8,847 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
The Fermionic Signature Operator and Quantum States in Rindler Space-Time
The fermionic signature operator is constructed in Rindler space-time. It is
shown to be an unbounded self-adjoint operator on the Hilbert space of
solutions of the massive Dirac equation. In two-dimensional Rindler space-time,
we prove that the resulting fermionic projector state coincides with the
Fulling-Rindler vacuum. Moreover, the fermionic signature operator gives a
covariant construction of general thermal states, in particular of the Unruh
state. The fermionic signature operator is shown to be well-defined in
asymptotically Rindler space-times. In four-dimensional Rindler space-time, our
construction gives rise to new quantum states.Comment: 27 pages, LaTeX, more details on self-adjoint extension (published
version
A study on iterative methods for solving Richards` equation
This work concerns linearization methods for efficiently solving the
Richards` equation,a degenerate elliptic-parabolic equation which models flow
in saturated/unsaturated porous media.The discretization of Richards` equation
is based on backward Euler in time and Galerkin finite el-ements in space. The
most valuable linearization schemes for Richards` equation, i.e. the
Newtonmethod, the Picard method, the Picard/Newton method and theLscheme are
presented and theirperformance is comparatively studied. The convergence, the
computational time and the conditionnumbers for the underlying linear systems
are recorded. The convergence of theLscheme is theo-retically proved and the
convergence of the other methods is discussed. A new scheme is
proposed,theLscheme/Newton method which is more robust and quadratically
convergent. The linearizationmethods are tested on illustrative numerical
examples
The space of essential matrices as a Riemannian quotient manifold
The essential matrix, which encodes the epipolar constraint between points in two projective views,
is a cornerstone of modern computer vision. Previous works have proposed different characterizations
of the space of essential matrices as a Riemannian manifold. However, they either do not consider the
symmetric role played by the two views, or do not fully take into account the geometric peculiarities
of the epipolar constraint. We address these limitations with a characterization as a quotient manifold
which can be easily interpreted in terms of camera poses. While our main focus in on theoretical
aspects, we include applications to optimization problems in computer vision.This work was supported by grants NSF-IIP-0742304, NSF-OIA-1028009, ARL MAST-CTA W911NF-08-2-0004, and ARL RCTA W911NF-10-2-0016, NSF-DGE-0966142, and NSF-IIS-1317788
On the Modulation Equations and Stability of Periodic GKdV Waves via Bloch Decompositions
In this paper, we complement recent results of Bronski and Johnson and of
Johnson and Zumbrun concerning the modulational stability of spatially periodic
traveling wave solutions of the generalized Korteweg-de Vries equation. In this
previous work it was shown by rigorous Evans function calculations that the
formal slow modulation approximation resulting in the Whitham system accurately
describes the spectral stability to long wavelength perturbations. Here, we
reproduce this result without reference to the Evans function by using direct
Bloch-expansion methods and spectral perturbation analysis. This approach has
the advantage of applying also in the more general multi-periodic setting where
no conveniently computable Evans function is yet devised. In particular, we
complement the picture of modulational stability described by Bronski and
Johnson by analyzing the projectors onto the total eigenspace bifurcating from
the origin in a neighborhood of the origin and zero Floquet parameter. We show
the resulting linear system is equivalent, to leading order and up to
conjugation, to the Whitham system and that, consequently, the characteristic
polynomial of this system agrees (to leading order) with the linearized
dispersion relation derived through Evans function calculation.Comment: 19 pages
Simultaneous Inference in General Parametric Models
Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth of the results. For the analyses we use the R add-on package multcomp, which provides a convenient interface to the general approach adopted here
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