1,280 research outputs found
Probabilistic Solutions to Differential Equations and their Application to Riemannian Statistics
We study a probabilistic numerical method for the solution of both boundary
and initial value problems that returns a joint Gaussian process posterior over
the solution. Such methods have concrete value in the statistics on Riemannian
manifolds, where non-analytic ordinary differential equations are involved in
virtually all computations. The probabilistic formulation permits marginalising
the uncertainty of the numerical solution such that statistics are less
sensitive to inaccuracies. This leads to new Riemannian algorithms for mean
value computations and principal geodesic analysis. Marginalisation also means
results can be less precise than point estimates, enabling a noticeable
speed-up over the state of the art. Our approach is an argument for a wider
point that uncertainty caused by numerical calculations should be tracked
throughout the pipeline of machine learning algorithms.Comment: 11 page (9 page conference paper, plus supplements
Geometry-aware Manipulability Learning, Tracking and Transfer
Body posture influences human and robots performance in manipulation tasks,
as appropriate poses facilitate motion or force exertion along different axes.
In robotics, manipulability ellipsoids arise as a powerful descriptor to
analyze, control and design the robot dexterity as a function of the
articulatory joint configuration. This descriptor can be designed according to
different task requirements, such as tracking a desired position or apply a
specific force. In this context, this paper presents a novel
\emph{manipulability transfer} framework, a method that allows robots to learn
and reproduce manipulability ellipsoids from expert demonstrations. The
proposed learning scheme is built on a tensor-based formulation of a Gaussian
mixture model that takes into account that manipulability ellipsoids lie on the
manifold of symmetric positive definite matrices. Learning is coupled with a
geometry-aware tracking controller allowing robots to follow a desired profile
of manipulability ellipsoids. Extensive evaluations in simulation with
redundant manipulators, a robotic hand and humanoids agents, as well as an
experiment with two real dual-arm systems validate the feasibility of the
approach.Comment: Accepted for publication in the Intl. Journal of Robotics Research
(IJRR). Website: https://sites.google.com/view/manipulability. Code:
https://github.com/NoemieJaquier/Manipulability. 24 pages, 20 figures, 3
tables, 4 appendice
Comparative Evaluation of Action Recognition Methods via Riemannian Manifolds, Fisher Vectors and GMMs: Ideal and Challenging Conditions
We present a comparative evaluation of various techniques for action
recognition while keeping as many variables as possible controlled. We employ
two categories of Riemannian manifolds: symmetric positive definite matrices
and linear subspaces. For both categories we use their corresponding nearest
neighbour classifiers, kernels, and recent kernelised sparse representations.
We compare against traditional action recognition techniques based on Gaussian
mixture models and Fisher vectors (FVs). We evaluate these action recognition
techniques under ideal conditions, as well as their sensitivity in more
challenging conditions (variations in scale and translation). Despite recent
advancements for handling manifolds, manifold based techniques obtain the
lowest performance and their kernel representations are more unstable in the
presence of challenging conditions. The FV approach obtains the highest
accuracy under ideal conditions. Moreover, FV best deals with moderate scale
and translation changes
Human Detection and Tracking for Video Surveillance A Cognitive Science Approach
With crimes on the rise all around the world, video surveillance is becoming
more important day by day. Due to the lack of human resources to monitor this
increasing number of cameras manually new computer vision algorithms to perform
lower and higher level tasks are being developed. We have developed a new
method incorporating the most acclaimed Histograms of Oriented Gradients the
theory of Visual Saliency and the saliency prediction model Deep Multi Level
Network to detect human beings in video sequences. Furthermore we implemented
the k Means algorithm to cluster the HOG feature vectors of the positively
detected windows and determined the path followed by a person in the video. We
achieved a detection precision of 83.11% and a recall of 41.27%. We obtained
these results 76.866 times faster than classification on normal images.Comment: ICCV 2017 Venice, Italy Pages 5 Figures
Log-Euclidean Bag of Words for Human Action Recognition
Representing videos by densely extracted local space-time features has
recently become a popular approach for analysing actions. In this paper, we
tackle the problem of categorising human actions by devising Bag of Words (BoW)
models based on covariance matrices of spatio-temporal features, with the
features formed from histograms of optical flow. Since covariance matrices form
a special type of Riemannian manifold, the space of Symmetric Positive Definite
(SPD) matrices, non-Euclidean geometry should be taken into account while
discriminating between covariance matrices. To this end, we propose to embed
SPD manifolds to Euclidean spaces via a diffeomorphism and extend the BoW
approach to its Riemannian version. The proposed BoW approach takes into
account the manifold geometry of SPD matrices during the generation of the
codebook and histograms. Experiments on challenging human action datasets show
that the proposed method obtains notable improvements in discrimination
accuracy, in comparison to several state-of-the-art methods
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Statistical Learning in Wasserstein Space
We seek a generalization of regression and principle component analysis (PCA) in a metric space where data points are distributions metrized by the Wasserstein metric. We recast these analyses as multimarginal optimal transport problems. The particular formulation allows efficient computation, ensures existence of optimal solutions, and admits a probabilistic interpretation over the space of paths (line segments). Application of the theory to the interpolation of empirical distributions, images, power spectra, as well as assessing uncertainty in experimental designs, is envisioned
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