{"id":"https://openalex.org/W2067342900","doi":"https://doi.org/10.1137/090751694","title":"Higher-Order Feature-Preserving Geometric Regularization","display_name":"Higher-Order Feature-Preserving Geometric Regularization","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2067342900","doi":"https://doi.org/10.1137/090751694","mag":"2067342900"},"language":"en","primary_location":{"id":"doi:10.1137/090751694","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090751694","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","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/A5017960512","display_name":"Marc Droske","orcid":"https://orcid.org/0009-0009-7050-4929"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marc Droske","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090707978","display_name":"Andrea L. Bertozzi","orcid":"https://orcid.org/0000-0003-0396-7391"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrea Bertozzi","raw_affiliation_strings":["bertozzi@math.ucla.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"bertozzi@math.ucla.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.539,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.90304357,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"3","issue":"1","first_page":"21","last_page":"51"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9973999857902527,"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":0.9973999857902527,"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":0.9955999851226807,"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":0.9843999743461609,"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/affine-transformation","display_name":"Affine transformation","score":0.6756417155265808},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6371819972991943},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6268570423126221},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5937291383743286},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5563797950744629},{"id":"https://openalex.org/keywords/segmentation","display_name":"Segmentation","score":0.5471256971359253},{"id":"https://openalex.org/keywords/geometric-flow","display_name":"Geometric flow","score":0.5242531299591064},{"id":"https://openalex.org/keywords/total-variation-denoising","display_name":"Total variation denoising","score":0.5006279945373535},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.49819374084472656},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.47481071949005127},{"id":"https://openalex.org/keywords/scale-space","display_name":"Scale space","score":0.4105570912361145},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4001755714416504},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.3974820077419281},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3714527487754822},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3663811683654785},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.3057382106781006},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.260463684797287},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.2054993212223053},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19651809334754944}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6756417155265808},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6371819972991943},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6268570423126221},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5937291383743286},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5563797950744629},{"id":"https://openalex.org/C89600930","wikidata":"https://www.wikidata.org/wiki/Q1423946","display_name":"Segmentation","level":2,"score":0.5471256971359253},{"id":"https://openalex.org/C32209215","wikidata":"https://www.wikidata.org/wiki/Q5535483","display_name":"Geometric flow","level":3,"score":0.5242531299591064},{"id":"https://openalex.org/C207282899","wikidata":"https://www.wikidata.org/wiki/Q7828156","display_name":"Total variation denoising","level":3,"score":0.5006279945373535},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.49819374084472656},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.47481071949005127},{"id":"https://openalex.org/C99102927","wikidata":"https://www.wikidata.org/wiki/Q3058184","display_name":"Scale space","level":4,"score":0.4105570912361145},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4001755714416504},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3974820077419281},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3714527487754822},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3663811683654785},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.3057382106781006},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.260463684797287},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.2054993212223053},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19651809334754944},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/090751694","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090751694","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.157.4752","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.157.4752","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucla.edu/~bertozzi/papers/BeDr05.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.185.1986","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.185.1986","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucla.edu/%7Ebertozzi/papers/SIMMS10.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.329.4174","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.329.4174","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucla.edu/~bertozzi/papers/droske09.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7400000095367432,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W7928106","https://openalex.org/W69453383","https://openalex.org/W86744704","https://openalex.org/W88640100","https://openalex.org/W125738643","https://openalex.org/W1493744162","https://openalex.org/W1511227929","https://openalex.org/W1541134818","https://openalex.org/W1544177383","https://openalex.org/W1565628910","https://openalex.org/W1567423801","https://openalex.org/W1569587969","https://openalex.org/W1580269359","https://openalex.org/W1587541211","https://openalex.org/W1588445649","https://openalex.org/W1595201262","https://openalex.org/W1596247731","https://openalex.org/W1963537884","https://openalex.org/W1963799857","https://openalex.org/W1973628819","https://openalex.org/W1979254382","https://openalex.org/W1983053523","https://openalex.org/W1996724333","https://openalex.org/W2002428563","https://openalex.org/W2002826252","https://openalex.org/W2023292900","https://openalex.org/W2036957339","https://openalex.org/W2041695053","https://openalex.org/W2048427115","https://openalex.org/W2059162655","https://openalex.org/W2061871850","https://openalex.org/W2062396579","https://openalex.org/W2073039128","https://openalex.org/W2080385522","https://openalex.org/W2082621526","https://openalex.org/W2084002682","https://openalex.org/W2084115655","https://openalex.org/W2089485013","https://openalex.org/W2097924771","https://openalex.org/W2100400186","https://openalex.org/W2103559027","https://openalex.org/W2104095591","https://openalex.org/W2109011174","https://openalex.org/W2114487471","https://openalex.org/W2139440232","https://openalex.org/W2144133758","https://openalex.org/W2150134853","https://openalex.org/W2157650260","https://openalex.org/W2159475546","https://openalex.org/W2162463235","https://openalex.org/W2166714473","https://openalex.org/W2171542563","https://openalex.org/W2208153982","https://openalex.org/W2248576022","https://openalex.org/W2944437997","https://openalex.org/W3039357072","https://openalex.org/W3211330693","https://openalex.org/W4251427381"],"related_works":["https://openalex.org/W2517104666","https://openalex.org/W2005437358","https://openalex.org/W1669643531","https://openalex.org/W2039154422","https://openalex.org/W2008656436","https://openalex.org/W2182382398","https://openalex.org/W2122581818","https://openalex.org/W1511788990","https://openalex.org/W4375959489","https://openalex.org/W2093622097"],"abstract_inverted_index":{"Abstract.":[0],"We":[1,42],"introduce":[2],"two":[3],"fourth-order":[4],"regularization":[5,45],"methods":[6,17],"that":[7],"remove":[8],"geometric":[9,14,95],"noise":[10],"without":[11],"destroying":[12],"significant":[13],"features.":[15],"These":[16],"leverage":[18],"ideas":[19],"from":[20],"image":[21],"denoising":[22],"and":[23,51],"simplification":[24],"of":[25,56,65,70,94],"high":[26],"contrast":[27],"images":[28],"in":[29,59],"which":[30],"piecewise":[31],"affine":[32],"functions":[33],"are":[34],"preserved":[35],"up":[36],"to":[37,54],"infinitesimally":[38],"small":[39],"transition":[40],"zones.":[41],"combine":[43],"the":[44,68,71,83,89],"techniques":[46,81],"with":[47],"active":[48],"contour":[49],"models":[50,90],"apply":[52],"them":[53],"segmentation":[55],"polygonal":[57],"objects":[58],"aerial":[60],"images.":[61],"To":[62],"avoid":[63],"loss":[64],"features":[66],"during":[67],"computation":[69],"external":[72],"driving":[73],"forces":[74],"we":[75,87],"use":[76,88],"total-variation":[77],"based":[78],"inverse":[79],"scale-space":[80],"on":[82,97],"input":[84],"data.":[85],"Furthermore,":[86],"for":[91],"feature-preserving":[92],"removal":[93],"texture":[96],"surfaces.":[98],"1.":[99],"Introduction.":[100],"Geometric":[101]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}