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Statements

Subject Item
n2:RIV%2F68407700%3A21230%2F13%3A00212564%21RIV14-TA0-21230___
rdf:type
skos:Concept n8:Vysledek
rdfs:seeAlso
http://cmp.felk.cvut.cz/~kukelova/publications/Kukelova-Bujnak-Pajdla-3dv-2013.pdf
dcterms:description
In this paper we provide a new fast and stable algebraic solution to the problem of L2 triangulation from three views. We use Lagrange multipliers to formulate the search for the minima of the L2 objective function subject to equality constraints. Interestingly, we show that by relaxing the triangulation such that we do not require a single point in 3D, we get, after a linear correction, a solver that is faster, more stable and practically as accurate as the state-of-the-art L2-optimal algebraic solvers [24, 7, 8, 9]. In our formulation, we obtain a system of eight polynomial equations in eight unknowns, which we solve using the Groebner basis method. We get less (31) solutions than was the number (47-66) of solutions obtained in [24, 7, 8, 9] and our solver is more robust than [8, 9] w.r.t. critical configurations. We evaluate the precision and speed of our solver on both synthetic and real datasets. In this paper we provide a new fast and stable algebraic solution to the problem of L2 triangulation from three views. We use Lagrange multipliers to formulate the search for the minima of the L2 objective function subject to equality constraints. Interestingly, we show that by relaxing the triangulation such that we do not require a single point in 3D, we get, after a linear correction, a solver that is faster, more stable and practically as accurate as the state-of-the-art L2-optimal algebraic solvers [24, 7, 8, 9]. In our formulation, we obtain a system of eight polynomial equations in eight unknowns, which we solve using the Groebner basis method. We get less (31) solutions than was the number (47-66) of solutions obtained in [24, 7, 8, 9] and our solver is more robust than [8, 9] w.r.t. critical configurations. We evaluate the precision and speed of our solver on both synthetic and real datasets.
dcterms:title
Fast and Stable Algebraic Solution to L2 Three-View Triangulation Fast and Stable Algebraic Solution to L2 Three-View Triangulation
skos:prefLabel
Fast and Stable Algebraic Solution to L2 Three-View Triangulation Fast and Stable Algebraic Solution to L2 Three-View Triangulation
skos:notation
RIV/68407700:21230/13:00212564!RIV14-TA0-21230___
n8:predkladatel
n9:orjk%3A21230
n3:aktivita
n4:P
n3:aktivity
P(TA02011275)
n3:dodaniDat
n5:2014
n3:domaciTvurceVysledku
Kúkelová, Zuzana n18:6245269
n3:druhVysledku
n12:D
n3:duvernostUdaju
n22:S
n3:entitaPredkladatele
n14:predkladatel
n3:idSjednocenehoVysledku
74700
n3:idVysledku
RIV/68407700:21230/13:00212564
n3:jazykVysledku
n15:eng
n3:klicovaSlova
triangulation; Groebner basis; L2 three-view triangulation
n3:klicoveSlovo
n10:Groebner%20basis n10:L2%20three-view%20triangulation n10:triangulation
n3:kontrolniKodProRIV
[EDC4F047CC9D]
n3:mistoKonaniAkce
Seattle
n3:mistoVydani
Los Alamitos
n3:nazevZdroje
3DV 2013 - International Conference on 3D Vision
n3:obor
n7:JD
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
3
n3:projekt
n19:TA02011275
n3:rokUplatneniVysledku
n5:2013
n3:tvurceVysledku
Pajdla, Tomáš Bujňák, M. Kúkelová, Zuzana
n3:typAkce
n11:WRD
n3:zahajeniAkce
2013-06-29+02:00
s:numberOfPages
8
n23:doi
10.1109/3DV.2013.50
n17:hasPublisher
IEEE Computer Society Press
n20:isbn
978-0-7695-5067-1
n24:organizacniJednotka
21230