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: <br> The curve chosen to represent a projected set of points is the projection of the curve chosen to...
| Main Authors: | , , , |
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| Format: | Conference item |
| Language: | English |
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Springer
1990
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| _version_ | 1826317719046193152 |
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| author | Forsyth, D Mundy, JL Zisserman, A Brown, CM |
| author_facet | Forsyth, D Mundy, JL Zisserman, A Brown, CM |
| author_sort | Forsyth, D |
| collection | OXFORD |
| 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:
<br>
The curve chosen to represent a projected set of points is the projection of the curve chosen to represent the original set.
<br>
We achieve this by using algebraic invariants of the polynomial in the fitting process. We demonstrate that our procedure works for plane conic curves. We show that for higher order plane curves, or for aggregates of plane conics, 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. |
| first_indexed | 2025-03-11T16:58:22Z |
| format | Conference item |
| id | oxford-uuid:9e87dc2e-e95f-481c-bad5-2bfb547e47b6 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-03-11T16:58:22Z |
| publishDate | 1990 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:9e87dc2e-e95f-481c-bad5-2bfb547e47b62025-02-28T15:10:04ZProjectively invariant representations using implicit algebraic curvesConference itemhttp://purl.org/coar/resource_type/c_5794uuid:9e87dc2e-e95f-481c-bad5-2bfb547e47b6EnglishSymplectic ElementsSpringer1990Forsyth, DMundy, JLZisserman, ABrown, CMWe 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: <br> The curve chosen to represent a projected set of points is the projection of the curve chosen to represent the original set. <br> We achieve this by using algebraic invariants of the polynomial in the fitting process. We demonstrate that our procedure works for plane conic curves. We show that for higher order plane curves, or for aggregates of plane conics, 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. |
| spellingShingle | Forsyth, D Mundy, JL Zisserman, A Brown, CM Projectively invariant representations using implicit algebraic curves |
| title | Projectively invariant representations using implicit algebraic curves |
| title_full | Projectively invariant representations using implicit algebraic curves |
| title_fullStr | Projectively invariant representations using implicit algebraic curves |
| title_full_unstemmed | Projectively invariant representations using implicit algebraic curves |
| title_short | Projectively invariant representations using implicit algebraic curves |
| title_sort | projectively invariant representations using implicit algebraic curves |
| work_keys_str_mv | AT forsythd projectivelyinvariantrepresentationsusingimplicitalgebraiccurves AT mundyjl projectivelyinvariantrepresentationsusingimplicitalgebraiccurves AT zissermana projectivelyinvariantrepresentationsusingimplicitalgebraiccurves AT browncm projectivelyinvariantrepresentationsusingimplicitalgebraiccurves |