760 research outputs found
An Epipolar Line from a Single Pixel
Computing the epipolar geometry from feature points between cameras with very
different viewpoints is often error prone, as an object's appearance can vary
greatly between images. For such cases, it has been shown that using motion
extracted from video can achieve much better results than using a static image.
This paper extends these earlier works based on the scene dynamics. In this
paper we propose a new method to compute the epipolar geometry from a video
stream, by exploiting the following observation: For a pixel p in Image A, all
pixels corresponding to p in Image B are on the same epipolar line.
Equivalently, the image of the line going through camera A's center and p is an
epipolar line in B. Therefore, when cameras A and B are synchronized, the
momentary images of two objects projecting to the same pixel, p, in camera A at
times t1 and t2, lie on an epipolar line in camera B. Based on this observation
we achieve fast and precise computation of epipolar lines. Calibrating cameras
based on our method of finding epipolar lines is much faster and more robust
than previous methods.Comment: WACV 201
On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages
We extend our study of Motion Planning via Manifold Samples (MMS), a general
algorithmic framework that combines geometric methods for the exact and
complete analysis of low-dimensional configuration spaces with sampling-based
approaches that are appropriate for higher dimensions. The framework explores
the configuration space by taking samples that are entire low-dimensional
manifolds of the configuration space capturing its connectivity much better
than isolated point samples. The contributions of this paper are as follows:
(i) We present a recursive application of MMS in a six-dimensional
configuration space, enabling the coordination of two polygonal robots
translating and rotating amidst polygonal obstacles. In the adduced experiments
for the more demanding test cases MMS clearly outperforms PRM, with over
20-fold speedup in a coordination-tight setting. (ii) A probabilistic
completeness proof for the most prevalent case, namely MMS with samples that
are affine subspaces. (iii) A closer examination of the test cases reveals that
MMS has, in comparison to standard sampling-based algorithms, a significant
advantage in scenarios containing high-dimensional narrow passages. This
provokes a novel characterization of narrow passages which attempts to capture
their dimensionality, an attribute that had been (to a large extent) unattended
in previous definitions.Comment: 20 page
Optimal randomized incremental construction for guaranteed logarithmic planar point location
Given a planar map of segments in which we wish to efficiently locate
points, we present the first randomized incremental construction of the
well-known trapezoidal-map search-structure that only requires expected preprocessing time while deterministically guaranteeing worst-case
linear storage space and worst-case logarithmic query time. This settles a long
standing open problem; the best previously known construction time of such a
structure, which is based on a directed acyclic graph, so-called the history
DAG, and with the above worst-case space and query-time guarantees, was
expected . The result is based on a deeper understanding of the
structure of the history DAG, its depth in relation to the length of its
longest search path, as well as its correspondence to the trapezoidal search
tree. Our results immediately extend to planar maps induced by finite
collections of pairwise interior disjoint well-behaved curves.Comment: The article significantly extends the theoretical aspects of the work
presented in http://arxiv.org/abs/1205.543
Deconstructing Approximate Offsets
We consider the offset-deconstruction problem: Given a polygonal shape Q with
n vertices, can it be expressed, up to a tolerance \eps in Hausdorff distance,
as the Minkowski sum of another polygonal shape P with a disk of fixed radius?
If it does, we also seek a preferably simple-looking solution P; then, P's
offset constitutes an accurate, vertex-reduced, and smoothened approximation of
Q. We give an O(n log n)-time exact decision algorithm that handles any
polygonal shape, assuming the real-RAM model of computation. A variant of the
algorithm, which we have implemented using CGAL, is based on rational
arithmetic and answers the same deconstruction problem up to an uncertainty
parameter \delta; its running time additionally depends on \delta. If the input
shape is found to be approximable, this algorithm also computes an approximate
solution for the problem. It also allows us to solve parameter-optimization
problems induced by the offset-deconstruction problem. For convex shapes, the
complexity of the exact decision algorithm drops to O(n), which is also the
time required to compute a solution P with at most one more vertex than a
vertex-minimal one.Comment: 18 pages, 11 figures, previous version accepted at SoCG 2011,
submitted to DC
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Safe Drinking Water in Kuna Yala: Field Notes from Panama
Starting in early 2003, Michael Halperin worked for two years as a Peace Corps volunteer in the indigenous Kuna island community of Ustupu, just off the Northeastern coast of Panama. His work focused on the issue of potable water and diarrheal disease. These field notes focus on the implementation of sustainable technologies and practices for clean water. Emphasized is the importance of local knowledge, partnerships, and indigenous leadership. This story chronicles a two-year process of considering, rejecting, and finally developing the most workable solution for safe water: solar water purification. Unlike boiling and chlorination, this method was acceptable to the Kuna because it does not conflict with cultural practices on the island. It is likely that this method of water purification can be sustained over time
A Behavioural Finance Explanation of a Gearing-ß Inverse Association Referencing Weill’s Liquidity Result (in English)
The authors investigated Arnold’s conjecture that Leverage (Financial Gearing) and Operating Gearing should be positively related to the equity ß of the Sharpe/Lintner CAPM. They find for a sample of the S&P 500 firms that have been on that index continuously for more than 15 years, that ß is negatively associated with Leverage and Operating Gearing. Using Weill’s results for transitional economies, the authors suggest that liquidity may provide an explanation for this anomalous ß-Gearing inversion. The implications are: that (1) one should revaluate the positive associations posited for Financial and Operating gearing with ß and (2) consider the possibility of managing liquidity as a way to affect ß.financial gearing; leverage; liquidity; beta
Quantum Hall Phase Diagram of Second Landau-level Half-filled Bilayers: Abelian versus Non-Abelian States
The quantum Hall phase diagram of the half-filled bilayer system in the
second Landau level is studied as a function of tunneling and layer separation
using exact diagonalization. We make the striking prediction that bilayer
structures would manifest two distinct branches of incompressible fractional
quantum Hall effect (FQHE) corresponding to the Abelian 331 state (at moderate
to low tunneling and large layer separation) and the non-Abelian Pfaffian state
(at large tunneling and small layer separation). The observation of these two
FQHE branches and the quantum phase transition between them will be compelling
evidence supporting the existence of the non-Abelian Pfaffian state in the
second Landau level.Comment: 4 pages, 3 figure
Robustness of high-fidelity Rydberg gates with single-site addressability
Controlled phase (CPHASE) gates can in principle be realized with trapped
neutral atoms by making use of the Rydberg blockade. Achieving the ultra-high
fidelities required for quantum computation with such Rydberg gates is however
compromised by experimental inaccuracies in pulse amplitudes and timings, as
well as by stray fields that cause fluctuations of the Rydberg levels. We
report here a comparative study of analytic and numerical pulse sequences for
the Rydberg CPHASE gate that specifically examines the robustness of the gate
fidelity with respect to such experimental perturbations. Analytical pulse
sequences of both simultaneous and stimulated Raman adiabatic passage (STIRAP)
are found to be at best moderately robust under these perturbations. In
contrast, optimal control theory is seen to allow generation of numerical
pulses that are inherently robust within a predefined tolerance window. The
resulting numerical pulse shapes display simple modulation patterns and their
spectra contain only one additional frequency beyond the basic resonant Rydberg
gate frequencies. Pulses of such low complexity should be experimentally
feasible, allowing gate fidelities of order 99.90 - 99.99% to be achievable
under realistic experimental conditions.Comment: 12 pages, 14 figure
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