Projectively invariant representations using implicit algebraic curves
We demonstrate that it is possible to compute polynomial representations of image curves which are unaffected by the projective frame in which the representation is computed. This means that: ‘The curve chosen to represent a projected set of points is the projection of the curve chosen to represent...
Gespeichert in:
| Veröffentlicht in: | Image and vision computing 1991, Vol.9 (2), p.130-136 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 136 |
|---|---|
| container_issue | 2 |
| container_start_page | 130 |
| container_title | Image and vision computing |
| container_volume | 9 |
| creator | Forsyth, David Mundy, Joseph L Zisserman, Andrew Brown, Christopher M |
| description | We demonstrate that it is possible to compute polynomial representations of image curves which are unaffected by the projective frame in which the representation is computed. This means that: ‘The curve chosen to represent a projected set of points is the projection of the curve chosen to represent the original set.’ We achieve this by using algebraic invariants of the polynomial in the fitting process. We demonstrate that the procedure works for plane conic curves. For higher order plane curves, or for aggregates of plane conies, algebraic invariants can yield powerful representations of shape that are unaffected by projection, and hence make good cues for model-based vision. Tests on synthetic and real data have yielded excellent results. |
| doi_str_mv | 10.1016/0262-8856(91)90023-I |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_25382456</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>026288569190023I</els_id><sourcerecordid>25382456</sourcerecordid><originalsourceid>FETCH-LOGICAL-c364t-2c222d2d7a93c12e8f958e4f19ec23dd31b300bea860911e514fd2001e7d41473</originalsourceid><addsrcrecordid>eNp9kE1LAzEQhoMoWKv_wMMeRPSwmq_NJhdBitVCQQ96DmkyW1K22TXZXei_d2ulR08Dw_O-wzwIXRP8QDARj5gKmktZiDtF7hXGlOWLEzQhshzXhMlTNDki5-gipQ3GuMSlmqD5R2w2YDs_QL3LfBhM9CZ0WYQ2QoLQmc43IWV98mGd-W1be-u7zNRrWEXjbWb7OEC6RGeVqRNc_c0p-pq_fM7e8uX762L2vMwtE7zLqaWUOupKo5glFGSlCgm8IgosZc4xsmIYr8BIgRUhUBBeOYoxgdJxwks2RbeH3jY23z2kTm99slDXJkDTJ00LJikvxAjyA2hjk1KESrfRb03caYL1XpreG9F7I1oR_StNL8bYzV-_SdbUVTTB-nTMciWkKPCIPR0wGH8dPESdrIdgwfk4ytSu8f_f-QH0vYD4</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>25382456</pqid></control><display><type>article</type><title>Projectively invariant representations using implicit algebraic curves</title><source>Elsevier ScienceDirect Journals Complete</source><creator>Forsyth, David ; Mundy, Joseph L ; Zisserman, Andrew ; Brown, Christopher M</creator><creatorcontrib>Forsyth, David ; Mundy, Joseph L ; Zisserman, Andrew ; Brown, Christopher M</creatorcontrib><description>We demonstrate that it is possible to compute polynomial representations of image curves which are unaffected by the projective frame in which the representation is computed. This means that: ‘The curve chosen to represent a projected set of points is the projection of the curve chosen to represent the original set.’ We achieve this by using algebraic invariants of the polynomial in the fitting process. We demonstrate that the procedure works for plane conic curves. For higher order plane curves, or for aggregates of plane conies, algebraic invariants can yield powerful representations of shape that are unaffected by projection, and hence make good cues for model-based vision. Tests on synthetic and real data have yielded excellent results.</description><identifier>ISSN: 0262-8856</identifier><identifier>EISSN: 1872-8138</identifier><identifier>DOI: 10.1016/0262-8856(91)90023-I</identifier><language>eng</language><publisher>Oxford: Elsevier B.V</publisher><subject>Applied sciences ; Computer aided design ; Computer science; control theory; systems ; curves ; Exact sciences and technology ; model matching ; polynomial representation ; projection ; Software</subject><ispartof>Image and vision computing, 1991, Vol.9 (2), p.130-136</ispartof><rights>1991</rights><rights>1992 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c364t-2c222d2d7a93c12e8f958e4f19ec23dd31b300bea860911e514fd2001e7d41473</citedby><cites>FETCH-LOGICAL-c364t-2c222d2d7a93c12e8f958e4f19ec23dd31b300bea860911e514fd2001e7d41473</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/0262-8856(91)90023-I$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,4024,27923,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=4968650$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Forsyth, David</creatorcontrib><creatorcontrib>Mundy, Joseph L</creatorcontrib><creatorcontrib>Zisserman, Andrew</creatorcontrib><creatorcontrib>Brown, Christopher M</creatorcontrib><title>Projectively invariant representations using implicit algebraic curves</title><title>Image and vision computing</title><description>We demonstrate that it is possible to compute polynomial representations of image curves which are unaffected by the projective frame in which the representation is computed. This means that: ‘The curve chosen to represent a projected set of points is the projection of the curve chosen to represent the original set.’ We achieve this by using algebraic invariants of the polynomial in the fitting process. We demonstrate that the procedure works for plane conic curves. For higher order plane curves, or for aggregates of plane conies, algebraic invariants can yield powerful representations of shape that are unaffected by projection, and hence make good cues for model-based vision. Tests on synthetic and real data have yielded excellent results.</description><subject>Applied sciences</subject><subject>Computer aided design</subject><subject>Computer science; control theory; systems</subject><subject>curves</subject><subject>Exact sciences and technology</subject><subject>model matching</subject><subject>polynomial representation</subject><subject>projection</subject><subject>Software</subject><issn>0262-8856</issn><issn>1872-8138</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1991</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKv_wMMeRPSwmq_NJhdBitVCQQ96DmkyW1K22TXZXei_d2ulR08Dw_O-wzwIXRP8QDARj5gKmktZiDtF7hXGlOWLEzQhshzXhMlTNDki5-gipQ3GuMSlmqD5R2w2YDs_QL3LfBhM9CZ0WYQ2QoLQmc43IWV98mGd-W1be-u7zNRrWEXjbWb7OEC6RGeVqRNc_c0p-pq_fM7e8uX762L2vMwtE7zLqaWUOupKo5glFGSlCgm8IgosZc4xsmIYr8BIgRUhUBBeOYoxgdJxwks2RbeH3jY23z2kTm99slDXJkDTJ00LJikvxAjyA2hjk1KESrfRb03caYL1XpreG9F7I1oR_StNL8bYzV-_SdbUVTTB-nTMciWkKPCIPR0wGH8dPESdrIdgwfk4ytSu8f_f-QH0vYD4</recordid><startdate>1991</startdate><enddate>1991</enddate><creator>Forsyth, David</creator><creator>Mundy, Joseph L</creator><creator>Zisserman, Andrew</creator><creator>Brown, Christopher M</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>1991</creationdate><title>Projectively invariant representations using implicit algebraic curves</title><author>Forsyth, David ; Mundy, Joseph L ; Zisserman, Andrew ; Brown, Christopher M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c364t-2c222d2d7a93c12e8f958e4f19ec23dd31b300bea860911e514fd2001e7d41473</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1991</creationdate><topic>Applied sciences</topic><topic>Computer aided design</topic><topic>Computer science; control theory; systems</topic><topic>curves</topic><topic>Exact sciences and technology</topic><topic>model matching</topic><topic>polynomial representation</topic><topic>projection</topic><topic>Software</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Forsyth, David</creatorcontrib><creatorcontrib>Mundy, Joseph L</creatorcontrib><creatorcontrib>Zisserman, Andrew</creatorcontrib><creatorcontrib>Brown, Christopher M</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Image and vision computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Forsyth, David</au><au>Mundy, Joseph L</au><au>Zisserman, Andrew</au><au>Brown, Christopher M</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Projectively invariant representations using implicit algebraic curves</atitle><jtitle>Image and vision computing</jtitle><date>1991</date><risdate>1991</risdate><volume>9</volume><issue>2</issue><spage>130</spage><epage>136</epage><pages>130-136</pages><issn>0262-8856</issn><eissn>1872-8138</eissn><abstract>We demonstrate that it is possible to compute polynomial representations of image curves which are unaffected by the projective frame in which the representation is computed. This means that: ‘The curve chosen to represent a projected set of points is the projection of the curve chosen to represent the original set.’ We achieve this by using algebraic invariants of the polynomial in the fitting process. We demonstrate that the procedure works for plane conic curves. For higher order plane curves, or for aggregates of plane conies, algebraic invariants can yield powerful representations of shape that are unaffected by projection, and hence make good cues for model-based vision. Tests on synthetic and real data have yielded excellent results.</abstract><cop>Oxford</cop><pub>Elsevier B.V</pub><doi>10.1016/0262-8856(91)90023-I</doi><tpages>7</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0262-8856 |
| ispartof | Image and vision computing, 1991, Vol.9 (2), p.130-136 |
| issn | 0262-8856 1872-8138 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_25382456 |
| source | Elsevier ScienceDirect Journals Complete |
| subjects | Applied sciences Computer aided design Computer science control theory systems curves Exact sciences and technology model matching polynomial representation projection Software |
| title | Projectively invariant representations using implicit algebraic curves |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T06%3A50%3A59IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Projectively%20invariant%20representations%20using%20implicit%20algebraic%20curves&rft.jtitle=Image%20and%20vision%20computing&rft.au=Forsyth,%20David&rft.date=1991&rft.volume=9&rft.issue=2&rft.spage=130&rft.epage=136&rft.pages=130-136&rft.issn=0262-8856&rft.eissn=1872-8138&rft_id=info:doi/10.1016/0262-8856(91)90023-I&rft_dat=%3Cproquest_cross%3E25382456%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=25382456&rft_id=info:pmid/&rft_els_id=026288569190023I&rfr_iscdi=true |