{"id":"https://openalex.org/W2106661360","doi":"https://doi.org/10.1109/cadcg.2009.5246913","title":"Linear independent moment invariant sets","display_name":"Linear independent moment invariant sets","publication_year":2009,"publication_date":"2009-08-01","ids":{"openalex":"https://openalex.org/W2106661360","doi":"https://doi.org/10.1109/cadcg.2009.5246913","mag":"2106661360"},"language":"en","primary_location":{"id":"doi:10.1109/cadcg.2009.5246913","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cadcg.2009.5246913","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics","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/A5072288842","display_name":"Luhong Diao","orcid":"https://orcid.org/0000-0002-2882-2490"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Luhong Diao","raw_affiliation_strings":["College of Applied Sciences, Beijing University of Technology, Beijing, China","College of Applied Sciences, Beijing University of Technology, 100124, China"],"affiliations":[{"raw_affiliation_string":"College of Applied Sciences, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]},{"raw_affiliation_string":"College of Applied Sciences, Beijing University of Technology, 100124, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100714089","display_name":"Hua Li","orcid":"https://orcid.org/0000-0003-4982-6455"},"institutions":[{"id":"https://openalex.org/I4210090176","display_name":"Institute of Computing Technology","ror":"https://ror.org/0090r4d87","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210090176"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hua Li","raw_affiliation_strings":["National Center of Intelligent Computing, Institute of Computing Technology, Chinese Academy and Sciences, Beijing, China","National Center of Intelligent Computing, Institute of Computing Technology, Chinese Academy of Science, Beijing 100080, China"],"affiliations":[{"raw_affiliation_string":"National Center of Intelligent Computing, Institute of Computing Technology, Chinese Academy and Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210090176"]},{"raw_affiliation_string":"National Center of Intelligent Computing, Institute of Computing Technology, Chinese Academy of Science, Beijing 100080, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100378893","display_name":"Sen Zhang","orcid":"https://orcid.org/0000-0002-8010-6045"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sen Zhang","raw_affiliation_strings":["College of Applied Sciences, Beijing University of Technology, Beijing, China","College of Applied Sciences, Beijing University of Technology, 100124, China"],"affiliations":[{"raw_affiliation_string":"College of Applied Sciences, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]},{"raw_affiliation_string":"College of Applied Sciences, Beijing University of Technology, 100124, China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100349558","display_name":"Lei Liu","orcid":"https://orcid.org/0000-0002-4698-2965"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Liu","raw_affiliation_strings":["College of Applied Sciences, Beijing University of Technology, Beijing, China","College of Applied Sciences, Beijing University of Technology, 100124, China"],"affiliations":[{"raw_affiliation_string":"College of Applied Sciences, Beijing University of Technology, Beijing, China","institution_ids":["https://openalex.org/I37796252"]},{"raw_affiliation_string":"College of Applied Sciences, Beijing University of Technology, 100124, China","institution_ids":["https://openalex.org/I37796252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5072288842"],"corresponding_institution_ids":["https://openalex.org/I37796252"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13935566,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"162","last_page":"165"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9853000044822693,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9853000044822693,"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/invariant","display_name":"Invariant (physics)","score":0.695411205291748},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6016344428062439},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.58585125207901},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.49202343821525574},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4095219373703003},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.382244348526001},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32245099544525146},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14444512128829956},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.088030606508255},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.08653080463409424},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.08243244886398315}],"concepts":[{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.695411205291748},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6016344428062439},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.58585125207901},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.49202343821525574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4095219373703003},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.382244348526001},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32245099544525146},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14444512128829956},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.088030606508255},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.08653080463409424},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.08243244886398315}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cadcg.2009.5246913","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cadcg.2009.5246913","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4000000059604645,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1970097244","https://openalex.org/W2028806211","https://openalex.org/W2035062046","https://openalex.org/W2037863673","https://openalex.org/W2056664221","https://openalex.org/W2098953696","https://openalex.org/W2103399972","https://openalex.org/W2105225261","https://openalex.org/W2108329881","https://openalex.org/W2136823057","https://openalex.org/W2137382111","https://openalex.org/W2146880335","https://openalex.org/W2152839250","https://openalex.org/W2159498975","https://openalex.org/W6675477417"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3125750421","https://openalex.org/W68147753","https://openalex.org/W2949765904","https://openalex.org/W4306949324","https://openalex.org/W4388544318","https://openalex.org/W618363683","https://openalex.org/W1978104062","https://openalex.org/W4281657016","https://openalex.org/W594289152"],"abstract_inverted_index":{"This":[0],"paper":[1],"presented":[2],"necessary":[3],"and":[4,20],"sufficient":[5],"condition":[6],"of":[7,38],"moment":[8,22],"invariants":[9,34],"under":[10],"general":[11],"linear":[12,31],"transformation.":[13],"Based":[14],"on":[15],"this":[16],"condition,":[17],"arbitrary":[18],"order":[19],"dimensional":[21],"invariant":[23],"sets":[24],"can":[25],"be":[26],"constructed.":[27],"Due":[28],"to":[29],"their":[30],"independence,":[32],"previous":[33],"are":[35],"special":[36],"cases":[37],"them.":[39]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}