About: Fast and Stable Algebraic Solution to L2 Three-View Triangulation

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://cmp.felk.cvut.cz/~kukelova/publications/Kukelova-Bujnak-Pajdla-3dv-2013.pdf
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. (en)
Title	Fast and Stable Algebraic Solution to L2 Three-View Triangulation Fast and Stable Algebraic Solution to L2 Three-View Triangulation (en)
skos:prefLabel	Fast and Stable Algebraic Solution to L2 Three-View Triangulation Fast and Stable Algebraic Solution to L2 Three-View Triangulation (en)
skos:notation	RIV/68407700:21230/13:00212564!RIV14-TA0-21230___
http://linked.open...avai/predkladatel	Fakulta elektrotechnická
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(TA02011275)
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Pajdla, Tomáš Kúkelová, Zuzana
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	74700
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/13:00212564
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	triangulation; Groebner basis; L2 three-view triangulation (en)
http://linked.open.../riv/klicoveSlovo	triangulation Groebner basis L2 three-view triangulation
http://linked.open...ontrolniKodProRIV	[EDC4F047CC9D]
http://linked.open...v/mistoKonaniAkce	Seattle
http://linked.open...i/riv/mistoVydani	Los Alamitos
http://linked.open...i/riv/nazevZdroje	3DV 2013 - International Conference on 3D Vision
http://linked.open...in/vavai/riv/obor	JD
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	ATOM - Automatic Three-dimensional Terrain Monitoring
http://linked.open...UplatneniVysledku	2013
http://linked.open...iv/tvurceVysledku	Kúkelová, Zuzana Pajdla, Tomáš Bujňák, M.
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2013-06-29 (xsd:date)
number of pages	8 (xsd:int)
http://bibframe.org/vocab/doi	10.1109/3DV.2013.50
http://purl.org/ne...btex#hasPublisher	IEEE Computer Society Press
https://schema.org/isbn	978-0-7695-5067-1
http://localhost/t...ganizacniJednotka	21230

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