439 research outputs found
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
Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
Dynamic mode decomposition (DMD) provides a practical means of extracting
insightful dynamical information from fluids datasets. Like any data processing
technique, DMD's usefulness is limited by its ability to extract real and
accurate dynamical features from noise-corrupted data. Here we show
analytically that DMD is biased to sensor noise, and quantify how this bias
depends on the size and noise level of the data. We present three modifications
to DMD that can be used to remove this bias: (i) a direct correction of the
identified bias using known noise properties, (ii) combining the results of
performing DMD forwards and backwards in time, and (iii) a total
least-squares-inspired algorithm. We discuss the relative merits of each
algorithm, and demonstrate the performance of these modifications on a range of
synthetic, numerical, and experimental datasets. We further compare our
modified DMD algorithms with other variants proposed in recent literature
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