24,944 research outputs found
Accurate 3D maps from depth images and motion sensors via nonlinear Kalman filtering
This paper investigates the use of depth images as localisation sensors for
3D map building. The localisation information is derived from the 3D data
thanks to the ICP (Iterative Closest Point) algorithm. The covariance of the
ICP, and thus of the localization error, is analysed, and described by a Fisher
Information Matrix. It is advocated this error can be much reduced if the data
is fused with measurements from other motion sensors, or even with prior
knowledge on the motion. The data fusion is performed by a recently introduced
specific extended Kalman filter, the so-called Invariant EKF, and is directly
based on the estimated covariance of the ICP. The resulting filter is very
natural, and is proved to possess strong properties. Experiments with a Kinect
sensor and a three-axis gyroscope prove clear improvement in the accuracy of
the localization, and thus in the accuracy of the built 3D map.Comment: Submitted to IROS 2012. 8 page
Invariant EKF Design for Scan Matching-aided Localization
Localization in indoor environments is a technique which estimates the
robot's pose by fusing data from onboard motion sensors with readings of the
environment, in our case obtained by scan matching point clouds captured by a
low-cost Kinect depth camera. We develop both an Invariant Extended Kalman
Filter (IEKF)-based and a Multiplicative Extended Kalman Filter (MEKF)-based
solution to this problem. The two designs are successfully validated in
experiments and demonstrate the advantage of the IEKF design
Harmonic Exponential Families on Manifolds
In a range of fields including the geosciences, molecular biology, robotics
and computer vision, one encounters problems that involve random variables on
manifolds. Currently, there is a lack of flexible probabilistic models on
manifolds that are fast and easy to train. We define an extremely flexible
class of exponential family distributions on manifolds such as the torus,
sphere, and rotation groups, and show that for these distributions the gradient
of the log-likelihood can be computed efficiently using a non-commutative
generalization of the Fast Fourier Transform (FFT). We discuss applications to
Bayesian camera motion estimation (where harmonic exponential families serve as
conjugate priors), and modelling of the spatial distribution of earthquakes on
the surface of the earth. Our experimental results show that harmonic densities
yield a significantly higher likelihood than the best competing method, while
being orders of magnitude faster to train.Comment: fixed typ
Interest communities and flow roles in directed networks: the Twitter network of the UK riots
Directionality is a crucial ingredient in many complex networks in which
information, energy or influence are transmitted. In such directed networks,
analysing flows (and not only the strength of connections) is crucial to reveal
important features of the network that might go undetected if the orientation
of connections is ignored. We showcase here a flow-based approach for community
detection in networks through the study of the network of the most influential
Twitter users during the 2011 riots in England. Firstly, we use directed Markov
Stability to extract descriptions of the network at different levels of
coarseness in terms of interest communities, i.e., groups of nodes within which
flows of information are contained and reinforced. Such interest communities
reveal user groupings according to location, profession, employer, and topic.
The study of flows also allows us to generate an interest distance, which
affords a personalised view of the attention in the network as viewed from the
vantage point of any given user. Secondly, we analyse the profiles of incoming
and outgoing long-range flows with a combined approach of role-based similarity
and the novel relaxed minimum spanning tree algorithm to reveal that the users
in the network can be classified into five roles. These flow roles go beyond
the standard leader/follower dichotomy and differ from classifications based on
regular/structural equivalence. We then show that the interest communities fall
into distinct informational organigrams characterised by a different mix of
user roles reflecting the quality of dialogue within them. Our generic
framework can be used to provide insight into how flows are generated,
distributed, preserved and consumed in directed networks.Comment: 32 pages, 14 figures. Supplementary Spreadsheet available from:
http://www2.imperial.ac.uk/~mbegueri/Docs/riotsCommunities.zip or
http://rsif.royalsocietypublishing.org/content/11/101/20140940/suppl/DC
On the experimental verification of quantum complexity in linear optics
The first quantum technologies to solve computational problems that are
beyond the capabilities of classical computers are likely to be devices that
exploit characteristics inherent to a particular physical system, to tackle a
bespoke problem suited to those characteristics. Evidence implies that the
detection of ensembles of photons, which have propagated through a linear
optical circuit, is equivalent to sampling from a probability distribution that
is intractable to classical simulation. However, it is probable that the
complexity of this type of sampling problem means that its solution is
classically unverifiable within a feasible number of trials, and the task of
establishing correct operation becomes one of gathering sufficiently convincing
circumstantial evidence. Here, we develop scalable methods to experimentally
establish correct operation for this class of sampling algorithm, which we
implement with two different types of optical circuits for 3, 4, and 5 photons,
on Hilbert spaces of up to 50,000 dimensions. With only a small number of
trials, we establish a confidence >99% that we are not sampling from a uniform
distribution or a classical distribution, and we demonstrate a unitary specific
witness that functions robustly for small amounts of data. Like the algorithmic
operations they endorse, our methods exploit the characteristics native to the
quantum system in question. Here we observe and make an application of a
"bosonic clouding" phenomenon, interesting in its own right, where photons are
found in local groups of modes superposed across two locations. Our broad
approach is likely to be practical for all architectures for quantum
technologies where formal verification methods for quantum algorithms are
either intractable or unknown.Comment: Comments welcom
Community detection and role identification in directed networks: understanding the Twitter network of the care.data debate
With the rise of social media as an important channel for the debate and discussion of public affairs, online social networks such as Twitter have become important platforms for public information and engagement by policy makers. To communicate effectively through Twitter, policy makers need to understand how influence and interest propagate within its network of users. In this chapter we use graph-theoretic methods to analyse the Twitter debate surrounding NHS Englands controversial care.data scheme. Directionality is a crucial feature of the Twitter social graph - information flows from the followed to the followers - but is often ignored in social network analyses; our methods are based on the behaviour of dynamic processes on the network and can be applied naturally to directed networks. We uncover robust communities of users and show that these communities reflect how information flows through the Twitter network. We are also able to classify users by their differing roles in directing the flow of information through the network. Our methods and results will be useful to policy makers who would like to use Twitter effectively as a communication medium
Computation of Light Scattering in Young Stellar Objects
A Monte Carlo light scattering code incorporating aligned non-spherical
particles is described. The major effects on the flux distribution, linear
polarisation and circular polarisation are presented, with emphasis on the
application to Young Stellar Objects (YSOs). The need for models with
non-spherical particles in order to successfully model polarisation data is
reviewed. The ability of this type of model to map magnetic field structure in
embedded YSOs is described. The possible application to the question of the
origin of biomolecular homochirality via UV circular polarisation in star
forming regions is also briefly discussed.Comment: Accepted by The Journal of Quantitative Spectroscopy and Radiative
Transfer. Replaced version corrects an error in the definition of the sense
of Cpol in the published version and other minor errors found at the proof
stag
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