{"id":"https://openalex.org/W2293071631","doi":"https://doi.org/10.1109/icip.2015.7351098","title":"Notes on image processing with partial differential equations","display_name":"Notes on image processing with partial differential equations","publication_year":2015,"publication_date":"2015-09-01","ids":{"openalex":"https://openalex.org/W2293071631","doi":"https://doi.org/10.1109/icip.2015.7351098","mag":"2293071631"},"language":"en","primary_location":{"id":"doi:10.1109/icip.2015.7351098","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2015.7351098","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Conference on Image Processing (ICIP)","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/A5102892220","display_name":"Behzad Kamgar-Parsi","orcid":null},"institutions":[{"id":"https://openalex.org/I1288214837","display_name":"United States Naval Research Laboratory","ror":"https://ror.org/04d23a975","country_code":"US","type":"facility","lineage":["https://openalex.org/I1288214837","https://openalex.org/I1330347796","https://openalex.org/I175003984","https://openalex.org/I3130687028"]},{"id":"https://openalex.org/I175003984","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57","country_code":"US","type":"government","lineage":["https://openalex.org/I1330347796","https://openalex.org/I175003984","https://openalex.org/I3130687028"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Behzad Kamgar-Parsi","raw_affiliation_strings":["Navy Center for Applied Research in AI, Naval Research Laboratory, Washington, DC","Office of Naval Research, Arlington, VA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Navy Center for Applied Research in AI, Naval Research Laboratory, Washington, DC","institution_ids":["https://openalex.org/I1288214837"]},{"raw_affiliation_string":"Office of Naval Research, Arlington, VA","institution_ids":["https://openalex.org/I175003984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029654352","display_name":"Behrooz Kamgar-Parsi","orcid":null},"institutions":[{"id":"https://openalex.org/I1288214837","display_name":"United States Naval Research Laboratory","ror":"https://ror.org/04d23a975","country_code":"US","type":"facility","lineage":["https://openalex.org/I1288214837","https://openalex.org/I1330347796","https://openalex.org/I175003984","https://openalex.org/I3130687028"]},{"id":"https://openalex.org/I175003984","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57","country_code":"US","type":"government","lineage":["https://openalex.org/I1330347796","https://openalex.org/I175003984","https://openalex.org/I3130687028"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Behrooz Kamgar-Parsi","raw_affiliation_strings":["Navy Center for Applied Research in AI, Naval Research Laboratory, Washington, DC","Office of Naval Research, Arlington, VA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Navy Center for Applied Research in AI, Naval Research Laboratory, Washington, DC","institution_ids":["https://openalex.org/I1288214837"]},{"raw_affiliation_string":"Office of Naval Research, Arlington, VA","institution_ids":["https://openalex.org/I175003984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075283505","display_name":"Kian Kamgar\u2010Parsi","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kian Kamgar-Parsi","raw_affiliation_strings":["Department of Physics, University of Michigan, Ann Arbor, MI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Michigan, Ann Arbor, MI","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3744,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.70852202,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"22","issue":null,"first_page":"1737","last_page":"1741"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9902999997138977,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9902999997138977,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9797999858856201,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11885","display_name":"MRI in cancer diagnosis","score":0.9722999930381775,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6490241885185242},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6471275091171265},{"id":"https://openalex.org/keywords/ambiguity","display_name":"Ambiguity","score":0.5210760831832886},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.5208954811096191},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4963987469673157},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4909379780292511},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.48717254400253296},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44492462277412415},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.43770402669906616},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4333884119987488},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4301915168762207},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.407687783241272},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3961411714553833},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38478729128837585},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3217077851295471},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.279483437538147},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2459016740322113},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20868292450904846},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09523403644561768},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08470088243484497}],"concepts":[{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6490241885185242},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6471275091171265},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.5210760831832886},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.5208954811096191},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4963987469673157},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4909379780292511},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.48717254400253296},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44492462277412415},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.43770402669906616},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4333884119987488},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4301915168762207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.407687783241272},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3961411714553833},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38478729128837585},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3217077851295471},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.279483437538147},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2459016740322113},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20868292450904846},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09523403644561768},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08470088243484497},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icip.2015.7351098","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2015.7351098","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Conference on Image Processing (ICIP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1535934056","https://openalex.org/W1536200267","https://openalex.org/W1579559187","https://openalex.org/W1668732012","https://openalex.org/W2016081265","https://openalex.org/W2018763953","https://openalex.org/W2097924771","https://openalex.org/W2122275806","https://openalex.org/W2126926806","https://openalex.org/W2150134853","https://openalex.org/W2165015795","https://openalex.org/W2503118008","https://openalex.org/W3011612142","https://openalex.org/W3023383796","https://openalex.org/W3038086992","https://openalex.org/W4298355191","https://openalex.org/W4302436815","https://openalex.org/W6631983884"],"related_works":["https://openalex.org/W2353179089","https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W2923538289","https://openalex.org/W2353125546","https://openalex.org/W1492103595","https://openalex.org/W2470643824","https://openalex.org/W1864774435","https://openalex.org/W4400595174","https://openalex.org/W2349635380"],"abstract_inverted_index":{"We":[0,57,72,155],"discuss":[1],"the":[2,9,31,36,55,81,88,128,152,166,175],"underlying":[3],"physics":[4],"of":[5,127,168],"transport":[6],"coefficients":[7,24],"in":[8,25,35,54,79,93,105,118,165],"PDE":[10,82],"image":[11],"processing":[12],"approach":[13],"and":[14,65,145,150,159],"present":[15,58],"a":[16,59,139],"more":[17],"principled":[18],"method":[19,61],"for":[20,49,62,91],"their":[21],"construction.":[22],"Transport":[23],"PDEs":[26],"play":[27],"important":[28],"roles,":[29],"e.g.,":[30],"diffusion":[32],"coefficient":[33],"c":[34,50,64,144],"Perona-Malik":[37],"equation":[38],"\u2202u/\u2202t":[39],"=":[40,98],"\u2207":[41,113],"<sup":[42,114],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[43,115],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">T</sup>":[44,116],"(c\u2207u).":[45],"Hence":[46],"different":[47],"models":[48],"have":[51],"been":[52],"proposed":[53],"literature.":[56],"physics-based":[60],"constructing":[63],"compare":[66],"its":[67],"performance":[68],"with":[69],"existing":[70],"models.":[71],"also":[73],"clarify":[74],"an":[75],"issue":[76],"that":[77,87,171],"arises":[78],"implementing":[80],"approach.":[83],"It":[84],"is":[85,163],"well-known":[86],"product":[89,153],"rule":[90],"derivatives":[92],"continuous":[94,176],"spaces,":[95],"namely,":[96,133],"\u2202(fg)":[97],"g\u2202f":[99],"+":[100],"f\u2202g,":[101],"does":[102],"not":[103],"hold":[104],"discrete":[106],"spaces.":[107],"Thus":[108],"computing":[109],"such":[110],"quantities":[111],"as":[112,138,147],"(c\u2207u)":[117],"spatially":[119],"discretized":[120],"images":[121],"becomes":[122],"ambiguous":[123],"depending":[124],"on":[125],"which":[126,161],"two":[129,148],"alternatives":[130],"we":[131],"use,":[132],"whether":[134],"to":[135,174],"treat":[136,143],"c\u2207u":[137],"single":[140],"function":[141],"or":[142],"\u2207u":[146],"functions":[149],"use":[151],"rule.":[154],"examine":[156],"this":[157],"ambiguity":[158],"show":[160],"alternative":[162],"better":[164],"sense":[167],"yielding":[169],"approximations":[170],"are":[172],"closer":[173],"space":[177],"results.":[178]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
