Logical/linear operators for image curves
We propose a language for designing image measurement operators suitable for early vision. We refer to them as logical/linear (L/L) operators, since they unify aspects of linear operator theory and Boolean logic. A family of these operators appropriate for measuring the low-order differential struct...
Saved in:
| Published in: | IEEE transactions on pattern analysis and machine intelligence Vol. 17; no. 10; pp. 982 - 996 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
IEEE
01.10.1995
|
| Subjects: | |
| ISSN: | 0162-8828 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | We propose a language for designing image measurement operators suitable for early vision. We refer to them as logical/linear (L/L) operators, since they unify aspects of linear operator theory and Boolean logic. A family of these operators appropriate for measuring the low-order differential structure of image curves is developed. These L/L operators are derived by decomposing a linear model into logical components to ensure that certain structural preconditions for the existence of an image curve are upheld. Tangential conditions guarantee continuity, while normal conditions select and categorize contrast profiles. The resulting operators allow for coarse measurement of curvilinear differential structure (orientation and curvature) while successfully segregating edge-and line-like features. By thus reducing the incidence of false-positive responses, these operators are a substantial improvement over (thresholded) linear operators which attempt to resolve the same class of features.< > |
|---|---|
| AbstractList | We propose a language for designing image measurement operators suitable for early vision. We refer to them as logical/linear (L/L) operators, since they unify aspects of linear operator theory and Boolean logic. A family of these operators appropriate for measuring the low-order differential structure of image curves is developed. These L/L operators are derived by decomposing a linear model into logical components to ensure that certain structural preconditions for the existence of an image curve are upheld. Tangential conditions guarantee continuity, while normal conditions select and categorize contrast profiles. The resulting operators allow for coarse measurement of curvilinear differential structure (orientation and curvature) while successfully segregating edge-and line-like features. By thus reducing the incidence of false-positive responses, these operators are a substantial improvement over (thresholded) linear operators which attempt to resolve the same class of features.< > We propose a language for designing image measurement operators suitable for early vision. We refer to them as logical/linear (L/L) operators, since they unify aspects of linear operator theory and Boolean logic. A family of these operators appropriate for measuring the low-order differential structure of image curves is developed. These L/L operators are derived by decomposing a linear model into logical components to ensure that certain structural preconditions for the existence of an image curve are upheld. Tangential conditions guarantee continuity, while normal conditions select and categorize contrast profiles. The resulting operators allow for coarse measurement of curvilinear differential structure (orientation and curvature) while successfully segregating edge-and line-like features. By thus reducing the incidence of false-positive responses, these operators are a substantial improvement over (thresholded) linear operators which attempt to resolve the same class of features |
| Author | Zucker, S.W. Iverson, L.A. |
| Author_xml | – sequence: 1 givenname: L.A. surname: Iverson fullname: Iverson, L.A. organization: Artificial Intelligence Center, SRI Int., Menlo Park, CA, USA – sequence: 2 givenname: S.W. surname: Zucker fullname: Zucker, S.W. |
| BookMark | eNptkL1PwzAUxD0UibYwsDJlQuqQxt9ORlRBQYrEArPlOM-VURoXO0HivycoFQNiOj3d705Pt0KLPvSA0A3BW0JwVTC-5ZILSRdoiYmkeVnS8hKtUnrHmHCB2RJt6nDw1nRF53swMQsniGYIMWUuxMwfzQEyO8ZPSFfowpkuwfVZ1-jt8eF195TXL_vn3X2dW6rUkDMraSscNwSo4pY3LVGOSqgULlVLXWmgkqRVQlSENq2QFXGibRoBaroqy9bobu49xfAxQhr00ScLXWd6CGPStGQYM6EmcDODNoaUIjh9itPD8UsTrH8G0IzreYCJLf6w1g9m8KEfovHdv4nbOeEB4Lf5bH4D2CxoBg |
| CODEN | ITPIDJ |
| CitedBy_id | crossref_primary_10_1134_S1054661814030109 crossref_primary_10_1109_TSMCB_2002_806486 crossref_primary_10_1109_34_659930 crossref_primary_10_1109_TPAMI_2004_50 crossref_primary_10_1109_TSMCA_2003_817057 crossref_primary_10_1016_j_cviu_2011_03_010 crossref_primary_10_1145_882262_882354 crossref_primary_10_1016_j_jphysparis_2003_09_003 crossref_primary_10_1016_j_jphysparis_2003_09_004 crossref_primary_10_1038_s41598_021_97879_z crossref_primary_10_1109_TIP_2004_828404 crossref_primary_10_3758_s13421_023_01478_4 crossref_primary_10_1068_p5265 crossref_primary_10_1109_3477_938262 crossref_primary_10_1023_A_1007905813513 crossref_primary_10_1080_05704928_2019_1580715 crossref_primary_10_1016_j_jphysparis_2009_05_005 crossref_primary_10_1109_83_887971 crossref_primary_10_1023_A_1011189501276 crossref_primary_10_1016_j_engappai_2022_105629 crossref_primary_10_1016_j_imavis_2006_08_007 crossref_primary_10_1109_TIP_2019_2924799 crossref_primary_10_1134_S1064562411060196 crossref_primary_10_1023_A_1008181109865 crossref_primary_10_1049_ip_vis_20030805 crossref_primary_10_1177_20416695251338721 crossref_primary_10_1109_34_689301 crossref_primary_10_1016_j_neuroimage_2007_01_014 crossref_primary_10_1109_34_977560 crossref_primary_10_1006_cviu_2001_0931 crossref_primary_10_1109_TPAMI_2005_84 crossref_primary_10_1162_neco_2006_18_4_871 crossref_primary_10_1023_A_1008183703117 crossref_primary_10_1109_TITB_2008_2007201 crossref_primary_10_1016_S1361_8415_02_00065_8 crossref_primary_10_1007_s12297_013_0242_6 crossref_primary_10_1155_ASP_2006_76278 crossref_primary_10_1109_34_643893 crossref_primary_10_1007_s11263_006_6853_9 crossref_primary_10_1109_TPAMI_2003_1190567 crossref_primary_10_1109_TPAMI_2003_1190568 crossref_primary_10_1371_journal_pone_0260266 crossref_primary_10_1109_TIP_2003_814250 crossref_primary_10_4028_www_scientific_net_MSF_992_907 crossref_primary_10_1016_j_jvcir_2012_05_004 crossref_primary_10_1023_A_1011273631202 crossref_primary_10_1515_JISYS_2008_17_1_3_229 crossref_primary_10_1023_A_1008144113494 crossref_primary_10_1023_A_1024454423670 crossref_primary_10_1134_S1054661821030226 crossref_primary_10_1016_j_jneumeth_2006_07_028 crossref_primary_10_1016_S0262_8856_97_00085_1 crossref_primary_10_1006_gmip_1997_0438 crossref_primary_10_1109_TIP_2007_894288 crossref_primary_10_1162_08997660360675017 crossref_primary_10_1109_TPAMI_2023_3333352 crossref_primary_10_1016_j_imavis_2006_07_022 crossref_primary_10_1088_2058_8585_ac1c5c crossref_primary_10_1186_1687_6180_2011_28 crossref_primary_10_1006_cviu_1999_0795 crossref_primary_10_1016_S0031_3203_99_00070_9 crossref_primary_10_1145_1409060_1409110 crossref_primary_10_1016_j_neucom_2012_09_027 crossref_primary_10_1016_S0042_6989_98_00085_6 crossref_primary_10_1051_itmconf_20171001002 |
| Cites_doi | 10.1007/BF00365595 10.1145/321623.321635 10.1113/jphysiol.1978.sp012488 10.1007/978-3-662-01492-9 10.1109/34.93808 10.1007/BF00203452 10.1016/0004-3702(77)90020-0 10.1007/978-1-4612-5282-5 10.1068/p110129 10.1162/neco.1989.1.1.68 10.1016/0042-6989(83)90046-9 10.1098/rspb.1988.0073 10.1016/0042-6989(84)90110-X 10.3758/BF03201436 10.1007/BF00318371 10.1109/TPAMI.1984.4767475 10.1109/TPAMI.1987.4767918 10.1109/CCV.1988.590037 10.1146/annurev.ne.08.030185.002555 10.1007/BF00123164 10.1007/BF00364136 10.1016/0262-8856(92)90011-Q 10.1109/TPAMI.1986.4767851 10.1007/BF00332913 10.1109/TSMC.1976.5409183 10.1098/rspb.1980.0020 10.1152/jn.1987.58.6.1233 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| DOI | 10.1109/34.464562 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science |
| EndPage | 996 |
| ExternalDocumentID | 10_1109_34_464562 464562 |
| GroupedDBID | --- -DZ -~X .DC 0R~ 29I 4.4 53G 5GY 5VS 6IK 97E 9M8 AAJGR AARMG AASAJ AAWTH ABAZT ABFSI ABQJQ ABVLG ACGFO ACGFS ACIWK ACNCT ADRHT AENEX AETEA AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 E.L EBS EJD F5P FA8 HZ~ H~9 IBMZZ ICLAB IEDLZ IFIPE IFJZH IPLJI JAVBF LAI M43 MS~ O9- OCL P2P PQQKQ RIA RIE RNI RNS RXW RZB TAE TN5 UHB VH1 XJT ~02 AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c277t-3c62d5f4a1e274c4bd17f26e97087d2f8ae961d755912bd5691f5dbb5e7bd59c3 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 107 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=10_1109_34_464562&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0162-8828 |
| IngestDate | Sun Nov 09 10:43:26 EST 2025 Tue Nov 18 22:38:05 EST 2025 Sat Nov 29 05:15:49 EST 2025 Wed Aug 27 02:47:52 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 10 |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c277t-3c62d5f4a1e274c4bd17f26e97087d2f8ae961d755912bd5691f5dbb5e7bd59c3 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 28300357 |
| PQPubID | 23500 |
| PageCount | 15 |
| ParticipantIDs | crossref_primary_10_1109_34_464562 crossref_citationtrail_10_1109_34_464562 ieee_primary_464562 proquest_miscellaneous_28300357 |
| PublicationCentury | 1900 |
| PublicationDate | 1995-10-01 |
| PublicationDateYYYYMMDD | 1995-10-01 |
| PublicationDate_xml | – month: 10 year: 1995 text: 1995-10-01 day: 01 |
| PublicationDecade | 1990 |
| PublicationTitle | IEEE transactions on pattern analysis and machine intelligence |
| PublicationTitleAbbrev | TPAMI |
| PublicationYear | 1995 |
| Publisher | IEEE |
| Publisher_xml | – name: IEEE |
| References | BIBP098222 BIBP098223 BIBP098224 rumelhart (BIBP098218) 1986; 1 BIBP098225 BIBP098227 BIBP098220 BIBP098221 marr (BIBP09829) 1982 herkovitz (BIBP09825) 1970 iverson (BIBP098228) 1993 BIBP09828 BIBP098219 perona (BIBP098234) 1991 BIBP098211 BIBP098233 BIBP09821 BIBP098213 BIBP098235 BIBP09822 BIBP098214 BIBP098236 BIBP098215 BIBP09824 BIBP098216 BIBP09826 koenderink (BIBP098212) 1984 duda (BIBP098229) 1973 BIBP09827 BIBP098230 BIBP098231 BIBP098232 BIBP098210 birkhoff (BIBP098217) 1977 young (BIBP098226) 1985 jones (BIBP09823) 1987; 58 |
| References_xml | – ident: BIBP098210 doi: 10.1007/BF00365595 – year: 1973 ident: BIBP098229 publication-title: Pattern Classification and Scene Analysis – ident: BIBP09821 doi: 10.1145/321623.321635 – ident: BIBP098213 doi: 10.1113/jphysiol.1978.sp012488 – ident: BIBP098216 doi: 10.1007/978-3-662-01492-9 – volume: 1 start-page: 318 year: 1986 ident: BIBP098218 article-title: learning internal representations by error propagation publication-title: ?Learning internal representations by error propagation ? – ident: BIBP098233 doi: 10.1109/34.93808 – ident: BIBP098225 doi: 10.1007/BF00203452 – ident: BIBP09827 doi: 10.1016/0004-3702(77)90020-0 – ident: BIBP098220 doi: 10.1007/978-1-4612-5282-5 – ident: BIBP098211 doi: 10.1068/p110129 – ident: BIBP098232 doi: 10.1162/neco.1989.1.1.68 – ident: BIBP098221 doi: 10.1016/0042-6989(83)90046-9 – ident: BIBP098236 doi: 10.1098/rspb.1988.0073 – year: 1993 ident: BIBP098228 article-title: toward discrete geometric models for early vision publication-title: ?Toward discrete geometric models for early vision ? – ident: BIBP098214 doi: 10.1016/0042-6989(84)90110-X – ident: BIBP098231 doi: 10.3758/BF03201436 – year: 1982 ident: BIBP09829 publication-title: Vision – start-page: 123 year: 1984 ident: BIBP098212 article-title: the internal representation of solid shape and visual exploration publication-title: Sensory Experience Adaptation and Perception – ident: BIBP098219 doi: 10.1007/BF00318371 – ident: BIBP098222 doi: 10.1109/TPAMI.1984.4767475 – year: 1985 ident: BIBP098226 article-title: the gaussian derivative theory of spatial vision: analysis of cortical receptive field line-weighting profiles – ident: BIBP09828 doi: 10.1109/TPAMI.1987.4767918 – ident: BIBP09824 doi: 10.1109/CCV.1988.590037 – start-page: 52 year: 1991 ident: BIBP098234 article-title: detecting and localizing edges composed of steps, peaks, and rooks publication-title: Proc Third Int?l Conf Computer Vision – ident: BIBP098215 doi: 10.1146/annurev.ne.08.030185.002555 – ident: BIBP09826 doi: 10.1007/BF00123164 – ident: BIBP098224 doi: 10.1007/BF00364136 – ident: BIBP098235 doi: 10.1016/0262-8856(92)90011-Q – ident: BIBP09822 doi: 10.1109/TPAMI.1986.4767851 – ident: BIBP098230 doi: 10.1007/BF00332913 – ident: BIBP098227 doi: 10.1109/TSMC.1976.5409183 – year: 1970 ident: BIBP09825 article-title: on boundary detection – ident: BIBP098223 doi: 10.1098/rspb.1980.0020 – year: 1977 ident: BIBP098217 publication-title: A Survey of Modern Algebra Fourth Edition – volume: 58 start-page: 1,233 year: 1987 ident: BIBP09823 article-title: an evaluation of the two-dimentional gabor filter model of simple receptive fields in cat striate cortex publication-title: J Neurophysiology doi: 10.1152/jn.1987.58.6.1233 |
| SSID | ssj0014503 |
| Score | 1.8477452 |
| Snippet | We propose a language for designing image measurement operators suitable for early vision. We refer to them as logical/linear (L/L) operators, since they unify... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 982 |
| SubjectTerms | Biological information theory Boolean functions Computer vision Detectors Ear Feature extraction Gaussian noise Image edge detection Integrated circuit noise Machine vision |
| Title | Logical/linear operators for image curves |
| URI | https://ieeexplore.ieee.org/document/464562 https://www.proquest.com/docview/28300357 |
| Volume | 17 |
| WOSCitedRecordID | wos10_1109_34_464562&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) issn: 0162-8828 databaseCode: RIE dateStart: 19790101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://ieeexplore.ieee.org/ omitProxy: false ssIdentifier: ssj0014503 providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwELagYoCBQgFRnhZigCElfiQXjwhRMaCKAaRukWM7UiVIqqbp78d2kgpEF7Y4OkvR-XyP3N13CN0mOrZ2jYpA5iQJuORWDwqQgWEOjYz6_k8_bAImk2Q6FW8tzrbvhTHG-OIzM3KPPpevS1W7X2UPLgvn9O02QNy0aq0TBjzyQ5CtA2MvuI0iWhAhEooHxkfNxl-mx89S-aOAvVUZ9__1PQdov3Ue8WNz2odoyxQD1O8GM-D2ng7Q3g-UwSN0_9qoN1fjb-Ual3Pjc-sVtg4rnn1ZjYJVvViZ6hh9jJ_fn16CdkJCoCjAMmAqpjrKuSTGRpeKZ5pATmMjIExA0zyRRsREgw0bCM10FAuSRzrLIgN2JRQ7Qb2iLMwpwhBqTbROeEQYpzTLCFNCC6ASpJCKDdFdx7xUtfDhborFZ-rDiFCkjKcNQ4boZk06bzAzNhENHEPXBN3b6-5AUivnLnkhC1PWVeqAykIWwdnGfedo1_ea-yq7C9RbLmpziXbUajmrFldeVL4B4WK7Tg |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3NS8MwFA8yBfXgdCrOrxXxoIduzVfTHEUcE-fwMGG3kiYpDLQd67q_3yRth6IXb015gfLy8j763vs9AG4jFRq7hrgvUhj5RBCjBzkTvsYWjQy5_k83bIJNJtFsxt9qnG3XC6O1dsVnum8fXS5f5bK0v8oGNgtn9e02JQQFVbPWJmVAqBuDbFwYc8VNHFHDCMGADzDpV1t_GB83TeWXCnZ2Zdj-1xcdgoPaffQeqvM-Als664B2M5rBq29qB-x_wxk8BvfjSsHZKn8j2V6-0C67XnjGZfXmn0aneLJcrnVxAt6HT9PHkV_PSPAlYmzlYxkiRVMioDbxpSSJgixFoeYsiJhCaSQ0D6FiJnCAKFE05DClKkmoZmbFJT4FrSzP9BnwWKAUVCoiFGKCUJJALLniDAkmuJC4C-4a5sWyBhC3cyw-YhdIBDzGJK4Y0gU3G9JFhZrxF1HHMnRD0LztNQcSG0m36QuR6bwsYgtVFmDKzv_c1wO7o-nrOB4_T14uwJ7rPHc1d5egtVqW-grsyPVqXiyvndh8AcpZvpU |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Logical%2Flinear+operators+for+image+curves&rft.jtitle=IEEE+transactions+on+pattern+analysis+and+machine+intelligence&rft.au=Iverson%2C+L.A.&rft.au=Zucker%2C+S.W.&rft.date=1995-10-01&rft.issn=0162-8828&rft.volume=17&rft.issue=10&rft.spage=982&rft.epage=996&rft_id=info:doi/10.1109%2F34.464562&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_34_464562 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0162-8828&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0162-8828&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0162-8828&client=summon |