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Palabras claves o descriptores: GROUP ACTION (Comienzo)
2 registros cumplieron la condición especificada en la base de información BIBCYT. ()
Registro 1 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Bazin, Pierre-Louis ; Boutin, Mireille
Título: Structure from Motion: A New Look from the Point of View of Invariant Theory
Páginas/Colación: pp. 1156 - 1174
Url: Ir a http://epubs.siam.org/sam-bin/dbq/article/40246http://epubs.siam.org/sam-bin/dbq/article/40246
SIAM Journal on Applied Mathematics Vol. 64, no. 4 April/June 2004
Información de existenciaInformación de existencia

Palabras Claves: Palabras: GROUP ACTION GROUP ACTION, Palabras: INVARIANTS INVARIANTS, Palabras: MOVING FRAME MOVING FRAME, Palabras: ORTHOGRAPHIC CAMERA ORTHOGRAPHIC CAMERA, Palabras: PINPOINT CAMERA PINPOINT CAMERA, Palabras: STRUCTURE FROM MOTION STRUCTURE FROM MOTION

Resumen
We present a novel simple formulation of the problem of 3D object reconstruction from images. In this formulation, the object is seen as lying at the intersection of the projection of orbits of custom built Lie group actions. The group parameters correspond to unknown irrelevant quantities such as the camera orientation, the depth parameters of the object with respect to the camera, and the focal length. We then use an algorithmic method based on moving frames à la Fels--Olver to obtain a fundamental set of invariants of these group actions. The invariants are used to define a set of equations determining the 3D object, thus providing a mathematical formulation of the problem where the irrelevant parameters do not appear.

Registro 2 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Cimpric, Jaka ; Kuhlmann, Salma ; Scheiderer, Claus
Título: Sums of squares and moment problems in equivariant situations
Páginas/Colación: pp. 735-765
Fecha: Febreuary 2009
Transactions of the American Mathematical Society Vol. 361, no. 2 February 2009
Información de existenciaInformación de existencia

Palabras Claves: Palabras: GROUP ACTIONS GROUP ACTIONS, Palabras: MOMENT PROBLEMS MOMENT PROBLEMS, Palabras: SEMI-ALGEBRAIC SETS SEMI-ALGEBRAIC SETS

Resumen
We begin a systematic study of positivity and moment problems in an equivariant setting

We begin a systematic study of positivity and moment problems in an equivariant setting. Given a reductive group $ G$over $ \mathbb{R}$acting on an affine $ \mathbb{R}$-variety $ V$, we consider the induced dual action on the coordinate ring $ \mathbb{R}[V]$and on the linear dual space of $ \mathbb{R}[V]$. In this setting, given an invariant closed semialgebraic subset $ K$of $ V(\mathbb{R})$, we study the problem of representation of invariant nonnegative polynomials on $ K$by invariant sums of squares, and the closely related problem of representation of invariant linear functionals on $ \mathbb{R}[V]$by invariant measures supported on $ K$. To this end, we analyse the relation between quadratic modules of $ \mathbb{R}[V]$and associated quadratic modules of the (finitely generated) subring $ \mathbb{R}[V]^G$of invariant polynomials. We apply our results to investigate the finite solvability of an equivariant version of the multidimensional $ K$-moment problem. Most of our results are specific to the case where the group $ G(\mathbb{R})$is compact.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno

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