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| Description
| - We introduce a framework for computing statistically optimal estimates of geometric reconstruction problems. While traditional algorithms often suffer from either local minima or non-optimality-or a combination of both-we pursue the goal of achieving global solutions of the statistically optimal cost-function. Our approach is based on a hierarchy of convex relaxations to solve non-convex optimization problems with polynomials. These convex relaxations generate a monotone sequence of lower bounds and we show how one can detect whether the global optimum is attained at a given relaxation. The technique is applied to a number of classical vision problems: triangulation, camera pose, homography estimation and last, but not least, epipolar geometry estimation. Experimental validation on both synthetic and real data is provided. In practice, only a few relaxations are needed for attaining the global optimum.
- We introduce a framework for computing statistically optimal estimates of geometric reconstruction problems. While traditional algorithms often suffer from either local minima or non-optimality-or a combination of both-we pursue the goal of achieving global solutions of the statistically optimal cost-function. Our approach is based on a hierarchy of convex relaxations to solve non-convex optimization problems with polynomials. These convex relaxations generate a monotone sequence of lower bounds and we show how one can detect whether the global optimum is attained at a given relaxation. The technique is applied to a number of classical vision problems: triangulation, camera pose, homography estimation and last, but not least, epipolar geometry estimation. Experimental validation on both synthetic and real data is provided. In practice, only a few relaxations are needed for attaining the global optimum. (en)
- Článek zavádí rámec pro výpočet statisticky optimálních odhadů v problémech geometrické rekonstrukce. Zatímco tradiční algoritmy často trpí díky lokálním minimům či neoptimalitě či kombinaci obou, my důsledně hledáme globální řešení statisticky optimální nákladové funkce. Náš přístup je založený na hierarchii konvexních relací řešících nekonvexní problémy s polynomy. Tyto konvexní relace generují monotónní posloupnost spodních ohraničení. Ukazujeme, jak je možné zjistit, zda globální optimum je dosaženo v takto daných omezeních. Tato technika je aplikována v řadě klasických vizuálních problémů jako triangulace, homograficky odhad, odhad epipolární geometrie atd. Výsledky jsme podložili experimentováním s umělými i realnými daty. V praxi je třeba jen pár omezení k dosažení globálního optima. (cs)
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| Title
| - Globally Optimal Estimates for Geometric Reconstruction Problems
- Globální optimální odhady pro problémy geometrické rekonstrukce (cs)
- Globally Optimal Estimates for Geometric Reconstruction Problems (en)
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| skos:prefLabel
| - Globally Optimal Estimates for Geometric Reconstruction Problems
- Globální optimální odhady pro problémy geometrické rekonstrukce (cs)
- Globally Optimal Estimates for Geometric Reconstruction Problems (en)
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| skos:notation
| - RIV/68407700:21230/07:03130318!RIV08-GA0-21230___
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| http://linked.open.../vavai/riv/strany
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
| - P(GA102/05/0011), P(GA102/06/0652), P(ME 698)
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| http://linked.open...iv/cisloPeriodika
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/68407700:21230/07:03130318
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - LMI relaxations; global optimization; non-convex optimization; semidefinite programming; structure from motion; triangulation (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...odStatuVydavatele
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...i/riv/nazevZdroje
| - International Journal of Computer Vision
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
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| http://linked.open...v/svazekPeriodika
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| http://linked.open...iv/tvurceVysledku
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| issn
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| number of pages
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| http://localhost/t...ganizacniJednotka
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