7,692 research outputs found
On-Manifold Preintegration for Real-Time Visual-Inertial Odometry
Current approaches for visual-inertial odometry (VIO) are able to attain
highly accurate state estimation via nonlinear optimization. However, real-time
optimization quickly becomes infeasible as the trajectory grows over time, this
problem is further emphasized by the fact that inertial measurements come at
high rate, hence leading to fast growth of the number of variables in the
optimization. In this paper, we address this issue by preintegrating inertial
measurements between selected keyframes into single relative motion
constraints. Our first contribution is a \emph{preintegration theory} that
properly addresses the manifold structure of the rotation group. We formally
discuss the generative measurement model as well as the nature of the rotation
noise and derive the expression for the \emph{maximum a posteriori} state
estimator. Our theoretical development enables the computation of all necessary
Jacobians for the optimization and a-posteriori bias correction in analytic
form. The second contribution is to show that the preintegrated IMU model can
be seamlessly integrated into a visual-inertial pipeline under the unifying
framework of factor graphs. This enables the application of
incremental-smoothing algorithms and the use of a \emph{structureless} model
for visual measurements, which avoids optimizing over the 3D points, further
accelerating the computation. We perform an extensive evaluation of our
monocular \VIO pipeline on real and simulated datasets. The results confirm
that our modelling effort leads to accurate state estimation in real-time,
outperforming state-of-the-art approaches.Comment: 20 pages, 24 figures, accepted for publication in IEEE Transactions
on Robotics (TRO) 201
Static/Dynamic Filtering for Mesh Geometry
The joint bilateral filter, which enables feature-preserving signal smoothing
according to the structural information from a guidance, has been applied for
various tasks in geometry processing. Existing methods either rely on a static
guidance that may be inconsistent with the input and lead to unsatisfactory
results, or a dynamic guidance that is automatically updated but sensitive to
noises and outliers. Inspired by recent advances in image filtering, we propose
a new geometry filtering technique called static/dynamic filter, which utilizes
both static and dynamic guidances to achieve state-of-the-art results. The
proposed filter is based on a nonlinear optimization that enforces smoothness
of the signal while preserving variations that correspond to features of
certain scales. We develop an efficient iterative solver for the problem, which
unifies existing filters that are based on static or dynamic guidances. The
filter can be applied to mesh face normals followed by vertex position update,
to achieve scale-aware and feature-preserving filtering of mesh geometry. It
also works well for other types of signals defined on mesh surfaces, such as
texture colors. Extensive experimental results demonstrate the effectiveness of
the proposed filter for various geometry processing applications such as mesh
denoising, geometry feature enhancement, and texture color filtering
Consistent ICP for the registration of sparse and inhomogeneous point clouds
In this paper, we derive a novel iterative closest point (ICP) technique that performs point cloud alignment in a robust and consistent way. Traditional ICP techniques minimize the point-to-point distances, which are successful when point clouds contain no noise or clutter and moreover are dense and more or less uniformly sampled. In the other case, it is better to employ point-to-plane or other metrics to locally approximate the surface of the objects. However, the point-to-plane metric does not yield a symmetric solution, i.e. the estimated transformation of point cloud p to point cloud q is not necessarily equal to the inverse transformation of point cloud q to point cloud p. In order to improve ICP, we will enforce such symmetry constraints as prior knowledge and make it also robust to noise and clutter. Experimental results show that our method is indeed much more consistent and accurate in presence of noise and clutter compared to existing ICP algorithms
Neptune at Summer Solstice: Zonal Mean Temperatures from Ground-Based Observations 2003-2007
Imaging and spectroscopy of Neptune's thermal infrared emission is used to
assess seasonal changes in Neptune's zonal mean temperatures between Voyager-2
observations (1989, heliocentric longitude Ls=236) and southern summer solstice
(2005, Ls=270). Our aim was to analyse imaging and spectroscopy from multiple
different sources using a single self-consistent radiative-transfer model to
assess the magnitude of seasonal variability. Globally-averaged stratospheric
temperatures measured from methane emission tend towards a quasi-isothermal
structure (158-164 K) above the 0.1-mbar level, and are found to be consistent
with spacecraft observations of AKARI. This remarkable consistency, despite
very different observing conditions, suggests that stratospheric temporal
variability, if present, is 5 K at 1 mbar and 3 K at 0.1 mbar during
this solstice period. Conversely, ethane emission is highly variable, with
abundance determinations varying by more than a factor of two. The retrieved
C2H6 abundances are extremely sensitive to the details of the T(p) derivation.
Stratospheric temperatures and ethane are found to be latitudinally uniform
away from the south pole (assuming a latitudinally-uniform distribution of
stratospheric methane). At low and midlatitudes, comparisons of synthetic
Voyager-era images with solstice-era observations suggest that tropospheric
zonal temperatures are unchanged since the Voyager 2 encounter, with cool
mid-latitudes and a warm equator and pole. A re-analysis of Voyager/IRIS 25-50
{\mu}m mapping of tropospheric temperatures and para-hydrogen disequilibrium
suggests a symmetric meridional circulation with cold air rising at
mid-latitudes (sub-equilibrium para-H2 conditions) and warm air sinking at the
equator and poles (super-equilibrium para-H2 conditions). The most significant
atmospheric changes are associated with the polar vortex (absent in 1989).Comment: 35 pages, 19 figures. Accepted for publication in Icaru
Hierarchical Bayesian Detection Algorithm for Early-Universe Relics in the Cosmic Microwave Background
A number of theoretically well-motivated additions to the standard
cosmological model predict weak signatures in the form of spatially localized
sources embedded in the cosmic microwave background (CMB) fluctuations. We
present a hierarchical Bayesian statistical formalism and a complete data
analysis pipeline for testing such scenarios. We derive an accurate
approximation to the full posterior probability distribution over the
parameters defining any theory that predicts sources embedded in the CMB, and
perform an extensive set of tests in order to establish its validity. The
approximation is implemented using a modular algorithm, designed to avoid a
posteriori selection effects, which combines a candidate-detection stage with a
full Bayesian model-selection and parameter-estimation analysis. We apply this
pipeline to theories that predict cosmic textures and bubble collisions,
extending previous analyses by using: (1) adaptive-resolution techniques,
allowing us to probe features of arbitrary size, and (2) optimal filters, which
provide the best possible sensitivity for detecting candidate signatures. We
conclude that the WMAP 7-year data do not favor the addition of either cosmic
textures or bubble collisions to the standard cosmological model, and place
robust constraints on the predicted number of such sources. The expected
numbers of bubble collisions and cosmic textures on the CMB sky within our
detection thresholds are constrained to be fewer than 4.0 and 5.2 at 95%
confidence, respectively.Comment: 34 pages, 18 figures. v3: corrected very minor typos to match
published versio
On the properties of discrete spatial filters for CFD
© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/The spatial filtering of variables in the context of Computational Fluid Dynamics (CFD) is a common practice. Most of the discrete filters used in CFD simulations are locally accurate models of continuous operators. However, when filters are adaptative, i.e. the filter width is not constant, or meshes are irregular, discrete filters sometimes break relevant global properties of the continuous models they are based on. For example, the principle of maxima and minima reduction or conservation are eventually infringed. In this paper, we analyze the properties of analytic continuous convolution filters and extract those we consider to define filtering. Then, we impose the accomplishment of these properties on explicit discrete filters by means of constraints. Three filters satisfying the derived conditions are deduced and compared to common differential discrete CFD filters on synthetic fields. Tests on the developed discrete filters show the fulfillment of the imposed properties. In particular, the problem of maxima and minima generation is resolved for physically relevant cases. The tests are conducted on the basis of the eigenvectors of graph Laplacian matrices of meshes. Thus, insight into the relations between filtering and oscillation growth on general meshes is provided. Further tests on singularity fields and on isentropic vortices have also been conducted to evaluate the performance of filters on basic CFD fields. Results confirm that imposing the proposed conditions makes discrete filters properties consistent with those of the continuous ones.Peer ReviewedPostprint (author's final draft
Data Assimilation: A Mathematical Introduction
These notes provide a systematic mathematical treatment of the subject of
data assimilation
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