{"id":"https://openalex.org/W2621540102","doi":"https://doi.org/10.1109/tip.2017.2713950","title":"Derivative Kernels: Numerics and Applications","display_name":"Derivative Kernels: Numerics and Applications","publication_year":2017,"publication_date":"2017-06-08","ids":{"openalex":"https://openalex.org/W2621540102","doi":"https://doi.org/10.1109/tip.2017.2713950","mag":"2621540102","pmid":"https://pubmed.ncbi.nlm.nih.gov/28613176"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2017.2713950","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2017.2713950","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5073426758","display_name":"Mahdi S. Hosseini","orcid":"https://orcid.org/0000-0002-9147-0731"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Mahdi S. Hosseini","raw_affiliation_strings":["The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada"],"affiliations":[{"raw_affiliation_string":"The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059152392","display_name":"Konstantinos N. Plataniotis","orcid":"https://orcid.org/0000-0003-3647-5473"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Konstantinos N. Plataniotis","raw_affiliation_strings":["The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada"],"affiliations":[{"raw_affiliation_string":"The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073426758"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":null,"apc_paid":null,"fwci":1.2743,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.87831876,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"26","issue":"10","first_page":"4596","last_page":"4611"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11105","display_name":"Advanced Image Processing Techniques","score":0.9998000264167786,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9998000264167786,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9994999766349792,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9994000196456909,"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/algorithm","display_name":"Algorithm","score":0.5720292329788208},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.540252149105072},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.5382549166679382},{"id":"https://openalex.org/keywords/ripple","display_name":"Ripple","score":0.5165407061576843},{"id":"https://openalex.org/keywords/frequency-domain","display_name":"Frequency domain","score":0.4831092357635498},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.45139357447624207},{"id":"https://openalex.org/keywords/impulse-response","display_name":"Impulse response","score":0.4390719532966614},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.42452871799468994},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4105866551399231},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37391090393066406},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3599558472633362},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3180535137653351},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.1447528600692749},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.11452963948249817}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5720292329788208},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.540252149105072},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.5382549166679382},{"id":"https://openalex.org/C2779599953","wikidata":"https://www.wikidata.org/wiki/Q1776117","display_name":"Ripple","level":3,"score":0.5165407061576843},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.4831092357635498},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.45139357447624207},{"id":"https://openalex.org/C72279823","wikidata":"https://www.wikidata.org/wiki/Q1139726","display_name":"Impulse response","level":2,"score":0.4390719532966614},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.42452871799468994},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4105866551399231},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37391090393066406},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3599558472633362},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3180535137653351},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.1447528600692749},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.11452963948249817},{"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tip.2017.2713950","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2017.2713950","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},{"id":"pmid:28613176","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28613176","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W130775616","https://openalex.org/W819977924","https://openalex.org/W1511797856","https://openalex.org/W1528209651","https://openalex.org/W1536682884","https://openalex.org/W1885185971","https://openalex.org/W1950594372","https://openalex.org/W1970239009","https://openalex.org/W1972717105","https://openalex.org/W1974524841","https://openalex.org/W1987166016","https://openalex.org/W1987385865","https://openalex.org/W1987448909","https://openalex.org/W1991605728","https://openalex.org/W2003370853","https://openalex.org/W2010166335","https://openalex.org/W2010548775","https://openalex.org/W2016045532","https://openalex.org/W2019904315","https://openalex.org/W2023586451","https://openalex.org/W2024047707","https://openalex.org/W2028612958","https://openalex.org/W2035677848","https://openalex.org/W2043490409","https://openalex.org/W2044011870","https://openalex.org/W2052277674","https://openalex.org/W2056658628","https://openalex.org/W2061145375","https://openalex.org/W2061818168","https://openalex.org/W2087747235","https://openalex.org/W2093427358","https://openalex.org/W2096768337","https://openalex.org/W2098579890","https://openalex.org/W2106002835","https://openalex.org/W2109200236","https://openalex.org/W2109606373","https://openalex.org/W2111728852","https://openalex.org/W2113350594","https://openalex.org/W2115425050","https://openalex.org/W2119605622","https://openalex.org/W2119662598","https://openalex.org/W2125287505","https://openalex.org/W2133665775","https://openalex.org/W2136423906","https://openalex.org/W2138436041","https://openalex.org/W2141957843","https://openalex.org/W2145023731","https://openalex.org/W2146475025","https://openalex.org/W2148502234","https://openalex.org/W2150134853","https://openalex.org/W2150823344","https://openalex.org/W2151103935","https://openalex.org/W2151821220","https://openalex.org/W2154765531","https://openalex.org/W2157331726","https://openalex.org/W2157519031","https://openalex.org/W2158842967","https://openalex.org/W2161907179","https://openalex.org/W2163060163","https://openalex.org/W2166538457","https://openalex.org/W2167272056","https://openalex.org/W2177274842","https://openalex.org/W2249820524","https://openalex.org/W2321241745","https://openalex.org/W2329746575","https://openalex.org/W2397071937","https://openalex.org/W2417716951","https://openalex.org/W2503118008","https://openalex.org/W2576017358","https://openalex.org/W2585841545","https://openalex.org/W3150857940","https://openalex.org/W4235198646","https://openalex.org/W4235564845","https://openalex.org/W4243103503","https://openalex.org/W4247811648","https://openalex.org/W4255272544","https://openalex.org/W6631716152"],"related_works":["https://openalex.org/W2611031068","https://openalex.org/W1704347466","https://openalex.org/W1996936972","https://openalex.org/W4283017538","https://openalex.org/W1545275724","https://openalex.org/W2802707792","https://openalex.org/W1034719509","https://openalex.org/W3015917873","https://openalex.org/W2753371762","https://openalex.org/W2124950181"],"abstract_inverted_index":{"A":[0],"generalized":[1],"framework":[2,21],"for":[3,9,29,76,84],"numerical":[4],"differentiation":[5,79],"(ND)":[6],"is":[7,60],"proposed":[8,57],"constructing":[10],"a":[11,98],"finite":[12],"impulse":[13],"response":[14,25],"(FIR)":[15],"filter":[16,59],"in":[17,63,112],"closed":[18],"form.":[19],"The":[20,93,134],"regulates":[22],"the":[23,49,56,64,117,131,138,142],"frequency":[24,34],"of":[26,102,106,119,141],"ND":[27,58],"filters":[28],"arbitrary":[30,85],"derivative-order":[31],"and":[32,42,90,109,146,153],"cutoff":[33,88],"selected":[35],"parameters":[36],"relying":[37],"on":[38,122,130],"interpolating":[39],"power":[40],"polynomials":[41],"maximally":[43],"flat":[44],"design":[45],"techniques.":[46],"Compared":[47],"with":[48,67,127,149],"state-of-the-art":[50],"solutions,":[51],"such":[52],"as":[53],"Gaussian":[54],"kernels,":[55],"sharply":[61],"localized":[62],"Fourier":[65],"domain":[66],"ripple-free":[68],"artifacts.":[69],"Here,":[70],"we":[71],"construct":[72],"2D":[73,143],"MaxFlat":[74,144],"kernels":[75],"image":[77,82],"directional":[78],"to":[80,151],"calculate":[81],"differentials":[83],"derivative":[86],"order,":[87],"level":[89],"steering":[91],"angle.":[92],"resulted":[94],"kernel":[95,145],"library":[96,121],"renders":[97],"new":[99],"solution":[100],"capable":[101],"delivering":[103],"discrete":[104],"approximation":[105],"gradients,":[107],"Hessian,":[108],"higher-order":[110],"tensors":[111],"numerous":[113],"applications.":[114],"We":[115],"tested":[116],"utility":[118],"this":[120],"three":[123],"different":[124],"imaging":[125],"applications":[126],"main":[128],"focus":[129],"unsharp":[132],"masking.":[133],"reported":[135],"results":[136],"highlight":[137],"high":[139],"efficiency":[140],"its":[147],"versatility":[148],"respect":[150],"robustness":[152],"parameter":[154],"control":[155],"accuracy.":[156]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}