3,977 research outputs found
Construction of and efficient sampling from the simplicial configuration model
Simplicial complexes are now a popular alternative to networks when it comes
to describing the structure of complex systems, primarily because they encode
multi-node interactions explicitly. With this new description comes the need
for principled null models that allow for easy comparison with empirical data.
We propose a natural candidate, the simplicial configuration model. The core of
our contribution is an efficient and uniform Markov chain Monte Carlo sampler
for this model. We demonstrate its usefulness in a short case study by
investigating the topology of three real systems and their randomized
counterparts (using their Betti numbers). For two out of three systems, the
model allows us to reject the hypothesis that there is no organization beyond
the local scale.Comment: 6 pages, 4 figure
Extrinsic Parameter Calibration for Line Scanning Cameras on Ground Vehicles with Navigation Systems Using a Calibration Pattern
Line scanning cameras, which capture only a single line of pixels, have been
increasingly used in ground based mobile or robotic platforms. In applications
where it is advantageous to directly georeference the camera data to world
coordinates, an accurate estimate of the camera's 6D pose is required. This
paper focuses on the common case where a mobile platform is equipped with a
rigidly mounted line scanning camera, whose pose is unknown, and a navigation
system providing vehicle body pose estimates. We propose a novel method that
estimates the camera's pose relative to the navigation system. The approach
involves imaging and manually labelling a calibration pattern with distinctly
identifiable points, triangulating these points from camera and navigation
system data and reprojecting them in order to compute a likelihood, which is
maximised to estimate the 6D camera pose. Additionally, a Markov Chain Monte
Carlo (MCMC) algorithm is used to estimate the uncertainty of the offset.
Tested on two different platforms, the method was able to estimate the pose to
within 0.06 m / 1.05 and 0.18 m / 2.39. We also propose
several approaches to displaying and interpreting the 6D results in a human
readable way.Comment: Published in MDPI Sensors, 30 October 201
Bayesian matching of unlabelled point sets using Procrustes and configuration models
The problem of matching unlabelled point sets using Bayesian inference is
considered. Two recently proposed models for the likelihood are compared, based
on the Procrustes size-and-shape and the full configuration. Bayesian inference
is carried out for matching point sets using Markov chain Monte Carlo
simulation. An improvement to the existing Procrustes algorithm is proposed
which improves convergence rates, using occasional large jumps in the burn-in
period. The Procrustes and configuration methods are compared in a simulation
study and using real data, where it is of interest to estimate the strengths of
matches between protein binding sites. The performance of both methods is
generally quite similar, and a connection between the two models is made using
a Laplace approximation
Approximate Bayesian Computation by Subset Simulation
A new Approximate Bayesian Computation (ABC) algorithm for Bayesian updating
of model parameters is proposed in this paper, which combines the ABC
principles with the technique of Subset Simulation for efficient rare-event
simulation, first developed in S.K. Au and J.L. Beck [1]. It has been named
ABC- SubSim. The idea is to choose the nested decreasing sequence of regions in
Subset Simulation as the regions that correspond to increasingly closer
approximations of the actual data vector in observation space. The efficiency
of the algorithm is demonstrated in two examples that illustrate some of the
challenges faced in real-world applications of ABC. We show that the proposed
algorithm outperforms other recent sequential ABC algorithms in terms of
computational efficiency while achieving the same, or better, measure of ac-
curacy in the posterior distribution. We also show that ABC-SubSim readily
provides an estimate of the evidence (marginal likelihood) for posterior model
class assessment, as a by-product
Robust Estimation of 3D Human Poses from a Single Image
Human pose estimation is a key step to action recognition. We propose a
method of estimating 3D human poses from a single image, which works in
conjunction with an existing 2D pose/joint detector. 3D pose estimation is
challenging because multiple 3D poses may correspond to the same 2D pose after
projection due to the lack of depth information. Moreover, current 2D pose
estimators are usually inaccurate which may cause errors in the 3D estimation.
We address the challenges in three ways: (i) We represent a 3D pose as a linear
combination of a sparse set of bases learned from 3D human skeletons. (ii) We
enforce limb length constraints to eliminate anthropomorphically implausible
skeletons. (iii) We estimate a 3D pose by minimizing the -norm error
between the projection of the 3D pose and the corresponding 2D detection. The
-norm loss term is robust to inaccurate 2D joint estimations. We use the
alternating direction method (ADM) to solve the optimization problem
efficiently. Our approach outperforms the state-of-the-arts on three benchmark
datasets
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