{"id":"https://openalex.org/W4306831629","doi":"https://doi.org/10.1109/tpami.2022.3215475","title":"Analytical Tensor Voting in ND Space and its Properties","display_name":"Analytical Tensor Voting in ND Space and its Properties","publication_year":2022,"publication_date":"2022-11-03","ids":{"openalex":"https://openalex.org/W4306831629","doi":"https://doi.org/10.1109/tpami.2022.3215475","pmid":"https://pubmed.ncbi.nlm.nih.gov/36260580"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2022.3215475","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2022.3215475","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5101949004","display_name":"Hongbin Lin","orcid":"https://orcid.org/0000-0001-6353-8535"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongbin Lin","raw_affiliation_strings":["School of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei, China"],"raw_orcid":"https://orcid.org/0000-0001-6353-8535","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106657803","display_name":"Dan Guo","orcid":"https://orcid.org/0000-0001-7523-7094"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dan Guo","raw_affiliation_strings":["School of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei, China"],"raw_orcid":"https://orcid.org/0000-0001-7523-7094","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060309231","display_name":"Jianing Wei","orcid":"https://orcid.org/0000-0002-8517-2164"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianing Wei","raw_affiliation_strings":["School of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Boran Guan","orcid":null},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Boran Guan","raw_affiliation_strings":["School of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Yanshan University, Qinhuangdao, Hebei, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100662062","display_name":"Zeyu Chen","orcid":"https://orcid.org/0000-0002-4534-5681"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zeyu Chen","raw_affiliation_strings":["School of Information Science and Engineering, Yanshan University, Qinhuangdao, Hebei, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Yanshan University, Qinhuangdao, Hebei, China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110084718","display_name":"Xiuping Peng","orcid":"https://orcid.org/0000-0003-0815-6491"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiuping Peng","raw_affiliation_strings":["School of Information Science and Engineering, Yanshan University, Qinhuangdao, Hebei, China"],"raw_orcid":"https://orcid.org/0000-0003-0815-6491","affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Yanshan University, Qinhuangdao, Hebei, China","institution_ids":["https://openalex.org/I39333907"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5101949004"],"corresponding_institution_ids":["https://openalex.org/I39333907"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11682796,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"5","first_page":"5404","last_page":"5416"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9925000071525574,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9925000071525574,"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":0.9918000102043152,"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/T10812","display_name":"Human Pose and Action Recognition","score":0.9896000027656555,"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/notation","display_name":"Notation","score":0.665155291557312},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6138147711753845},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.486664354801178},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4318881332874298},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3836149275302887},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3783096969127655},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33595842123031616},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29208433628082275},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.076372891664505}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.665155291557312},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6138147711753845},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.486664354801178},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4318881332874298},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3836149275302887},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3783096969127655},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33595842123031616},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29208433628082275},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.076372891664505},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2022.3215475","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2022.3215475","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:36260580","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36260580","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6000000238418579}],"awards":[{"id":"https://openalex.org/G7911492485","display_name":null,"funder_award_id":"E2020203188","funder_id":"https://openalex.org/F4320322163","funder_display_name":"Natural Science Foundation of Hebei Province"}],"funders":[{"id":"https://openalex.org/F4320322163","display_name":"Natural Science Foundation of Hebei Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W2006187473","https://openalex.org/W2018133129","https://openalex.org/W2036835491","https://openalex.org/W2044892552","https://openalex.org/W2067068317","https://openalex.org/W2096250715","https://openalex.org/W2097100609","https://openalex.org/W2106407231","https://openalex.org/W2116211213","https://openalex.org/W2118295753","https://openalex.org/W2120777512","https://openalex.org/W2122966045","https://openalex.org/W2125315716","https://openalex.org/W2129291676","https://openalex.org/W2131272198","https://openalex.org/W2138887330","https://openalex.org/W2146228873","https://openalex.org/W2159031739","https://openalex.org/W2159998603","https://openalex.org/W2160821342","https://openalex.org/W2161758457","https://openalex.org/W2163959910","https://openalex.org/W2414079435","https://openalex.org/W2510574730","https://openalex.org/W2560609797","https://openalex.org/W2790604360","https://openalex.org/W2804689771","https://openalex.org/W2915208296","https://openalex.org/W3035030518","https://openalex.org/W3037950838","https://openalex.org/W4301482610","https://openalex.org/W6683692917"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2963177394","https://openalex.org/W2073681303","https://openalex.org/W2024638892","https://openalex.org/W763418848","https://openalex.org/W1595229445","https://openalex.org/W1965815883","https://openalex.org/W149041114","https://openalex.org/W4313359513","https://openalex.org/W322408318"],"abstract_inverted_index":{"This":[0],"article":[1],"aims":[2],"to":[3,58,77,98,145],"propose":[4],"a":[5,70],"novel":[6,71],"Analytical":[7],"Tensor":[8],"Voting":[9],"(ATV)":[10],"mechanism,":[11,140],"which":[12,153],"enables":[13,154],"robust":[14,156],"perceptual":[15,195],"grouping":[16,196],"and":[17,35,48,104,136,157,181,188],"salient":[18,159],"information":[19,160],"extraction":[20,161],"for":[21],"noisy":[22,163],"N-dimensional":[23],"(ND)":[24],"data.":[25,165],"Firstly,":[26],"the":[27,30,39,43,53,59,66,79,82,90,100,114,118,122,126,132,142,155,171,185,191],"approximation":[28],"of":[29,41,55,81,117,170,190],"decaying":[31,134],"function":[32,135],"is":[33,75,96,111,129,151],"investigated":[34],"adopted":[36,133],"based":[37],"on":[38,179],"idea":[40],"penalizing":[42],"1-tensor":[44,60],"votes":[45],"by":[46,52,113],"distance":[47],"curvature,":[49],"respectively,":[50],"followed":[51],"derivation":[54],"analytical":[56,143],"solution":[57,144],"voting":[61,147],"in":[62,85,148,194,198],"ND":[63,149,164],"space":[64,150],"from":[65,162],"geometric":[67],"view.":[68],"Secondly,":[69],"spherical":[72,93,138],"representation":[73,80,139],"mechanism":[74,128,174],"proposed":[76,137,172,192],"facilitate":[78],"elementary":[83,109],"tensors":[84],"various":[86],"dimensional":[87,92,202],"spaces,":[88],"where":[89,141],"high":[91],"coordinate":[94],"system":[95],"utilized":[97],"construct":[99],"controllable":[101],"unit":[102,123],"vectors":[103],"corresponding":[105],"1-tensors.":[106],"Accordingly,":[107],"any":[108],"K-tensor":[110],"represented":[112],"surface":[115],"integration":[116],"constructed":[119,130],"1-tensors":[120],"over":[121],"K-sphere.":[124],"Thirdly,":[125],"ATV":[127,173],"using":[131],"tensor":[146],"derived,":[152],"accurate":[158],"Finally,":[166],"several":[167],"interesting":[168],"properties":[169],"are":[175],"investigated.":[176],"Experimental":[177],"results":[178],"synthetic":[180],"real":[182],"data":[183],"validate":[184],"effectiveness,":[186],"efficiency":[187],"robustness":[189],"method":[193],"tasks":[197],"3D,10D":[199],"or":[200],"higher":[201],"spaces.":[203]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}