164 research outputs found
Beyond Gauss: Image-Set Matching on the Riemannian Manifold of PDFs
State-of-the-art image-set matching techniques typically implicitly model
each image-set with a Gaussian distribution. Here, we propose to go beyond
these representations and model image-sets as probability distribution
functions (PDFs) using kernel density estimators. To compare and match
image-sets, we exploit Csiszar f-divergences, which bear strong connections to
the geodesic distance defined on the space of PDFs, i.e., the statistical
manifold. Furthermore, we introduce valid positive definite kernels on the
statistical manifolds, which let us make use of more powerful classification
schemes to match image-sets. Finally, we introduce a supervised dimensionality
reduction technique that learns a latent space where f-divergences reflect the
class labels of the data. Our experiments on diverse problems, such as
video-based face recognition and dynamic texture classification, evidence the
benefits of our approach over the state-of-the-art image-set matching methods
Efficient Clustering on Riemannian Manifolds: A Kernelised Random Projection Approach
Reformulating computer vision problems over Riemannian manifolds has
demonstrated superior performance in various computer vision applications. This
is because visual data often forms a special structure lying on a lower
dimensional space embedded in a higher dimensional space. However, since these
manifolds belong to non-Euclidean topological spaces, exploiting their
structures is computationally expensive, especially when one considers the
clustering analysis of massive amounts of data. To this end, we propose an
efficient framework to address the clustering problem on Riemannian manifolds.
This framework implements random projections for manifold points via kernel
space, which can preserve the geometric structure of the original space, but is
computationally efficient. Here, we introduce three methods that follow our
framework. We then validate our framework on several computer vision
applications by comparing against popular clustering methods on Riemannian
manifolds. Experimental results demonstrate that our framework maintains the
performance of the clustering whilst massively reducing computational
complexity by over two orders of magnitude in some cases
Image patch analysis of sunspots and active regions. II. Clustering via matrix factorization
Separating active regions that are quiet from potentially eruptive ones is a
key issue in Space Weather applications. Traditional classification schemes
such as Mount Wilson and McIntosh have been effective in relating an active
region large scale magnetic configuration to its ability to produce eruptive
events. However, their qualitative nature prevents systematic studies of an
active region's evolution for example. We introduce a new clustering of active
regions that is based on the local geometry observed in Line of Sight
magnetogram and continuum images. We use a reduced-dimension representation of
an active region that is obtained by factoring the corresponding data matrix
comprised of local image patches. Two factorizations can be compared via the
definition of appropriate metrics on the resulting factors. The distances
obtained from these metrics are then used to cluster the active regions. We
find that these metrics result in natural clusterings of active regions. The
clusterings are related to large scale descriptors of an active region such as
its size, its local magnetic field distribution, and its complexity as measured
by the Mount Wilson classification scheme. We also find that including data
focused on the neutral line of an active region can result in an increased
correspondence between our clustering results and other active region
descriptors such as the Mount Wilson classifications and the value. We
provide some recommendations for which metrics, matrix factorization
techniques, and regions of interest to use to study active regions.Comment: Accepted for publication in the Journal of Space Weather and Space
Climate (SWSC). 33 pages, 12 figure
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