{"id":"https://openalex.org/W2167182854","doi":"https://doi.org/10.1109/msp.2003.1215230","title":"Threshold modulation and stability in error diffusion","display_name":"Threshold modulation and stability in error diffusion","publication_year":2003,"publication_date":"2003-07-01","ids":{"openalex":"https://openalex.org/W2167182854","doi":"https://doi.org/10.1109/msp.2003.1215230","mag":"2167182854"},"language":"en","primary_location":{"id":"doi:10.1109/msp.2003.1215230","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2003.1215230","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"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 Signal Processing Magazine","raw_type":"journal-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/A5077810135","display_name":"Reiner Eschbach","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"R. Eschbach","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032649501","display_name":"Zhigang Fan","orcid":"https://orcid.org/0000-0002-4628-1915"},"institutions":[{"id":"https://openalex.org/I4210132870","display_name":"Xerox (United States)","ror":"https://ror.org/03jwzwq24","country_code":"US","type":"company","lineage":["https://openalex.org/I4210132870"]},{"id":"https://openalex.org/I33976269","display_name":"Xerox (France)","ror":"https://ror.org/033q0mv79","country_code":"FR","type":"company","lineage":["https://openalex.org/I33976269","https://openalex.org/I4210132870"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Zhigang Fan","raw_affiliation_strings":["Xerox Corporate Research and Technology"],"affiliations":[{"raw_affiliation_string":"Xerox Corporate Research and Technology","institution_ids":["https://openalex.org/I33976269","https://openalex.org/I4210132870"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111854641","display_name":"Keith T. Knox","orcid":null},"institutions":[{"id":"https://openalex.org/I1295339012","display_name":"Boeing (United States)","ror":"https://ror.org/04sm5zn07","country_code":"US","type":"company","lineage":["https://openalex.org/I1295339012"]},{"id":"https://openalex.org/I1280414376","display_name":"United States Air Force Research Laboratory","ror":"https://ror.org/02e2egq70","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280414376","https://openalex.org/I1330347796","https://openalex.org/I4210102105","https://openalex.org/I4389425425"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"K.T. Knox","raw_affiliation_strings":["Air Force Research Laboratory, Boeing LTS, Hawaii"],"affiliations":[{"raw_affiliation_string":"Air Force Research Laboratory, Boeing LTS, Hawaii","institution_ids":["https://openalex.org/I1280414376","https://openalex.org/I1295339012"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029118169","display_name":"Gabriel G. Marcu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"G. Marcu","raw_affiliation_strings":["ColorSync Group, Apple Computer, Inc"],"affiliations":[{"raw_affiliation_string":"ColorSync Group, Apple Computer, Inc","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5077810135"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.755,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.72198723,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":"4","first_page":"39","last_page":"50"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11666","display_name":"Color Science and Applications","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11666","display_name":"Color Science and Applications","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11019","display_name":"Image Enhancement Techniques","score":0.992900013923645,"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/stability","display_name":"Stability (learning theory)","score":0.750351071357727},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7414076924324036},{"id":"https://openalex.org/keywords/modulation","display_name":"Modulation (music)","score":0.716464102268219},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.6441195011138916},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5655766725540161},{"id":"https://openalex.org/keywords/error-detection-and-correction","display_name":"Error detection and correction","score":0.5388026237487793},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.43381959199905396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19193482398986816},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.14550265669822693},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.07158133387565613},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0693717896938324}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.750351071357727},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7414076924324036},{"id":"https://openalex.org/C123079801","wikidata":"https://www.wikidata.org/wiki/Q750240","display_name":"Modulation (music)","level":2,"score":0.716464102268219},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.6441195011138916},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5655766725540161},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.5388026237487793},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.43381959199905396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19193482398986816},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.14550265669822693},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.07158133387565613},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0693717896938324},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/msp.2003.1215230","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2003.1215230","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"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 Signal Processing Magazine","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W2120994","https://openalex.org/W67088060","https://openalex.org/W135707529","https://openalex.org/W1483769964","https://openalex.org/W1484761964","https://openalex.org/W1527441237","https://openalex.org/W1601698742","https://openalex.org/W1603083770","https://openalex.org/W1840364912","https://openalex.org/W1912920681","https://openalex.org/W1966810924","https://openalex.org/W1970409525","https://openalex.org/W1971738720","https://openalex.org/W1973980205","https://openalex.org/W1975337949","https://openalex.org/W1976613062","https://openalex.org/W1986791901","https://openalex.org/W1991794713","https://openalex.org/W1998519878","https://openalex.org/W2006483120","https://openalex.org/W2012148743","https://openalex.org/W2016339060","https://openalex.org/W2032947781","https://openalex.org/W2038796357","https://openalex.org/W2043181831","https://openalex.org/W2052015971","https://openalex.org/W2052199407","https://openalex.org/W2053717006","https://openalex.org/W2056031681","https://openalex.org/W2056696251","https://openalex.org/W2064505555","https://openalex.org/W2067720199","https://openalex.org/W2075383542","https://openalex.org/W2079029755","https://openalex.org/W2083188656","https://openalex.org/W2088808916","https://openalex.org/W2100205120","https://openalex.org/W2108826114","https://openalex.org/W2111665311","https://openalex.org/W2121401617","https://openalex.org/W2134442116","https://openalex.org/W2137529530","https://openalex.org/W2154249007","https://openalex.org/W2155989478","https://openalex.org/W2158474074","https://openalex.org/W2160624871","https://openalex.org/W2169057201","https://openalex.org/W2197680205","https://openalex.org/W2225997039","https://openalex.org/W2256533540","https://openalex.org/W2262710141","https://openalex.org/W2270471329","https://openalex.org/W2297838093","https://openalex.org/W2415468032","https://openalex.org/W2487933172","https://openalex.org/W4285719527","https://openalex.org/W6602755918"],"related_works":["https://openalex.org/W2386796262","https://openalex.org/W3177740930","https://openalex.org/W2377071794","https://openalex.org/W1484549928","https://openalex.org/W1974805659","https://openalex.org/W2811388477","https://openalex.org/W2380243770","https://openalex.org/W2377495875","https://openalex.org/W2390973415","https://openalex.org/W2074837817"],"abstract_inverted_index":{"Many":[0,62],"modifications":[1,64],"to":[2,8,13,17,21,56,71,78,135],"error":[3,45,139],"diffusion":[4],"have":[5,33,65,96],"been":[6,34,66],"proposed":[7,98],"improve":[9,57,79],"the":[10,30,60,69,80,89,93,102,110,138],"algorithm":[11,81],"and":[12,20,44,58,87,131],"extend":[14,59],"its":[15],"application":[16],"print":[18],"media":[19],"color.":[22],"In":[23],"this":[24,125],"article,":[25],"we":[26],"describe":[27],"some":[28],"of":[29,39,48,85,92],"lessons":[31],"that":[32],"learned":[35],"in":[36,53,124,137],"two":[37],"areas":[38,50],"error-diffusion":[40],"research:":[41],"threshold":[42],"modulation":[43],"stability.":[46],"Both":[47],"these":[49,73,129],"are":[51,112,118],"important":[52],"understanding":[54],"how":[55],"algorithm.":[61],"suggested":[63],"made":[67],"over":[68],"years":[70],"eliminate":[72],"unwanted":[74],"textures.":[75],"One":[76],"method":[77],"involves":[82],"different":[83],"ways":[84],"calculating":[86],"distributing":[88],"errors.":[90,103],"Some":[91],"modified":[94],"algorithms":[95],"even":[97],"amplifying":[99],"or":[100,114],"suppressing":[101],"Strange":[104],"effects":[105],"can":[106],"occur,":[107],"however,":[108],"when":[109],"errors":[111],"amplified":[113],"if":[115],"negative":[116],"components":[117],"introduced.":[119],"The":[120],"stability":[121],"analysis":[122],"presented":[123],"article":[126],"will":[127],"illustrate":[128],"instabilities":[130],"explain":[132],"their":[133],"relationship":[134],"changes":[136],"distribution.":[140]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}