23,007 research outputs found
Mapping, Localization and Path Planning for Image-based Navigation using Visual Features and Map
Building on progress in feature representations for image retrieval,
image-based localization has seen a surge of research interest. Image-based
localization has the advantage of being inexpensive and efficient, often
avoiding the use of 3D metric maps altogether. That said, the need to maintain
a large number of reference images as an effective support of localization in a
scene, nonetheless calls for them to be organized in a map structure of some
kind.
The problem of localization often arises as part of a navigation process. We
are, therefore, interested in summarizing the reference images as a set of
landmarks, which meet the requirements for image-based navigation. A
contribution of this paper is to formulate such a set of requirements for the
two sub-tasks involved: map construction and self-localization. These
requirements are then exploited for compact map representation and accurate
self-localization, using the framework of a network flow problem. During this
process, we formulate the map construction and self-localization problems as
convex quadratic and second-order cone programs, respectively. We evaluate our
methods on publicly available indoor and outdoor datasets, where they
outperform existing methods significantly.Comment: CVPR 2019, for implementation see https://github.com/janinethom
On the boundary and intersection motives of genus 2 Hilbert-Siegel varieties
We study genus 2 Hilbert-Siegel varieties, i.e. Shimura varieties
corresponding to the group \mbox{GSp}_{4,F} over a totally real field ,
along with the relative Chow motives of abelian type
over obtained from irreducible representations of
\mbox{GSp}_{4,F}. We analyse the weight filtration on the degeneration of
such motives at the boundary of the Baily-Borel compactification and we find a
criterion on the highest weight which characterises the absence of
the middle weights 0 and 1 in the corresponding degeneration. Thanks to
Wildeshaus' theory, the absence of these weights allows us to construct
Hecke-equivariant Chow motives over , whose realizations equal
interior (or intersection) cohomology of with -coefficients.
We give applications to the construction of motives associated to automorphic
representations.Comment: 39 pages; comments very welcome! (v2): some typos fixed, minor
changes in the text (v3): other typos fixed, some prerequisites shortened
(now 36 pages), minor changes in the text (v4) final version, accepted for
publication in Documenta Mathematica (40 pages
Asymptotic Analysis of Inpainting via Universal Shearlet Systems
Recently introduced inpainting algorithms using a combination of applied
harmonic analysis and compressed sensing have turned out to be very successful.
One key ingredient is a carefully chosen representation system which provides
(optimally) sparse approximations of the original image. Due to the common
assumption that images are typically governed by anisotropic features,
directional representation systems have often been utilized. One prominent
example of this class are shearlets, which have the additional benefitallowing
faithful implementations. Numerical results show that shearlets significantly
outperform wavelets in inpainting tasks. One of those software packages,
www.shearlab.org, even offers the flexibility of usingdifferent parameter for
each scale, which is not yet covered by shearlet theory.
In this paper, we first introduce universal shearlet systems which are
associated with an arbitrary scaling sequence, thereby modeling the previously
mentioned flexibility. In addition, this novel construction allows for a smooth
transition between wavelets and shearlets and therefore enables us to analyze
them in a uniform fashion. For a large class of such scaling sequences, we
first prove that the associated universal shearlet systems form band-limited
Parseval frames for consisting of Schwartz functions.
Secondly, we analyze the performance for inpainting of this class of universal
shearlet systems within a distributional model situation using an
-analysis minimization algorithm for reconstruction. Our main result in
this part states that, provided the scaling sequence is comparable to the size
of the (scale-dependent) gap, nearly-perfect inpainting is achieved at
sufficiently fine scales
Multi-body Non-rigid Structure-from-Motion
Conventional structure-from-motion (SFM) research is primarily concerned with
the 3D reconstruction of a single, rigidly moving object seen by a static
camera, or a static and rigid scene observed by a moving camera --in both cases
there are only one relative rigid motion involved. Recent progress have
extended SFM to the areas of {multi-body SFM} (where there are {multiple rigid}
relative motions in the scene), as well as {non-rigid SFM} (where there is a
single non-rigid, deformable object or scene). Along this line of thinking,
there is apparently a missing gap of "multi-body non-rigid SFM", in which the
task would be to jointly reconstruct and segment multiple 3D structures of the
multiple, non-rigid objects or deformable scenes from images. Such a multi-body
non-rigid scenario is common in reality (e.g. two persons shaking hands,
multi-person social event), and how to solve it represents a natural
{next-step} in SFM research. By leveraging recent results of subspace
clustering, this paper proposes, for the first time, an effective framework for
multi-body NRSFM, which simultaneously reconstructs and segments each 3D
trajectory into their respective low-dimensional subspace. Under our
formulation, 3D trajectories for each non-rigid structure can be well
approximated with a sparse affine combination of other 3D trajectories from the
same structure (self-expressiveness). We solve the resultant optimization with
the alternating direction method of multipliers (ADMM). We demonstrate the
efficacy of the proposed framework through extensive experiments on both
synthetic and real data sequences. Our method clearly outperforms other
alternative methods, such as first clustering the 2D feature tracks to groups
and then doing non-rigid reconstruction in each group or first conducting 3D
reconstruction by using single subspace assumption and then clustering the 3D
trajectories into groups.Comment: 21 pages, 16 figure
Prescribing Gauss curvature of surfaces in 3-dimensional spacetimes, Application to the Minkowski problem in the Minkowski space
We study the existence of surfaces with constant or prescribed Gauss
curvature in certain Lorentzian spacetimes. We prove in particular that every
(non-elementary) 3-dimensional maximal globally hyperbolic spatially compact
spacetime with constant non-negative curvature is foliated by compact spacelike
surfaces with constant Gauss curvature. In the constant negative curvature
case, such a foliation exists outside the convex core. The existence of these
foliations, together with a theorem of C. Gerhardt, yield several corollaries.
For example, they allow to solve the Minkowski problem in the 3-dimensional
Minkowski space for datas that are invariant under the action of a co-compact
Fuchsian group
Fermions in three-dimensional spinfoam quantum gravity
We study the coupling of massive fermions to the quantum mechanical dynamics
of spacetime emerging from the spinfoam approach in three dimensions. We first
recall the classical theory before constructing a spinfoam model of quantum
gravity coupled to spinors. The technique used is based on a finite expansion
in inverse fermion masses leading to the computation of the vacuum to vacuum
transition amplitude of the theory. The path integral is derived as a sum over
closed fermionic loops wrapping around the spinfoam. The effects of quantum
torsion are realised as a modification of the intertwining operators assigned
to the edges of the two-complex, in accordance with loop quantum gravity. The
creation of non-trivial curvature is modelled by a modification of the pure
gravity vertex amplitudes. The appendix contains a review of the geometrical
and algebraic structures underlying the classical coupling of fermions to three
dimensional gravity.Comment: 40 pages, 3 figures, version accepted for publication in GER
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