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...

Descripción completa

Detalles Bibliográficos
Autores principales: Forsyth, D, Mundy, JL, Zisserman, A, Brown, CM
Formato: Conference item
Lenguaje:English
Publicado: Springer 1990
_version_ 1826317719046193152
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