{"id":"https://openalex.org/W2097531308","doi":"https://doi.org/10.1109/icip.2008.4712167","title":"Dealing with degeneracy in essential matrix estimation","display_name":"Dealing with degeneracy in essential matrix estimation","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2097531308","doi":"https://doi.org/10.1109/icip.2008.4712167","mag":"2097531308"},"language":"en","primary_location":{"id":"doi:10.1109/icip.2008.4712167","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2008.4712167","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 15th IEEE International Conference on Image Processing","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/A5031999770","display_name":"Peter Decker","orcid":"https://orcid.org/0000-0003-0345-7738"},"institutions":[{"id":"https://openalex.org/I2802076133","display_name":"University of Koblenz and Landau","ror":"https://ror.org/01j9f6752","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802076133"]},{"id":"https://openalex.org/I4387153937","display_name":"Universit\u00e4t Koblenz","ror":"https://ror.org/0433e6t24","country_code":null,"type":"education","lineage":["https://openalex.org/I4387153937"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Peter Decker","raw_affiliation_strings":["Active Vision Group, Institute for Computational Visualistics, University of Koblenz and Landau, Koblenz, Germany","Inst. of Comput. Visualistics, Univ. of Koblenz-Landau, Koblenz"],"affiliations":[{"raw_affiliation_string":"Active Vision Group, Institute for Computational Visualistics, University of Koblenz and Landau, Koblenz, Germany","institution_ids":["https://openalex.org/I2802076133"]},{"raw_affiliation_string":"Inst. of Comput. Visualistics, Univ. of Koblenz-Landau, Koblenz","institution_ids":["https://openalex.org/I2802076133","https://openalex.org/I4387153937"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008718172","display_name":"Dietrich Paulus","orcid":"https://orcid.org/0000-0002-2967-5277"},"institutions":[{"id":"https://openalex.org/I4387153937","display_name":"Universit\u00e4t Koblenz","ror":"https://ror.org/0433e6t24","country_code":null,"type":"education","lineage":["https://openalex.org/I4387153937"]},{"id":"https://openalex.org/I2802076133","display_name":"University of Koblenz and Landau","ror":"https://ror.org/01j9f6752","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802076133"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dietrich Paulus","raw_affiliation_strings":["Active Vision Group, Institute for Computational Visualistics, University of Koblenz and Landau, Koblenz, Germany","Inst. of Comput. Visualistics, Univ. of Koblenz-Landau, Koblenz"],"affiliations":[{"raw_affiliation_string":"Active Vision Group, Institute for Computational Visualistics, University of Koblenz and Landau, Koblenz, Germany","institution_ids":["https://openalex.org/I2802076133"]},{"raw_affiliation_string":"Inst. of Comput. Visualistics, Univ. of Koblenz-Landau, Koblenz","institution_ids":["https://openalex.org/I2802076133","https://openalex.org/I4387153937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053626021","display_name":"Tobias Feldmann","orcid":null},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tobias Feldmann","raw_affiliation_strings":["Institute for Algorithms and Cognitive Systems, University of Karlsruhe, Karlsruhe, Germany","Inst. for Algorithms & Cognitive Syst., Univ. of Karlsruhe (TH), Karlsruhe"],"affiliations":[{"raw_affiliation_string":"Institute for Algorithms and Cognitive Systems, University of Karlsruhe, Karlsruhe, Germany","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"Inst. for Algorithms & Cognitive Syst., Univ. of Karlsruhe (TH), Karlsruhe","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5031999770"],"corresponding_institution_ids":["https://openalex.org/I2802076133","https://openalex.org/I4387153937"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.10182235,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"5","issue":null,"first_page":"1964","last_page":"1967"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10191","display_name":"Robotics and Sensor-Based Localization","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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":0.9998999834060669,"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/T10627","display_name":"Advanced Image and Video Retrieval Techniques","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"}}],"keywords":[{"id":"https://openalex.org/keywords/ransac","display_name":"RANSAC","score":0.8827256560325623},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.7288172841072083},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7085592746734619},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.685606062412262},{"id":"https://openalex.org/keywords/essential-matrix","display_name":"Essential matrix","score":0.6386979818344116},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.6255689859390259},{"id":"https://openalex.org/keywords/pose","display_name":"Pose","score":0.6079977750778198},{"id":"https://openalex.org/keywords/augmented-reality","display_name":"Augmented reality","score":0.5978115200996399},{"id":"https://openalex.org/keywords/motion-estimation","display_name":"Motion estimation","score":0.5912846922874451},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.5912752747535706},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5777338743209839},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5625895857810974},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4807593524456024},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4806627035140991},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.4660806357860565},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4502909183502197},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.28570815920829773},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19826194643974304},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.186580628156662},{"id":"https://openalex.org/keywords/state-transition-matrix","display_name":"State-transition matrix","score":0.18143892288208008},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07503092288970947}],"concepts":[{"id":"https://openalex.org/C114744707","wikidata":"https://www.wikidata.org/wiki/Q218533","display_name":"RANSAC","level":3,"score":0.8827256560325623},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.7288172841072083},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7085592746734619},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.685606062412262},{"id":"https://openalex.org/C49996920","wikidata":"https://www.wikidata.org/wiki/Q17089185","display_name":"Essential matrix","level":5,"score":0.6386979818344116},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.6255689859390259},{"id":"https://openalex.org/C52102323","wikidata":"https://www.wikidata.org/wiki/Q1671968","display_name":"Pose","level":2,"score":0.6079977750778198},{"id":"https://openalex.org/C153715457","wikidata":"https://www.wikidata.org/wiki/Q254183","display_name":"Augmented reality","level":2,"score":0.5978115200996399},{"id":"https://openalex.org/C10161872","wikidata":"https://www.wikidata.org/wiki/Q557891","display_name":"Motion estimation","level":2,"score":0.5912846922874451},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.5912752747535706},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5777338743209839},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5625895857810974},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4807593524456024},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4806627035140991},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.4660806357860565},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4502909183502197},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.28570815920829773},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19826194643974304},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.186580628156662},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.18143892288208008},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07503092288970947},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C201995342","wikidata":"https://www.wikidata.org/wiki/Q682496","display_name":"Systems engineering","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/icip.2008.4712167","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2008.4712167","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2008 15th IEEE International Conference on Image Processing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W2085261163","https://openalex.org/W2099927035","https://openalex.org/W2102481828","https://openalex.org/W2106199912","https://openalex.org/W2130017587","https://openalex.org/W2143083111","https://openalex.org/W2148963710","https://openalex.org/W2151103935","https://openalex.org/W2296147781","https://openalex.org/W4243425824"],"related_works":["https://openalex.org/W4229588126","https://openalex.org/W1018308721","https://openalex.org/W4229059082","https://openalex.org/W4390872624","https://openalex.org/W2896146757","https://openalex.org/W2377994660","https://openalex.org/W2106530324","https://openalex.org/W2148633354","https://openalex.org/W2399901417","https://openalex.org/W205218959"],"abstract_inverted_index":{"Estimation":[0],"of":[1,52,83],"3-D":[2],"egomotion":[3,41],"from":[4,43,60,95],"video":[5],"input,":[6],"also":[7],"known":[8,67],"as":[9],"visual":[10],"odometry,":[11],"is":[12,79],"an":[13,118],"important":[14],"issue":[15],"for":[16,26,121],"many":[17],"applications":[18],"today.":[19],"Augmented":[20],"reality":[21],"(AR)":[22],"and":[23,33,56,113],"robotic":[24],"systems":[25],"example":[27],"rely":[28],"heavily":[29],"on":[30,49],"correct":[31],"pose":[32],"motion":[34],"estimation.":[35],"In":[36],"this":[37],"paper":[38],"we":[39],"discuss":[40],"estimation":[42,51],"a":[44,80],"single":[45],"camera.":[46],"We":[47,98],"focus":[48],"the":[50,53,65,72,110,115],"essential":[54,91],"matrix":[55,92],"problems":[57],"which":[58,78,105],"arise":[59],"degenerate":[61,96,123],"configurations":[62,124],"when":[63],"using":[64],"well":[66],"normalized":[68],"8-point":[69],"algorithm.":[70],"Lately,":[71],"BEEM":[73,111],"algorithm":[74],"has":[75],"been":[76],"published,":[77],"combined":[81],"approach":[82,112],"several":[84],"RANSAC":[85],"methods.":[86],"It":[87],"tries":[88],"to":[89],"guide":[90],"generation":[93],"away":[94],"configurations.":[97],"argue,":[99],"that":[100],"there":[101],"are":[102,106],"still":[103],"cases":[104],"not":[107],"covered":[108],"by":[109],"encourage":[114],"combination":[116],"with":[117],"improved":[119],"method":[120],"detecting":[122],"(IDD).":[125]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}