalex.org/W2151958211","https://openalex.org/W2152032596","https://openalex.org/W2153645845","https://openalex.org/W2154432345","https://openalex.org/W2157285426","https://openalex.org/W2164173056","https://openalex.org/W2167373005","https://openalex.org/W2169776045","https://openalex.org/W2171705458","https://openalex.org/W2172188317","https://openalex.org/W2182932938","https://openalex.org/W2240948833","https://openalex.org/W2610857016","https://openalex.org/W2799207262","https://openalex.org/W2998888370","https://openalex.org/W3003345659","https://openalex.org/W3011612142","https://openalex.org/W3039357072","https://openalex.org/W3148091194"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W2019780691","https://openalex.org/W2558424905","https://openalex.org/W2551189280","https://openalex.org/W4299595414","https://openalex.org/W2919045150","https://openalex.org/W2997902164","https://openalex.org/W1968317357","https://openalex.org/W2171089757"],"abstract_inverted_index":{"Discrete":[0],"filtering":[1,81,95,125,149,218,243,300],"of":[2,76,79,90,104,143,177,208,215,266,298],"information":[3,181,198],"over":[4],"triangulated":[5,137],"surfaces":[6,87],"has":[7,23,68],"proved":[8],"very":[9,110],"useful":[10],"in":[11,84],"computer":[12],"graphics":[13],"applications.":[14],"This":[15],"technique":[16],"is":[17,108,201],"based":[18,227],"on":[19,71,136,165,228],"diffusion":[20,129,221],"equations":[21,130,222],"and":[22,33,40,54,93,99,123,139,151,161,175,188,205,223,235,252,271,273,279,287],"been":[24,69,193],"extensively":[25],"applied":[26],"to":[27,146,219,259,306],"image":[28,249,256],"processing,":[29],"harmonic":[30],"map":[31],"regularization":[32],"texture":[34],"generating,":[35],"etc.":[36],"[C.":[37,50],"L.":[38],"Bajaj":[39],"G.":[41],"Xu,":[42],"ACM":[43],"Trans.":[44,58],"Graph.,":[45,61],"22":[46],"(2003),":[47],"pp.":[48,64],"4\u201332],":[49],"Wu,":[51],"J.":[52],"Deng,":[53],"F.":[55],"Chen,":[56],"IEEE":[57],"Vis.":[59],"Comput.":[60],"14":[62],"(2008),":[63],"666\u2013679].":[65],"However,":[66],"little":[67],"done":[70],"analysis":[72,103,207],"(especially":[73],"quantitative":[74,106],"analysis)":[75],"the":[77,94,102,105,119,197,212,216,220,242,255,267,299,308],"behavior":[78,107,191],"these":[80,148],"procedures.":[82],"Since":[83],"applications":[85],"mesh":[86],"can":[88,96],"be":[89,97],"arbitrary":[91],"topology":[92,186],"nonlinear":[98,280],"even":[100],"anisotropic,":[101],"a":[109],"difficult":[111],"issue.":[112],"In":[113,195],"this":[114,237],"paper,":[115],"we":[116],"first":[117],"present":[118],"discrete":[120,144,168],"linear,":[121],"nonlinear,":[122],"anisotropic":[124,288],"schemes":[126],"via":[127],"discretizing":[128],"with":[131],"appropriately":[132],"defined":[133],"differential":[134],"operators":[135],"surfaces,":[138],"then":[140],"use":[141],"concepts":[142],"scale-spaces":[145],"describe":[147],"procedures":[150],"analyze":[152],"their":[153,274],"properties":[154,157],"respectively.":[155],"Scale-space":[156],"such":[158,232],"as":[159,185,233,248,282,284],"existence":[160],"uniqueness,":[162],"continuous":[163],"dependence":[164],"initial":[166],"value,":[167],"semigroup":[169],"property,":[170],"grey":[171,179],"level":[172],"shift":[173],"invariance":[174],"conservation":[176],"total":[178],"level,":[180],"reduction":[182,199,247],"(also":[183],"known":[184],"simplification),":[187],"constant":[189],"limit":[190],"have":[192],"proved.":[194],"particular,":[196],"property":[200],"analyzed":[202],"by":[203],"eigenvalue":[204],"eigenvector":[206],"matrices.":[209],"Different":[210],"from":[211],"direct":[213],"observation":[214],"local":[217],"other":[224],"interpretation":[225],"methods":[226],"wholly":[229],"global":[230],"quantities":[231],"energy":[234],"entropy,":[236],"viewpoint":[238],"helps":[239],"us":[240],"understand":[241],"both":[244],"globally":[245],"(information":[246],"components":[250],"shrink)":[251],"locally":[253],"(how":[254],"component":[257],"contributes":[258],"its":[260],"shrink":[261],"rate).":[262],"With":[263],"careful":[264],"consideration":[265],"correspondence":[268],"between":[269,277,285],"eigenvalues":[270],"eigenvectors":[272],"features,":[275],"differences":[276],"linear":[278],"filtering,":[281,289],"well":[283],"isotropic":[286],"are":[290,304],"discussed.":[291],"We":[292],"also":[293],"get":[294],"some":[295],"stability":[296],"results":[297],"schemes.":[301],"Several":[302],"examples":[303],"provided":[305],"illustrate":[307],"properties.":[309]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
