{"id":"https://openalex.org/W4361006869","doi":"https://doi.org/10.3390/sym15040803","title":"State-Aware High-Order Diffusion Method for Edge Detection in the Wavelet Domain","display_name":"State-Aware High-Order Diffusion Method for Edge Detection in the Wavelet Domain","publication_year":2023,"publication_date":"2023-03-25","ids":{"openalex":"https://openalex.org/W4361006869","doi":"https://doi.org/10.3390/sym15040803"},"language":"en","primary_location":{"id":"doi:10.3390/sym15040803","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040803","pdf_url":"https://www.mdpi.com/2073-8994/15/4/803/pdf?version=1679740535","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/4/803/pdf?version=1679740535","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048297311","display_name":"Chenhua Liu","orcid":"https://orcid.org/0000-0002-0336-9407"},"institutions":[{"id":"https://openalex.org/I46305995","display_name":"Taiyuan University of Science and Technology","ror":"https://ror.org/01wcbdc92","country_code":"CN","type":"education","lineage":["https://openalex.org/I46305995"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chenhua Liu","raw_affiliation_strings":["Institute of Digital Media and Communications, School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China"],"raw_orcid":"https://orcid.org/0000-0002-0336-9407","affiliations":[{"raw_affiliation_string":"Institute of Digital Media and Communications, School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China","institution_ids":["https://openalex.org/I46305995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003248833","display_name":"Anhong Wang","orcid":"https://orcid.org/0000-0001-5413-0490"},"institutions":[{"id":"https://openalex.org/I46305995","display_name":"Taiyuan University of Science and Technology","ror":"https://ror.org/01wcbdc92","country_code":"CN","type":"education","lineage":["https://openalex.org/I46305995"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Anhong Wang","raw_affiliation_strings":["Institute of Digital Media and Communications, School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Digital Media and Communications, School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China","institution_ids":["https://openalex.org/I46305995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003248833"],"corresponding_institution_ids":["https://openalex.org/I46305995"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0977,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.32233841,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"15","issue":"4","first_page":"803","last_page":"803"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","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/T10688","display_name":"Image and Signal Denoising Methods","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/T11659","display_name":"Advanced Image Fusion Techniques","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/T13114","display_name":"Image Processing Techniques and Applications","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/wavelet","display_name":"Wavelet","score":0.8877619504928589},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6056051850318909},{"id":"https://openalex.org/keywords/wavelet-packet-decomposition","display_name":"Wavelet packet decomposition","score":0.5985645055770874},{"id":"https://openalex.org/keywords/cascade-algorithm","display_name":"Cascade algorithm","score":0.5796579122543335},{"id":"https://openalex.org/keywords/stationary-wavelet-transform","display_name":"Stationary wavelet transform","score":0.5678301453590393},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.5256325602531433},{"id":"https://openalex.org/keywords/second-generation-wavelet-transform","display_name":"Second-generation wavelet transform","score":0.5147662162780762},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5094946026802063},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4914306402206421},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.48932260274887085},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.431427925825119},{"id":"https://openalex.org/keywords/lifting-scheme","display_name":"Lifting scheme","score":0.41781699657440186},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3468475937843323}],"concepts":[{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.8877619504928589},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6056051850318909},{"id":"https://openalex.org/C155777637","wikidata":"https://www.wikidata.org/wiki/Q2736187","display_name":"Wavelet packet decomposition","level":4,"score":0.5985645055770874},{"id":"https://openalex.org/C88829872","wikidata":"https://www.wikidata.org/wiki/Q5048176","display_name":"Cascade algorithm","level":5,"score":0.5796579122543335},{"id":"https://openalex.org/C73339587","wikidata":"https://www.wikidata.org/wiki/Q1375942","display_name":"Stationary wavelet transform","level":5,"score":0.5678301453590393},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.5256325602531433},{"id":"https://openalex.org/C111350171","wikidata":"https://www.wikidata.org/wiki/Q7443700","display_name":"Second-generation wavelet transform","level":5,"score":0.5147662162780762},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5094946026802063},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4914306402206421},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.48932260274887085},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.431427925825119},{"id":"https://openalex.org/C199550912","wikidata":"https://www.wikidata.org/wiki/Q3238415","display_name":"Lifting scheme","level":5,"score":0.41781699657440186},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3468475937843323}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15040803","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040803","pdf_url":"https://www.mdpi.com/2073-8994/15/4/803/pdf?version=1679740535","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:20b6279bf490475898f3aafdccce3ef2","is_oa":false,"landing_page_url":"https://doaj.org/article/20b6279bf490475898f3aafdccce3ef2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"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":"Symmetry, Vol 15, Iss 4, p 803 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/4/803/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15040803","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 15; Issue 4; Pages: 803","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15040803","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040803","pdf_url":"https://www.mdpi.com/2073-8994/15/4/803/pdf?version=1679740535","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4361006869.pdf"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W191129667","https://openalex.org/W1099223310","https://openalex.org/W1586417863","https://openalex.org/W1977472541","https://openalex.org/W1991319968","https://openalex.org/W2021535288","https://openalex.org/W2027712695","https://openalex.org/W2052809371","https://openalex.org/W2073863740","https://openalex.org/W2103559027","https://openalex.org/W2122287830","https://openalex.org/W2135036909","https://openalex.org/W2146842127","https://openalex.org/W2150134853","https://openalex.org/W2214394684","https://openalex.org/W2470437475","https://openalex.org/W2521133303","https://openalex.org/W2602725909","https://openalex.org/W2603909116","https://openalex.org/W2746459132","https://openalex.org/W2772548996","https://openalex.org/W2775347070","https://openalex.org/W2800722299","https://openalex.org/W2808776451","https://openalex.org/W2891946237","https://openalex.org/W2903018872","https://openalex.org/W2903387682","https://openalex.org/W2903914551","https://openalex.org/W2917736069","https://openalex.org/W2928275747","https://openalex.org/W2970918582","https://openalex.org/W2978362126","https://openalex.org/W3036995978","https://openalex.org/W3049135510","https://openalex.org/W3120800187","https://openalex.org/W3123461793","https://openalex.org/W3174025490","https://openalex.org/W3197788104","https://openalex.org/W4318822211"],"related_works":["https://openalex.org/W2085792030","https://openalex.org/W68308810","https://openalex.org/W2358271565","https://openalex.org/W2391053410","https://openalex.org/W1983773606","https://openalex.org/W2046633342","https://openalex.org/W2274421086","https://openalex.org/W2351059076","https://openalex.org/W2127536479","https://openalex.org/W2351270432"],"abstract_inverted_index":{"This":[0,146],"paper":[1,147,207],"addresses":[2],"how":[3],"to":[4,8,29,38,47,60,210],"use":[5],"high-order":[6,72],"diffusion":[7,141],"restore":[9],"the":[10,14,31,39,49,56,61,68,71,94,102,111,121,143,154,163,166,172,192,217],"wavelet":[11,15,32,50,64,78,97,106,117,126,132,167],"coefficients":[12,33,107,118,127],"in":[13,75,205,226],"domain.":[16],"To":[17,100],"avoid":[18],"image":[19,27,57,149,158,200,219],"distortion,":[20],"wavelets":[21],"with":[22,214],"symmetry":[23],"are":[24,160],"used":[25],"for":[26],"decomposition":[28],"obtain":[30,48,120,196],"of":[34,41,63,70,87,96,105,113,116,125,142,165,171,228],"each":[35],"sub-band.":[36],"Due":[37],"influence":[40],"noise,":[42],"it":[43],"is":[44,82,91,134,175],"particularly":[45],"important":[46],"coefficients,":[51],"which":[52],"can":[53,195],"accurately":[54],"reflect":[55],"information.":[58],"According":[59],"characteristics":[62],"threshold":[65,98],"shrinkage":[66],"and":[67,119,157,185,198,231],"advantages":[69,225],"variational":[73],"method":[74,90],"denoising,":[76],"a":[77,138],"coefficient":[79,133],"restoration":[80],"scheme":[81,223],"proposed.":[83],"The":[84,130,169,187,202],"theoretical":[85],"basis":[86],"our":[88],"proposed":[89,173,193],"established":[92],"through":[93],"analysis":[95],"theory.":[99],"keep":[101],"original":[103],"structure":[104],"unchanged,":[108],"we":[109],"introduce":[110],"concept":[112],"state":[114,123,144],"quantity":[115,124],"corresponding":[122],"using":[128],"normalization.":[129],"denoising":[131,181],"obtained":[135,220],"by":[136,162,221],"performing":[137],"fourth-order":[139],"anisotropic":[140],"quantities.":[145],"takes":[148],"edge":[150,183,232],"feature":[151],"extraction":[152],"as":[153],"experimental":[155,188],"content":[156],"edges":[159,218],"detected":[161],"module":[164],"coefficients.":[168],"effectiveness":[170],"algorithm":[174,194,203],"objectively":[176],"verified":[177],"from":[178],"three":[179],"aspects:":[180],"effect,":[182],"continuity,":[184],"accuracy.":[186],"results":[189],"show":[190],"that":[191],"continuous":[197],"precise":[199],"edges.":[201],"presented":[204],"this":[206,222],"also":[208],"applies":[209],"texture":[211],"images.":[212],"Compared":[213],"other":[215],"algorithms,":[216],"shows":[224],"terms":[227],"noise":[229],"removal":[230],"protection.":[233]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
