53 research outputs found
QUARCH: A New Quasi-Affine Reconstruction Stratum From Vague Relative Camera Orientation Knowledge
International audienceWe present a new quasi-affine reconstruction of a scene and its application to camera self-calibration. We refer to this reconstruction as QUARCH (QUasi-Affine Reconstruction with respect to Camera centers and the Hodographs of horopters). A QUARCH can be obtained by solving a semidefinite programming problem when, (i) the images have been captured by a moving camera with constant intrinsic parameters, and (ii) a vague knowledge of the relative orientation (under or over 120°) between camera pairs is available. The resulting reconstruction comes close enough to an affine one allowing thus an easy upgrade of the QUARCH to its affine and metric counterparts. We also present a constrained Levenberg-Marquardt method for nonlinear optimization subject to Linear Matrix Inequality (LMI) constraints so as to ensure that the QUARCH LMIs are satisfied during optimization. Experiments with synthetic and real data show the benefits of QUARCH in reliably obtaining a metric reconstruction
QUARCH: A New Quasi-Affine Reconstruction Stratum From Vague Relative Camera Orientation Knowledge
International audienceWe present a new quasi-affine reconstruction of a scene and its application to camera self-calibration. We refer to this reconstruction as QUARCH (QUasi-Affine Reconstruction with respect to Camera centers and the Hodographs of horopters). A QUARCH can be obtained by solving a semidefinite programming problem when, (i) the images have been captured by a moving camera with constant intrinsic parameters, and (ii) a vague knowledge of the relative orientation (under or over 120°) between camera pairs is available. The resulting reconstruction comes close enough to an affine one allowing thus an easy upgrade of the QUARCH to its affine and metric counterparts. We also present a constrained Levenberg-Marquardt method for nonlinear optimization subject to Linear Matrix Inequality (LMI) constraints so as to ensure that the QUARCH LMIs are satisfied during optimization. Experiments with synthetic and real data show the benefits of QUARCH in reliably obtaining a metric reconstruction
The Quantum Geometry of Spin and Statistics
Both, spin and statistics of a quantum system can be seen to arise from
underlying (quantum) group symmetries. We show that the spin-statistics theorem
is equivalent to a unification of these symmetries. Besides covering the
Bose-Fermi case we classify the corresponding possibilities for anyonic spin
and statistics. We incorporate the underlying extended concept of symmetry into
quantum field theory in a generalised path integral formulation capable of
handling general braid statistics. For bosons and fermions the different path
integrals and Feynman rules naturally emerge without introducing Grassmann
variables. We also consider the anyonic example of quons and obtain the path
integral counterpart to the usual canonical approach.Comment: 23 pages, LaTeX with AMS and XY-Pic macros, minor corrections and
references adde
The spectral data for Hamiltonian stationary Lagrangian tori in R^4
This article determines the spectral data, in the integrable systems sense,
for all weakly conformally immersed Hamiltonian stationary Lagrangian in
. This enables us to describe their moduli space and the locus of branch
points of such an immersion. This is also an informative example in integrable
systems geometry, since the group of ambient isometries acts non-trivially on
the spectral data and the relevant energy functional (the area) need not be
constant under deformations by higher flows.Comment: 30 pages. Version 3: a complete rewrite of version 2 with new results
and two significant correction
Equivalences of twisted K3 surfaces
We prove that two derived equivalent twisted K3 surfaces have isomorphic
periods. The converse is shown for K3 surfaces with large Picard number. It is
also shown that all possible twisted derived equivalences between arbitrary
twisted K3 surfaces form a subgroup of the group of all orthogonal
transformations of the cohomology of a K3 surface.
The passage from twisted derived equivalences to an action on the cohomology
is made possible by twisted Chern characters that will be introduced for
arbitrary smooth projective varieties.Comment: Final version. 35 pages. to appear in Math. An
Field Theory on Curved Noncommutative Spacetimes
We study classical scalar field theories on noncommutative curved spacetimes.
Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005),
3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative
spacetimes by using (Abelian) Drinfel'd twists and the associated *-products
and *-differential geometry. In particular, we allow for position dependent
noncommutativity and do not restrict ourselves to the Moyal-Weyl deformation.
We construct action functionals for real scalar fields on noncommutative curved
spacetimes, and derive the corresponding deformed wave equations. We provide
explicit examples of deformed Klein-Gordon operators for noncommutative
Minkowski, de Sitter, Schwarzschild and Randall-Sundrum spacetimes, which solve
the noncommutative Einstein equations. We study the construction of deformed
Green's functions and provide a diagrammatic approach for their perturbative
calculation. The leading noncommutative corrections to the Green's functions
for our examples are derived.Comment: SIGMA Special Issue on Noncommutative Spaces and Field
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