{"id":"https://openalex.org/W7162086526","doi":"https://doi.org/10.48550/arxiv.2605.22578","title":"Beyond Chamfer Distance: Granular Order-aware Evaluation Metric For Online Mapping","display_name":"Beyond Chamfer Distance: Granular Order-aware Evaluation Metric For Online Mapping","publication_year":2026,"publication_date":"2026-05-21","ids":{"openalex":"https://openalex.org/W7162086526","doi":"https://doi.org/10.48550/arxiv.2605.22578"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.22578","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.22578","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.22578","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026992224","display_name":"Chouaib Bencheikh Lehocine","orcid":"https://orcid.org/0000-0003-1301-3735"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lehocine, Chouaib Bencheikh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010159086","display_name":"Adam Lilja","orcid":"https://orcid.org/0000-0001-5733-4472"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lilja, Adam","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136792858","display_name":"Junsheng Fu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fu, Junsheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5035123040","display_name":"Lars Hammarstrand","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hammarstrand, Lars","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.47130000591278076,"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":0.47130000591278076,"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/T13282","display_name":"Automated Road and Building Extraction","score":0.15520000457763672,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/T11106","display_name":"Data Management and Algorithms","score":0.09939999878406525,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/metric","display_name":"Metric (unit)","score":0.7268999814987183},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.49790000915527344},{"id":"https://openalex.org/keywords/bottleneck","display_name":"Bottleneck","score":0.490200012922287},{"id":"https://openalex.org/keywords/segmentation","display_name":"Segmentation","score":0.486299991607666},{"id":"https://openalex.org/keywords/chamfer","display_name":"Chamfer (geometry)","score":0.48260000348091125},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.46970000863075256},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.4377000033855438},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.43290001153945923},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.39739999175071716}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.7268999814987183},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6176000237464905},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5741999745368958},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.49790000915527344},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.490200012922287},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.486299991607666},{"id":"https://openalex.org/C2776313386","wikidata":"https://www.wikidata.org/wiki/Q18018756","display_name":"Chamfer (geometry)","level":2,"score":0.48260000348091125},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.46970000863075256},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.4377000033855438},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.39739999175071716},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3970000147819519},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.38530001044273376},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3783000111579895},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.3776000142097473},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.36579999327659607},{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.3562000095844269},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.34549999237060547},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.3400999903678894},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.303600013256073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28529998660087585},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.265500009059906},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.2531000077724457},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.2524000108242035}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.22578","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.22578","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.22578","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.22578","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Online":[0],"map":[1,24],"estimation":[2],"is":[3],"a":[4,129,147,170,187],"crucial":[5],"component":[6],"of":[7,29,38,109,144],"autonomous":[8],"driving":[9],"systems":[10],"that":[11,31,105,132,157,190],"reduces":[12],"the":[13,91,118,141,180],"reliance":[14],"on":[15,43,49,87,153],"costly":[16],"high-definition":[17],"maps.":[18],"State-of-the-art":[19],"(SOTA)":[20],"methods":[21,40,75,164],"commonly":[22],"predict":[23],"elements":[25],"as":[26,179],"ordered":[27],"sequences":[28],"points":[30],"form":[32],"polylines":[33],"and":[34,61,126,137],"polygons.":[35],"The":[36],"evaluation":[37,108,120,197],"these":[39,85],"relies":[41],"predominantly":[42],"mean":[44],"average":[45],"precision":[46],"(mAP)":[47],"based":[48],"thresholded":[50],"Chamfer":[51],"distance":[52],"(CD).":[53],"This":[54,174],"framework":[55],"lacks":[56],"sensitivity":[57],"to":[58,72,193],"point":[59],"ordering":[60],"provides":[62],"limited":[63],"granularity":[64],"in":[65,183],"assessing":[66],"geometric":[67,138],"quality,":[68],"making":[69],"it":[70],"difficult":[71],"distinguish":[73],"which":[74],"truly":[76],"excel":[77],"over":[78],"others.":[79],"In":[80],"this":[81],"work,":[82],"we":[83,95,122,155],"address":[84],"limitations":[86],"two":[88],"fronts.":[89],"For":[90,117],"single-instance":[92],"similarity":[93],"measure,":[94],"introduce":[96],"sequence":[97],"optimal":[98],"sub-pattern":[99],"assignment":[100],"(SOSPA),":[101],"an":[102],"order-aware":[103],"metric":[104,115,131],"enables":[106],"fine-grained":[107],"individual":[110],"geometries":[111],"while":[112,168],"satisfying":[113],"all":[114],"axioms.":[116],"multi-instance":[119],"framework,":[121],"propose":[123],"polyline":[124],"localisation":[125],"detection":[127,135,177],"(PLD),":[128],"soft":[130,149],"jointly":[133],"captures":[134],"quality":[136],"accuracy,":[139],"replacing":[140],"hard":[142],"thresholding":[143],"mAP":[145,191],"with":[146],"principled":[148],"assignment.":[150],"Through":[151],"evaluations":[152],"nuScenes,":[154],"demonstrate":[156],"PLD":[158],"effectively":[159],"ranks":[160],"SOTA":[161],"online":[162],"mapping":[163],"(MapTRv2,":[165],"StreamMapNet,":[166],"MapTracker)":[167],"providing":[169],"decomposed":[171],"error":[172],"analysis.":[173],"analysis":[175],"identifies":[176],"capability":[178],"dominant":[181],"bottleneck":[182],"current":[184],"methods,":[185],"revealing":[186],"performance":[188],"trend":[189],"fails":[192],"capture.":[194],"Code":[195],"for":[196],"using":[198],"our":[199],"metrics":[200],"will":[201],"be":[202],"released.":[203]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-23T00:00:00"}