1,626 research outputs found
Geometric approach to sampling and communication
Relationships that exist between the classical, Shannon-type, and
geometric-based approaches to sampling are investigated. Some aspects of coding
and communication through a Gaussian channel are considered. In particular, a
constructive method to determine the quantizing dimension in Zador's theorem is
provided. A geometric version of Shannon's Second Theorem is introduced.
Applications to Pulse Code Modulation and Vector Quantization of Images are
addressed.Comment: 19 pages, submitted for publicatio
Video Registration in Egocentric Vision under Day and Night Illumination Changes
With the spread of wearable devices and head mounted cameras, a wide range of
application requiring precise user localization is now possible. In this paper
we propose to treat the problem of obtaining the user position with respect to
a known environment as a video registration problem. Video registration, i.e.
the task of aligning an input video sequence to a pre-built 3D model, relies on
a matching process of local keypoints extracted on the query sequence to a 3D
point cloud. The overall registration performance is strictly tied to the
actual quality of this 2D-3D matching, and can degrade if environmental
conditions such as steep changes in lighting like the ones between day and
night occur. To effectively register an egocentric video sequence under these
conditions, we propose to tackle the source of the problem: the matching
process. To overcome the shortcomings of standard matching techniques, we
introduce a novel embedding space that allows us to obtain robust matches by
jointly taking into account local descriptors, their spatial arrangement and
their temporal robustness. The proposal is evaluated using unconstrained
egocentric video sequences both in terms of matching quality and resulting
registration performance using different 3D models of historical landmarks. The
results show that the proposed method can outperform state of the art
registration algorithms, in particular when dealing with the challenges of
night and day sequences
Embedding Riemannian Manifolds by the Heat Kernel of the Connection Laplacian
Given a class of closed Riemannian manifolds with prescribed geometric
conditions, we introduce an embedding of the manifolds into based on
the heat kernel of the Connection Laplacian associated with the Levi-Civita
connection on the tangent bundle. As a result, we can construct a distance in
this class which leads to a pre-compactness theorem on the class under
consideration
D-branes in Generalized Geometry and Dirac-Born-Infeld Action
The purpose of this paper is to formulate the Dirac-Born-Infeld (DBI) action
in a framework of generalized geometry and clarify its symmetry. A D-brane is
defined as a Dirac structure where scalar fields and gauge field are treated on
an equal footing in a static gauge. We derive generalized Lie derivatives
corresponding to the diffeomorphism and B-field gauge transformations and show
that the DBI action is invariant under non-linearly realized symmetries for all
types of diffeomorphisms and B-field gauge transformations. Consequently, we
can interpret not only the scalar field but also the gauge field on the D-brane
as the generalized Nambu-Goldstone boson.Comment: 32 pages, 4 figures, ver2:typos corrected, references adde
Lipshitz matchbox manifolds
A matchbox manifold is a connected, compact foliated space with totally
disconnected transversals; or in other notation, a generalized lamination. It
is said to be Lipschitz if there exists a metric on its transversals for which
the holonomy maps are Lipschitz. Examples of Lipschitz matchbox manifolds
include the exceptional minimal sets for -foliations of compact manifolds,
tiling spaces, the classical solenoids, and the weak solenoids of McCord and
Schori, among others. We address the question: When does a Lipschitz matchbox
manifold admit an embedding as a minimal set for a smooth dynamical system, or
more generally for as an exceptional minimal set for a -foliation of a
smooth manifold? We gives examples which do embed, and develop criteria for
showing when they do not embed, and give examples. We also discuss the
classification theory for Lipschitz weak solenoids.Comment: The paper has been significantly revised, with several proofs
correcte
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