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Object-Image Correspondence for Algebraic Curves under Projections

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dc.contributor.author Burdis, J.M.
dc.contributor.author Kogan, I.A.
dc.contributor.author Hong, H.
dc.date.accessioned 2019-02-19T19:01:58Z
dc.date.available 2019-02-19T19:01:58Z
dc.date.issued 2013
dc.identifier.citation Object-Image Correspondence for Algebraic Curves under Projections / J.M. Burdis, I.A. Koga, H. Hong // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 33 назв. — англ. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 14H50; 14Q05; 14L24; 53A55; 68T45
dc.identifier.other DOI: http://dx.doi.org/10.3842/SIGMA.2013.023
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/149227
dc.description.abstract We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. The motivation comes from the problem of establishing a correspondence between an object and an image, taken by a camera with unknown position and parameters. A straightforward approach to this problem consists of setting up a system of conditions on the projection parameters and then checking whether or not this system has a solution. The computational advantage of the algorithm presented here, in comparison to algorithms based on the straightforward approach, lies in a significant reduction of a number of real parameters that need to be eliminated in order to establish existence or non-existence of a projection that maps a given spatial curve to a given planar curve. Our algorithm is based on projection criteria that reduce the projection problem to a certain modification of the equivalence problem of planar curves under affine and projective transformations. To solve the latter problem we make an algebraic adaptation of signature construction that has been used to solve the equivalence problems for smooth curves. We introduce a notion of a classifying set of rational differential invariants and produce explicit formulas for such invariants for the actions of the projective and the affine groups on the plane. uk_UA
dc.description.sponsorship This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html. The project was supported in part by NSA grant H98230-11-1-0129. We would like to thank the referees for careful reading of our manuscript and valuable suggestions. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Object-Image Correspondence for Algebraic Curves under Projections uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA


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