68,667 research outputs found
Approximating Dynamic Time Warping and Edit Distance for a Pair of Point Sequences
We give the first subquadratic-time approximation schemes for dynamic time
warping (DTW) and edit distance (ED) of several natural families of point
sequences in , for any fixed . In particular, our
algorithms compute -approximations of DTW and ED in time
near-linear for point sequences drawn from k-packed or k-bounded curves, and
subquadratic for backbone sequences. Roughly speaking, a curve is
-packed if the length of its intersection with any ball of radius
is at most , and a curve is -bounded if the sub-curve
between two curve points does not go too far from the two points compared to
the distance between the two points. In backbone sequences, consecutive points
are spaced at approximately equal distances apart, and no two points lie very
close together. Recent results suggest that a subquadratic algorithm for DTW or
ED is unlikely for an arbitrary pair of point sequences even for . Our
algorithms work by constructing a small set of rectangular regions that cover
the entries of the dynamic programming table commonly used for these distance
measures. The weights of entries inside each rectangle are roughly the same, so
we are able to use efficient procedures to approximately compute the cheapest
paths through these rectangles
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
Geometric Approach to Digital Quantum Information
We present geometric methods for uniformly discretizing the continuous
N-qubit Hilbert space. When considered as the vertices of a geometrical figure,
the resulting states form the equivalent of a Platonic solid. The
discretization technique inherently describes a class of pi/2 rotations that
connect neighboring states in the set, i.e. that leave the geometrical figures
invariant. These rotations are shown to generate the Clifford group, a general
group of discrete transformations on N qubits. Discretizing the N-qubit Hilbert
space allows us to define its digital quantum information content, and we show
that this information content grows as N^2. While we believe the discrete sets
are interesting because they allow extra-classical behavior--such as quantum
entanglement and quantum parallelism--to be explored while circumventing the
continuity of Hilbert space, we also show how they may be a useful tool for
problems in traditional quantum computation. We describe in detail the discrete
sets for one and two qubits.Comment: Introduction rewritten; 'Sample Application' section added. To appear
in J. of Quantum Information Processin
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