{"id":"https://openalex.org/W4414581524","doi":"https://doi.org/10.48550/arxiv.2505.18625","title":"Tropical Geometry Based Edge Detection Using Min-Plus and Max-Plus Algebra","display_name":"Tropical Geometry Based Edge Detection Using Min-Plus and Max-Plus Algebra","publication_year":2025,"publication_date":"2025-05-24","ids":{"openalex":"https://openalex.org/W4414581524","doi":"https://doi.org/10.48550/arxiv.2505.18625"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2505.18625","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.18625","pdf_url":"https://arxiv.org/pdf/2505.18625","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2505.18625","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119753607","display_name":"Shivam Kumar Jha S.","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S, Shivam Kumar Jha","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078366856","display_name":"Jaya NN Iyer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Iyer, Jaya NN","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5119753607"],"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/T12983","display_name":"Satellite Image Processing and Photogrammetry","score":0.7864000201225281,"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"}},"topics":[{"id":"https://openalex.org/T12983","display_name":"Satellite Image Processing and Photogrammetry","score":0.7864000201225281,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/edge-detection","display_name":"Edge detection","score":0.7936000227928162},{"id":"https://openalex.org/keywords/canny-edge-detector","display_name":"Canny edge detector","score":0.6873999834060669},{"id":"https://openalex.org/keywords/deriche-edge-detector","display_name":"Deriche edge detector","score":0.5293999910354614},{"id":"https://openalex.org/keywords/image-gradient","display_name":"Image gradient","score":0.5156999826431274},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.5094000101089478},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4325999915599823},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.4171999990940094},{"id":"https://openalex.org/keywords/grayscale","display_name":"Grayscale","score":0.36550000309944153},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.36399999260902405},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.3612000048160553}],"concepts":[{"id":"https://openalex.org/C193536780","wikidata":"https://www.wikidata.org/wiki/Q1513153","display_name":"Edge detection","level":4,"score":0.7936000227928162},{"id":"https://openalex.org/C14705441","wikidata":"https://www.wikidata.org/wiki/Q597183","display_name":"Canny edge detector","level":5,"score":0.6873999834060669},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5551000237464905},{"id":"https://openalex.org/C167074055","wikidata":"https://www.wikidata.org/wiki/Q5262565","display_name":"Deriche edge detector","level":5,"score":0.5293999910354614},{"id":"https://openalex.org/C182037307","wikidata":"https://www.wikidata.org/wiki/Q17039097","display_name":"Image gradient","level":5,"score":0.5156999826431274},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.5094000101089478},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4325999915599823},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42730000615119934},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.4171999990940094},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40389999747276306},{"id":"https://openalex.org/C78201319","wikidata":"https://www.wikidata.org/wiki/Q685727","display_name":"Grayscale","level":3,"score":0.36550000309944153},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.36399999260902405},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3612000048160553},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.35920000076293945},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.35580000281333923},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.35420000553131104},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.3529999852180481},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.3391999900341034},{"id":"https://openalex.org/C185568154","wikidata":"https://www.wikidata.org/wiki/Q530242","display_name":"Mathematical morphology","level":4,"score":0.33889999985694885},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3330000042915344},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3262999951839447},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3188999891281128},{"id":"https://openalex.org/C2778328480","wikidata":"https://www.wikidata.org/wiki/Q1639904","display_name":"Hybrid image","level":3,"score":0.31839999556541443},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.3176000118255615},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.31200000643730164},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.2971000075340271},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.26660001277923584},{"id":"https://openalex.org/C99102927","wikidata":"https://www.wikidata.org/wiki/Q3058184","display_name":"Scale space","level":4,"score":0.2639000117778778},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2574999928474426}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2505.18625","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.18625","pdf_url":"https://arxiv.org/pdf/2505.18625","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2505.18625","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.18625","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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2505.18625","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2505.18625","pdf_url":"https://arxiv.org/pdf/2505.18625","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3,43,48,124],"tropical":[4,21,82,121],"geometry-based":[5],"edge":[6,33,66,106,110,130],"detection":[7,96,131],"framework":[8,55],"that":[9,81],"reformulates":[10],"convolution":[11],"and":[12,17,30,47,61,77,91,99,112,126],"gradient":[13],"computations":[14],"using":[15,104],"min-plus":[16,45],"max-plus":[18,49],"algebra.":[19],"The":[20,54],"formulation":[22,128],"emphasizes":[23],"dominant":[24],"intensity":[25],"variations,":[26],"contributing":[27],"to":[28,64],"sharper":[29],"more":[31],"continuous":[32],"representations.":[34],"Three":[35],"variants":[36],"are":[37],"explored:":[38],"an":[39],"adaptive":[40],"threshold-based":[41],"method,":[42,46],"multi-kernel":[44],"method":[50],"emphasizing":[51],"structural":[52,113],"continuity.":[53],"integrates":[56],"multi-scale":[57],"processing,":[58],"Hessian":[59],"filtering,":[60],"wavelet":[62],"shrinkage":[63],"enhance":[65],"transitions":[67],"while":[68],"maintaining":[69],"computational":[70],"efficiency.":[71],"Experiments":[72],"on":[73],"MATLAB":[74],"built-in":[75],"grayscale":[76],"color":[78],"images":[79],"suggest":[80],"formulations":[83],"integrated":[84],"with":[85],"classical":[86],"operators,":[87],"such":[88],"as":[89,123],"Canny":[90],"LoG,":[92],"can":[93],"improve":[94],"boundary":[95],"in":[97,132],"low-contrast":[98],"textured":[100],"regions.":[101],"Quantitative":[102],"evaluation":[103],"standard":[105],"metrics":[107],"indicates":[108],"favorable":[109],"clarity":[111],"coherence.":[114],"These":[115],"results":[116],"highlight":[117],"the":[118],"potential":[119],"of":[120],"algebra":[122],"scalable":[125],"noise-aware":[127],"for":[129],"practical":[133],"image":[134],"analysis":[135],"tasks.":[136]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
