503 research outputs found
Application of the Fisher-Rao metric to ellipse detection
The parameter space for the ellipses in a two dimensional image is a five dimensional manifold, where each point of the manifold corresponds to an ellipse in the image. The parameter space becomes a Riemannian manifold under a Fisher-Rao metric, which is derived from a Gaussian model for the blurring of ellipses in the image. Two points in the parameter space are close together under the Fisher-Rao metric if the corresponding ellipses are close together in the image. The Fisher-Rao metric is accurately approximated by a simpler metric under the assumption that the blurring is small compared with the sizes of the ellipses under consideration. It is shown that the parameter space for the ellipses in the image has a finite volume under the approximation to the Fisher-Rao metric. As a consequence the parameter space can be replaced, for the purpose of ellipse detection, by a finite set of points sampled from it. An efficient algorithm for sampling the parameter space is described. The algorithm uses the fact that the approximating metric is flat, and therefore locally Euclidean, on each three dimensional family of ellipses with a fixed orientation and a fixed eccentricity. Once the sample points have been obtained, ellipses are detected in a given image by checking each sample point in turn to see if the corresponding ellipse is supported by the nearby image pixel values. The resulting algorithm for ellipse detection is implemented. A multiresolution version of the algorithm is also implemented. The experimental results suggest that ellipses can be reliably detected in a given low resolution image and that the number of false detections
can be reduced using the multiresolution algorithm
Granular Pressure and the Thickness of a Layer Jamming on a Rough Incline
Dense granular media have a compaction between the random loose and random
close packings. For these dense media the concept of a granular pressure
depending on compaction is not unanimously accepted because they are often in a
"frozen" state which prevents them to explore all their possible microstates, a
necessary condition for defining a pressure and a compressibility
unambiguously. While periodic tapping or cyclic fluidization have already being
used for that exploration, we here suggest that a succession of flowing states
with velocities slowly decreasing down to zero can also be used for that
purpose. And we propose to deduce the pressure in \emph{dense and flowing}
granular media from experiments measuring the thickness of the granular layer
that remains on a rough incline just after the flow has stopped.Comment: 10 pages, 2 figure
Stress and Strain in Flat Piling of Disks
We have created a flat piling of disks in a numerical experiment using the
Distinct Element Method (DEM) by depositing them under gravity. In the
resulting pile, we then measured increments in stress and strain that were
associated with a small decrease in gravity. We first describe the stress in
terms of the strain using isotropic elasticity theory. Then, from a
micro-mechanical view point, we calculate the relation between the stress and
strain using the mean strain assumption. We compare the predicted values of
Young's modulus and Poisson's ratio with those that were measured in the
numerical experiment.Comment: 9 pages, 1 table, 8 figures, and 2 pages for captions of figure
Long-time asymptotics of the long-range Emch-Radin model
The long-time asymptotic behavior is studied for a long-range variant of the
Emch-Radin model of interacting spins. We derive upper and lower bounds on the
expectation values of a class of observables. We prove analytically that the
time scale at which the system relaxes to equilibrium diverges with the system
size N, displaying quasistationary nonequilibrium behavior. This finding
implies that, for large enough N, equilibration will not be observed in an
experiment of finite duration.Comment: 12 pages, 2 figures. Compared to the published version, a 1/2 has
been corrected in Eq. (9) and subsequent equations; the modifications are
insubstantial and leave the main results of the article unaltered. arXiv
admin note: substantial text overlap with arXiv:1103.083
A QCQP Approach to Triangulation
Triangulation of a three-dimensional point from at least two noisy 2-D images
can be formulated as a quadratically constrained quadratic program. We propose
an algorithm to extract candidate solutions to this problem from its
semidefinite programming relaxations. We then describe a sufficient condition
and a polynomial time test for certifying when such a solution is optimal. This
test has no false positives. Experiments indicate that false negatives are
rare, and the algorithm has excellent performance in practice. We explain this
phenomenon in terms of the geometry of the triangulation problem.Comment: 14 pages, to appear in the proceedings of the 12th European
Conference of Computer Vision, Firenze, Italy, 7-13 October 201
A Fisher-Rao metric for paracatadioptric images of lines
In a central paracatadioptric imaging system a perspective camera takes an image of a scene reflected in a paraboloidal mirror. A 360° field of view is obtained, but
the image is severely distorted. In particular, straight lines in the scene project to circles in the image. These distortions make it diffcult to detect projected lines using standard image processing algorithms. The distortions are removed using a Fisher-Rao metric which is defined on the space of projected lines in the paracatadioptric image. The space of projected lines is divided into subsets such that on each subset the Fisher-Rao metric is closely approximated by the Euclidean metric. Each subset is sampled at the vertices of a square grid and values are assigned to the sampled points using an adaptation of the trace transform. The result is a set of digital images to which standard image processing algorithms can be applied.
The effectiveness of this approach to line detection is illustrated using two algorithms, both of which are based on the Sobel edge operator. The task of line detection is reduced to the task of finding isolated peaks in a Sobel image. An experimental comparison is made between these two algorithms and third algorithm taken from the literature and
based on the Hough transform
Euclidean Structure from N>=2 Parallel Circles: Theory and Algorithms
International audienceOur problem is that of recovering, in one view, the 2D Euclidean structure, induced by the projections of N parallel circles. This structure is a prerequisite for camera calibration and pose computation. Until now, no general method has been described for N > 2. The main contribution of this work is to state the problem in terms of a system of linear equations to solve.We give a closed-form solution as well as bundle adjustment-like refinements, increasing the technical applicability and numerical stability. Our theoretical approach generalizes and extends all those described in existing works for N = 2 in several respects, as we can treat simultaneously pairs of orthogonal lines and pairs of circles within a unified framework. The proposed algorithm may be easily implemented, using well-known numerical algorithms. Its performance is illustrated by simulations and experiments with real images
Transcriptomic identification of starfish neuropeptide precursors yields new insights into neuropeptide evolution
Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.This work was supported by a PhD studentship funded by QMUL and awarded to D.C.S. and a Leverhulme Trust grant (RPG-
2013-351) awarded to M.R.E. Sequencing of the A. rubens neural transcriptome was funded by an EPSRC grant (EP/J501360/1
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