2,491 research outputs found
Robust Temporally Coherent Laplacian Protrusion Segmentation of 3D Articulated Bodies
In motion analysis and understanding it is important to be able to fit a
suitable model or structure to the temporal series of observed data, in order
to describe motion patterns in a compact way, and to discriminate between them.
In an unsupervised context, i.e., no prior model of the moving object(s) is
available, such a structure has to be learned from the data in a bottom-up
fashion. In recent times, volumetric approaches in which the motion is captured
from a number of cameras and a voxel-set representation of the body is built
from the camera views, have gained ground due to attractive features such as
inherent view-invariance and robustness to occlusions. Automatic, unsupervised
segmentation of moving bodies along entire sequences, in a temporally-coherent
and robust way, has the potential to provide a means of constructing a
bottom-up model of the moving body, and track motion cues that may be later
exploited for motion classification. Spectral methods such as locally linear
embedding (LLE) can be useful in this context, as they preserve "protrusions",
i.e., high-curvature regions of the 3D volume, of articulated shapes, while
improving their separation in a lower dimensional space, making them in this
way easier to cluster. In this paper we therefore propose a spectral approach
to unsupervised and temporally-coherent body-protrusion segmentation along time
sequences. Volumetric shapes are clustered in an embedding space, clusters are
propagated in time to ensure coherence, and merged or split to accommodate
changes in the body's topology. Experiments on both synthetic and real
sequences of dense voxel-set data are shown. This supports the ability of the
proposed method to cluster body-parts consistently over time in a totally
unsupervised fashion, its robustness to sampling density and shape quality, and
its potential for bottom-up model constructionComment: 31 pages, 26 figure
Compact Hash Codes for Efficient Visual Descriptors Retrieval in Large Scale Databases
In this paper we present an efficient method for visual descriptors retrieval
based on compact hash codes computed using a multiple k-means assignment. The
method has been applied to the problem of approximate nearest neighbor (ANN)
search of local and global visual content descriptors, and it has been tested
on different datasets: three large scale public datasets of up to one billion
descriptors (BIGANN) and, supported by recent progress in convolutional neural
networks (CNNs), also on the CIFAR-10 and MNIST datasets. Experimental results
show that, despite its simplicity, the proposed method obtains a very high
performance that makes it superior to more complex state-of-the-art methods
OL\'E: Orthogonal Low-rank Embedding, A Plug and Play Geometric Loss for Deep Learning
Deep neural networks trained using a softmax layer at the top and the
cross-entropy loss are ubiquitous tools for image classification. Yet, this
does not naturally enforce intra-class similarity nor inter-class margin of the
learned deep representations. To simultaneously achieve these two goals,
different solutions have been proposed in the literature, such as the pairwise
or triplet losses. However, such solutions carry the extra task of selecting
pairs or triplets, and the extra computational burden of computing and learning
for many combinations of them. In this paper, we propose a plug-and-play loss
term for deep networks that explicitly reduces intra-class variance and
enforces inter-class margin simultaneously, in a simple and elegant geometric
manner. For each class, the deep features are collapsed into a learned linear
subspace, or union of them, and inter-class subspaces are pushed to be as
orthogonal as possible. Our proposed Orthogonal Low-rank Embedding (OL\'E) does
not require carefully crafting pairs or triplets of samples for training, and
works standalone as a classification loss, being the first reported deep metric
learning framework of its kind. Because of the improved margin between features
of different classes, the resulting deep networks generalize better, are more
discriminative, and more robust. We demonstrate improved classification
performance in general object recognition, plugging the proposed loss term into
existing off-the-shelf architectures. In particular, we show the advantage of
the proposed loss in the small data/model scenario, and we significantly
advance the state-of-the-art on the Stanford STL-10 benchmark
Ambitoric geometry II: Extremal toric surfaces and Einstein 4-orbifolds
We provide an explicit resolution of the existence problem for extremal
Kaehler metrics on toric 4-orbifolds M with second Betti number b2(M)=2. More
precisely we show that M admits such a metric if and only if its rational
Delzant polytope (which is a labelled quadrilateral) is K-polystable in the
relative, toric sense (as studied by S. Donaldson, E. Legendre, G. Szekelyhidi
et al.). Furthermore, in this case, the extremal Kaehler metric is ambitoric,
i.e., compatible with a conformally equivalent, oppositely oriented toric
Kaehler metric, which turns out to be extremal as well. These results provide a
computational test for the K-stability of labelled quadrilaterals.
Extremal ambitoric structures were classified locally in Part I of this work,
but herein we only use the straightforward fact that explicit Kaehler metrics
obtained there are extremal, and the identification of Bach-flat (conformally
Einstein) examples among them. Using our global results, the latter yield
countably infinite families of compact toric Bach-flat Kaehler orbifolds,
including examples which are globally conformally Einstein, and examples which
are conformal to complete smooth Einstein metrics on an open subset, thus
extending the work of many authors.Comment: 31 pages, 3 figures, partially replaces and extends arXiv:1010.099
Point configurations that are asymmetric yet balanced
A configuration of particles confined to a sphere is balanced if it is in
equilibrium under all force laws (that act between pairs of points with
strength given by a fixed function of distance). It is straightforward to show
that every sufficiently symmetrical configuration is balanced, but the converse
is far from obvious. In 1957 Leech completely classified the balanced
configurations in R^3, and his classification is equivalent to the converse for
R^3. In this paper we disprove the converse in high dimensions. We construct
several counterexamples, including one with trivial symmetry group.Comment: 10 page
Point configurations that are asymmetric yet balanced
A configuration of particles confined to a sphere is balanced if it is in
equilibrium under all force laws (that act between pairs of points with
strength given by a fixed function of distance). It is straightforward to show
that every sufficiently symmetrical configuration is balanced, but the converse
is far from obvious. In 1957 Leech completely classified the balanced
configurations in R^3, and his classification is equivalent to the converse for
R^3. In this paper we disprove the converse in high dimensions. We construct
several counterexamples, including one with trivial symmetry group.Comment: 10 page
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