{"id":"https://openalex.org/W2541695503","doi":"https://doi.org/10.1109/iccv.2009.5459288","title":"The Normalized Subspace Inclusion: Robust clustering of motion subspaces","display_name":"The Normalized Subspace Inclusion: Robust clustering of motion subspaces","publication_year":2009,"publication_date":"2009-09-01","ids":{"openalex":"https://openalex.org/W2541695503","doi":"https://doi.org/10.1109/iccv.2009.5459288","mag":"2541695503"},"language":"en","primary_location":{"id":"doi:10.1109/iccv.2009.5459288","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iccv.2009.5459288","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE 12th International Conference on Computer Vision","raw_type":"proceedings-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/A5057535416","display_name":"Nuno Pinho da Silva","orcid":"https://orcid.org/0000-0001-5965-6459"},"institutions":[{"id":"https://openalex.org/I4387152517","display_name":"Instituto Superior T\u00e9cnico","ror":"https://ror.org/03db2by73","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Nuno Pinho da Silva","raw_affiliation_strings":["ISR, Instituto Superior T\u00e9cnico, Lisboa, Portugal"],"affiliations":[{"raw_affiliation_string":"ISR, Instituto Superior T\u00e9cnico, Lisboa, Portugal","institution_ids":["https://openalex.org/I4387152517"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068389832","display_name":"Jo\u00e3o Paulo Costeira","orcid":"https://orcid.org/0000-0001-6769-2935"},"institutions":[{"id":"https://openalex.org/I4387152517","display_name":"Instituto Superior T\u00e9cnico","ror":"https://ror.org/03db2by73","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103","https://openalex.org/I4387152517"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Joaao Paulo Costeira","raw_affiliation_strings":["ISR, Instituto Superior T\u00e9cnico, Lisboa, Portugal"],"affiliations":[{"raw_affiliation_string":"ISR, Instituto Superior T\u00e9cnico, Lisboa, Portugal","institution_ids":["https://openalex.org/I4387152517"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057535416"],"corresponding_institution_ids":["https://openalex.org/I4387152517"],"apc_list":null,"apc_paid":null,"fwci":1.6406,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.8691788,"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":"1444","last_page":"1450"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10531","display_name":"Advanced Vision and Imaging","score":0.9997000098228455,"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":0.9997000098228455,"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/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10638","display_name":"Optical measurement and interference techniques","score":0.9954000115394592,"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/linear-subspace","display_name":"Linear subspace","score":0.8680566549301147},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.7092378735542297},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6054404973983765},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5953744649887085},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5912944078445435},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5137406587600708},{"id":"https://openalex.org/keywords/structure-from-motion","display_name":"Structure from motion","score":0.5117871165275574},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.49580177664756775},{"id":"https://openalex.org/keywords/segmentation","display_name":"Segmentation","score":0.48889532685279846},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.46514880657196045},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.4519098997116089},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4404814839363098},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.4239645302295685},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.41590651869773865},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33166155219078064},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.19286784529685974},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11775308847427368}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8680566549301147},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7092378735542297},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6054404973983765},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5953744649887085},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5912944078445435},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5137406587600708},{"id":"https://openalex.org/C146159030","wikidata":"https://www.wikidata.org/wiki/Q7625099","display_name":"Structure from motion","level":3,"score":0.5117871165275574},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.49580177664756775},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.48889532685279846},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.46514880657196045},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.4519098997116089},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4404814839363098},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.4239645302295685},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.41590651869773865},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33166155219078064},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.19286784529685974},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11775308847427368},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iccv.2009.5459288","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iccv.2009.5459288","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE 12th International Conference on Computer Vision","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7699999809265137,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W56210758","https://openalex.org/W1599555836","https://openalex.org/W2032986522","https://openalex.org/W2036068690","https://openalex.org/W2041861271","https://openalex.org/W2052311585","https://openalex.org/W2100730563","https://openalex.org/W2116706028","https://openalex.org/W2117138194","https://openalex.org/W2118154608","https://openalex.org/W2134810690","https://openalex.org/W2138835141","https://openalex.org/W2150600350","https://openalex.org/W2151155403","https://openalex.org/W2153233077","https://openalex.org/W2160167256","https://openalex.org/W2177347332","https://openalex.org/W2798909945","https://openalex.org/W6635730818","https://openalex.org/W6677833576","https://openalex.org/W6684031994"],"related_works":["https://openalex.org/W2896134808","https://openalex.org/W140666874","https://openalex.org/W3172436493","https://openalex.org/W4287164812","https://openalex.org/W2957492749","https://openalex.org/W1887135636","https://openalex.org/W2386063599","https://openalex.org/W1975884855","https://openalex.org/W3213150849","https://openalex.org/W4285605394"],"abstract_inverted_index":{"Perceiving":[0],"dynamic":[1],"scenes":[2],"of":[3,9,40,45,72,113,123],"rigid":[4,19,73,99,124],"bodies,":[5],"through":[6],"affine":[7],"projections":[8],"moving":[10],"3D":[11],"point":[12],"clouds,":[13],"boils":[14],"down":[15],"to":[16,85,130],"clustering":[17,51],"the":[18,24,38,41,46,70,79,107,114,117,121],"motion":[20,100],"subspaces":[21],"supported":[22],"by":[23],"points'":[25],"image":[26],"trajectories.":[27],"For":[28],"a":[29,95],"physically":[30],"meaningful":[31],"interpretation,":[32],"clusters":[33],"must":[34],"be":[35,131],"consistent":[36],"with":[37,135],"geometry":[39],"underlying":[42],"subspaces.":[43],"Most":[44],"existing":[47],"measures":[48],"for":[49,98,133],"subspace":[50],"are":[52,67],"ambiguous,":[53],"or":[54],"geometrically":[55],"inconsistent.":[56],"A":[57],"practical":[58],"consequence":[59],"is":[60],"that":[61],"methods":[62],"based":[63],"on":[64,90,106],"such":[65],"(dis)similarities":[66],"unstable":[68],"when":[69,120],"number":[71,122],"bodies":[74,125],"increase.":[75],"This":[76],"paper":[77],"introduces":[78],"Normalized":[80],"Subspace":[81],"Inclusion":[82],"(NSI)":[83],"criterion":[84],"resolve":[86],"these":[87],"issues.":[88],"Relying":[89],"this":[91],"similarity,":[92],"we":[93],"propose":[94],"robust":[96],"methodology":[97],"segmentation,":[101],"and":[102],"test":[103],"it,":[104],"extensively,":[105],"Hopkins155":[108],"database.":[109],"The":[110],"geometric":[111],"consistency":[112],"NSI":[115],"assures":[116],"method's":[118],"accuracy":[119],"increases,":[126],"while":[127],"robustness":[128],"proves":[129],"suitable":[132],"dealing":[134],"challenging":[136],"imaging":[137],"conditions.":[138]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-23T09:07:50.710637","created_date":"2025-10-10T00:00:00"}
