2,925 research outputs found
A factorization approach to inertial affine structure from motion
We consider the problem of reconstructing a 3-D scene from a moving camera with high frame rate using the affine projection model. This problem is traditionally known as Affine Structure from Motion (Affine SfM), and can be solved using an elegant low-rank factorization formulation. In this paper, we assume that an accelerometer and gyro are rigidly mounted with the camera, so that synchronized linear acceleration and angular velocity measurements are available together with the image measurements. We extend the standard Affine SfM algorithm to integrate these measurements through the use of image derivatives
Bearing-based formation control with second-order agent dynamics
We consider the distributed formation control problem for a network of agents using visual measurements. We propose solutions that are based on bearing (and optionally distance) measurements, and agents with double integrator dynamics. We assume that a subset of the agents can track, in addition to their neighbors, a set of static features in the environment. These features are not considered to be part of the formation, but they are used to asymptotically control the velocity of the agents. We analyze the convergence properties of the proposed protocols analytically and through simulations.Published versionSupporting documentatio
A Note on Rectangle Covering with Congruent Disks
In this note we prove that, if is the greatest area of a rectangle
which can be covered with unit disks, then , and
these are the best constants; moreover, for , we
have and
.Comment: 8 pages, 3 figures, some corrections made in version
A factorization approach to inertial affine structure from motion
We consider the problem of reconstructing a 3-D scene from a moving camera with high frame rate using the affine projection model. This problem is traditionally known as Affine Structure from Motion (Affine SfM), and can be solved using an elegant low-rank factorization formulation. In this paper, we assume that an accelerometer and gyro are rigidly mounted with the camera, so that synchronized linear acceleration and angular velocity measurements are available together with the image measurements. We extend the standard Affine SfM algorithm to integrate these measurements through the use of image derivatives
PHILOSOPHY AND METHODS OF EXAMINING THE IMPACT OF THE EUROPEAN REGIONAL POLICY
It is a very generally accepted view that financial support received from the European Union generates a large growth surplus. The potential effects of the structural funds calculated in model simulations carried out by the European Commission support theEuropean Union, regional policy, evaluation methods
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
Non-natural metrics on the tangent bundle
Natural metrics provide a way to induce a metric on the tangent bundle from the metric on its base manifold. The most studied type is the Sasaki metric, which applies the base metric separately to the vertical and horizontal components. We study a more general class of metrics which introduces interactions between the vertical and horizontal components, with scalar weights. Additionally, we explicitly clarify how to apply our and other induced metrics on the tangent bundle to vector fields where the vertical component is not constant along the fibers. We give application to the Special Orthogonal Group SO(3) as an example.Published versio
On twisted group C-algebras associated with FC-hypercentral groups and other related groups
We show that the twisted group C-algebra associated with a discrete
FC-hypercentral group is simple (resp. has a unique tracial state) if and only
if Kleppner's condition is satisfied. This generalizes a result of J. Packer
for countable nilpotent groups. We also consider a larger class of groups, for
which we can show that the corresponding reduced twisted group C-algebras
have a unique tracial state if and only if Kleppner's condition holds.Comment: 16 pages. Some minor changes, mostly in subsection 2.3; two
references adde
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