{"id":"https://openalex.org/W3043395667","doi":"https://doi.org/10.1109/tmm.2020.3009501","title":"Solving Jigsaw Puzzles via Nonconvex Quadratic Programming With the Projected Power Method","display_name":"Solving Jigsaw Puzzles via Nonconvex Quadratic Programming With the Projected Power Method","publication_year":2020,"publication_date":"2020-07-15","ids":{"openalex":"https://openalex.org/W3043395667","doi":"https://doi.org/10.1109/tmm.2020.3009501","mag":"3043395667"},"language":"en","primary_location":{"id":"doi:10.1109/tmm.2020.3009501","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmm.2020.3009501","pdf_url":null,"source":{"id":"https://openalex.org/S137030581","display_name":"IEEE Transactions on Multimedia","issn_l":"1520-9210","issn":["1520-9210","1941-0077"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Multimedia","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/A5103082861","display_name":"Yan Fang","orcid":"https://orcid.org/0000-0003-0600-5497"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fang Yan","raw_affiliation_strings":["School of Information Science and Engineering, Shandong Normal University, Jinan, China"],"raw_orcid":"https://orcid.org/0000-0003-0600-5497","affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Shandong Normal University, Jinan, China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007211501","display_name":"Yuanjie Zheng","orcid":"https://orcid.org/0000-0002-5786-2491"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanjie Zheng","raw_affiliation_strings":["Institute of Biomedical Sciences, Shandong Normal University, Jinan, China","Key Lab of Intelligent Computing & Information Security, Universities of Shandong, Jinan, China","School of Information Science and Engineering, Shandong Normal University, Jinan, China","Shandong Provincial Key Laboratory for Novel Distributed Computer Software Technology, Jinan, China"],"raw_orcid":"https://orcid.org/0000-0002-5786-2491","affiliations":[{"raw_affiliation_string":"Institute of Biomedical Sciences, Shandong Normal University, Jinan, China","institution_ids":["https://openalex.org/I28006308"]},{"raw_affiliation_string":"Key Lab of Intelligent Computing & Information Security, Universities of Shandong, Jinan, China","institution_ids":[]},{"raw_affiliation_string":"School of Information Science and Engineering, Shandong Normal University, Jinan, China","institution_ids":["https://openalex.org/I28006308"]},{"raw_affiliation_string":"Shandong Provincial Key Laboratory for Novel Distributed Computer Software Technology, Jinan, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085588064","display_name":"Jinyu Cong","orcid":"https://orcid.org/0000-0002-5435-5259"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinyu Cong","raw_affiliation_strings":["School of Information Science and Engineering, Shandong Normal University, Jinan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Shandong Normal University, Jinan, China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100324275","display_name":"Liu Liu","orcid":"https://orcid.org/0000-0002-4546-2183"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Liu Liu","raw_affiliation_strings":["UBTECH Sydney Artificial Intelligence Centre and the School of Computer Science, Faculty of Engineering, The University of Sydney, Darlington, NSW, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UBTECH Sydney Artificial Intelligence Centre and the School of Computer Science, Faculty of Engineering, The University of Sydney, Darlington, NSW, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074103823","display_name":"Dacheng Tao","orcid":"https://orcid.org/0000-0001-7225-5449"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Dacheng Tao","raw_affiliation_strings":["UBTECH Sydney Artificial Intelligence Centre and the School of Computer Science, Faculty of Engineering, The University of Sydney, Darlington, NSW, Australia"],"raw_orcid":"https://orcid.org/0000-0001-7225-5449","affiliations":[{"raw_affiliation_string":"UBTECH Sydney Artificial Intelligence Centre and the School of Computer Science, Faculty of Engineering, The University of Sydney, Darlington, NSW, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012332153","display_name":"Sujuan Hou","orcid":"https://orcid.org/0000-0002-6547-6048"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Sujuan Hou","raw_affiliation_strings":["School of Information Science and Engineering, Shandong Normal University, Jinan, China"],"raw_orcid":"https://orcid.org/0000-0002-6547-6048","affiliations":[{"raw_affiliation_string":"School of Information Science and Engineering, Shandong Normal University, Jinan, China","institution_ids":["https://openalex.org/I28006308"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5103082861"],"corresponding_institution_ids":["https://openalex.org/I28006308"],"apc_list":null,"apc_paid":null,"fwci":0.4906,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.65886332,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"23","issue":null,"first_page":"2310","last_page":"2320"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14339","display_name":"Image Processing and 3D Reconstruction","score":1.0,"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/T14339","display_name":"Image Processing and 3D Reconstruction","score":1.0,"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/T12364","display_name":"Archaeological Research and Protection","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1912","display_name":"Space and Planetary Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11211","display_name":"3D Surveying and Cultural Heritage","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/1907","display_name":"Geology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/jigsaw","display_name":"Jigsaw","score":0.982641339302063},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7214751839637756},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.672980785369873},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.5710831880569458},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5381456613540649},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.5082966685295105},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.468874454498291},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34366220235824585},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3435361385345459},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33978956937789917},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2760542929172516},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23060712218284607}],"concepts":[{"id":"https://openalex.org/C2779405079","wikidata":"https://www.wikidata.org/wiki/Q356040","display_name":"Jigsaw","level":2,"score":0.982641339302063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7214751839637756},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.672980785369873},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.5710831880569458},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5381456613540649},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.5082966685295105},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.468874454498291},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34366220235824585},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3435361385345459},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33978956937789917},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2760542929172516},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23060712218284607},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tmm.2020.3009501","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tmm.2020.3009501","pdf_url":null,"source":{"id":"https://openalex.org/S137030581","display_name":"IEEE Transactions on Multimedia","issn_l":"1520-9210","issn":["1520-9210","1941-0077"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Multimedia","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3866360226","display_name":null,"funder_award_id":"61702313","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7030860546","display_name":null,"funder_award_id":"81871508","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7585241959","display_name":null,"funder_award_id":"2017M612338","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G8498003072","display_name":null,"funder_award_id":"61773246","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W165381567","https://openalex.org/W643635367","https://openalex.org/W1941539351","https://openalex.org/W1949523763","https://openalex.org/W1976015505","https://openalex.org/W1978259121","https://openalex.org/W1978383339","https://openalex.org/W1982931780","https://openalex.org/W1987653866","https://openalex.org/W1992101337","https://openalex.org/W1993428550","https://openalex.org/W2001316417","https://openalex.org/W2004407037","https://openalex.org/W2040466831","https://openalex.org/W2055430302","https://openalex.org/W2059383484","https://openalex.org/W2077230361","https://openalex.org/W2084810551","https://openalex.org/W2087900192","https://openalex.org/W2102108803","https://openalex.org/W2108681527","https://openalex.org/W2128745377","https://openalex.org/W2129615061","https://openalex.org/W2130975683","https://openalex.org/W2140926781","https://openalex.org/W2141155330","https://openalex.org/W2142949395","https://openalex.org/W2148300333","https://openalex.org/W2151765755","https://openalex.org/W2154431390","https://openalex.org/W2166135831","https://openalex.org/W2168547291","https://openalex.org/W2171195527","https://openalex.org/W2205007824","https://openalex.org/W2205290124","https://openalex.org/W2283023501","https://openalex.org/W2318684976","https://openalex.org/W2461705298","https://openalex.org/W2519016089","https://openalex.org/W2580520913","https://openalex.org/W2689968489","https://openalex.org/W2749341689","https://openalex.org/W2883144317","https://openalex.org/W2963824344","https://openalex.org/W2963829083","https://openalex.org/W2998875450","https://openalex.org/W3100450900","https://openalex.org/W3102206315","https://openalex.org/W3113425034","https://openalex.org/W4242721750","https://openalex.org/W6621125592","https://openalex.org/W6675609692","https://openalex.org/W6681274554","https://openalex.org/W6732886222","https://openalex.org/W6739584322","https://openalex.org/W6743125973"],"related_works":["https://openalex.org/W4313442009","https://openalex.org/W3106062205","https://openalex.org/W3083639670","https://openalex.org/W2291971009","https://openalex.org/W2614642134","https://openalex.org/W3112136298","https://openalex.org/W2949155634","https://openalex.org/W2951352292","https://openalex.org/W2382039200","https://openalex.org/W4298854296"],"abstract_inverted_index":{"Jigsaw":[0],"puzzles":[1],"consist":[2],"of":[3,37,74,90],"reconstructing":[4],"a":[5,51,79],"picture":[6],"that":[7,56,83,110],"has":[8],"been":[9],"divided":[10],"into":[11],"many":[12],"interlocking":[13],"pieces.":[14,97],"This":[15,43],"paper":[16],"describes":[17],"an":[18,85],"automatic":[19],"global":[20],"method":[21,112],"for":[22],"solving":[23],"the":[24,32,35,38,60,70,91,103],"square-piece":[25],"jigsaw":[26,39,96],"puzzle":[27,75],"problem":[28,55],"in":[29,102],"which":[30],"neither":[31],"orientations":[33,73],"nor":[34],"locations":[36,71],"pieces":[40,76],"are":[41],"known.":[42],"hard":[44],"combinatorial":[45],"sorting":[46],"task":[47],"is":[48,57],"formulated":[49],"as":[50],"nonconvex":[52],"quadratic":[53,81],"programming":[54],"solved":[58],"via":[59],"projected":[61],"power":[62],"method.":[63],"Specifically,":[64],"this":[65],"work":[66],"aims":[67],"to":[68],"specify":[69],"and":[72,106],"by":[77],"maximizing":[78],"constrained":[80],"function":[82],"resolves":[84],"optimized":[86],"permutation":[87],"matrix":[88],"composed":[89],"noisy":[92],"pairwise":[93],"affinities":[94],"between":[95],"The":[98],"experimental":[99],"results":[100],"obtained":[101],"MIT,":[104],"McGill":[105],"Pomeranz":[107],"datasets":[108],"indicate":[109],"our":[111],"outperforms":[113],"state-of-the-art":[114],"techniques.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
