10,675 research outputs found
Poisson approximation of the length spectrum of random surfaces
Multivariate Poisson approximation of the length spectrum of random surfaces
is studied by means of the Chen-Stein method. This approach delivers simple and
explicit error bounds in Poisson limit theorems. They are used to prove that
Poisson approximation applies to curves of length up to order
with being the genus of the surface.Comment: 22 pages, 2 figures. To appear in Indiana Univ. Math.
Probability around the Quantum Gravity. Part 1: Pure Planar Gravity
In this paper we study stochastic dynamics which leaves quantum gravity
equilibrium distribution invariant. We start theoretical study of this dynamics
(earlier it was only used for Monte-Carlo simulation). Main new results concern
the existence and properties of local correlation functions in the
thermodynamic limit. The study of dynamics constitutes a third part of the
series of papers where more general class of processes were studied (but it is
self-contained), those processes have some universal significance in
probability and they cover most concrete processes, also they have many
examples in computer science and biology. At the same time the paper can serve
an introduction to quantum gravity for a probabilist: we give a rigorous
exposition of quantum gravity in the planar pure gravity case. Mostly we use
combinatorial techniques, instead of more popular in physics random matrix
models, the central point is the famous exponent.Comment: 40 pages, 11 figure
The probabilistic nature of McShane's identity: planar tree coding of simple loops
In this article, we discuss a probabilistic interpretation of McShane's
identity as describing a finite measure on the space of embedded paths though a
point.Comment: 25 page
AROMA: Automatic Generation of Radio Maps for Localization Systems
WLAN localization has become an active research field recently. Due to the
wide WLAN deployment, WLAN localization provides ubiquitous coverage and adds
to the value of the wireless network by providing the location of its users
without using any additional hardware. However, WLAN localization systems
usually require constructing a radio map, which is a major barrier of WLAN
localization systems' deployment. The radio map stores information about the
signal strength from different signal strength streams at selected locations in
the site of interest. Typical construction of a radio map involves measurements
and calibrations making it a tedious and time-consuming operation. In this
paper, we present the AROMA system that automatically constructs accurate
active and passive radio maps for both device-based and device-free WLAN
localization systems. AROMA has three main goals: high accuracy, low
computational requirements, and minimum user overhead. To achieve high
accuracy, AROMA uses 3D ray tracing enhanced with the uniform theory of
diffraction (UTD) to model the electric field behavior and the human shadowing
effect. AROMA also automates a number of routine tasks, such as importing
building models and automatic sampling of the area of interest, to reduce the
user's overhead. Finally, AROMA uses a number of optimization techniques to
reduce the computational requirements. We present our system architecture and
describe the details of its different components that allow AROMA to achieve
its goals. We evaluate AROMA in two different testbeds. Our experiments show
that the predicted signal strength differs from the measurements by a maximum
average absolute error of 3.18 dBm achieving a maximum localization error of
2.44m for both the device-based and device-free cases.Comment: 14 pages, 17 figure
Fast Back-Projection for Non-Line of Sight Reconstruction
Recent works have demonstrated non-line of sight (NLOS) reconstruction by
using the time-resolved signal frommultiply scattered light. These works
combine ultrafast imaging systems with computation, which back-projects the
recorded space-time signal to build a probabilistic map of the hidden geometry.
Unfortunately, this computation is slow, becoming a bottleneck as the imaging
technology improves. In this work, we propose a new back-projection technique
for NLOS reconstruction, which is up to a thousand times faster than previous
work, with almost no quality loss. We base on the observation that the hidden
geometry probability map can be built as the intersection of the three-bounce
space-time manifolds defined by the light illuminating the hidden geometry and
the visible point receiving the scattered light from such hidden geometry. This
allows us to pose the reconstruction of the hidden geometry as the voxelization
of these space-time manifolds, which has lower theoretic complexity and is
easily implementable in the GPU. We demonstrate the efficiency and quality of
our technique compared against previous methods in both captured and synthetic
dat
SurfelMeshing: Online Surfel-Based Mesh Reconstruction
We address the problem of mesh reconstruction from live RGB-D video, assuming
a calibrated camera and poses provided externally (e.g., by a SLAM system). In
contrast to most existing approaches, we do not fuse depth measurements in a
volume but in a dense surfel cloud. We asynchronously (re)triangulate the
smoothed surfels to reconstruct a surface mesh. This novel approach enables to
maintain a dense surface representation of the scene during SLAM which can
quickly adapt to loop closures. This is possible by deforming the surfel cloud
and asynchronously remeshing the surface where necessary. The surfel-based
representation also naturally supports strongly varying scan resolution. In
particular, it reconstructs colors at the input camera's resolution. Moreover,
in contrast to many volumetric approaches, ours can reconstruct thin objects
since objects do not need to enclose a volume. We demonstrate our approach in a
number of experiments, showing that it produces reconstructions that are
competitive with the state-of-the-art, and we discuss its advantages and
limitations. The algorithm (excluding loop closure functionality) is available
as open source at https://github.com/puzzlepaint/surfelmeshing .Comment: Version accepted to IEEE Transactions on Pattern Analysis and Machine
Intelligenc
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