106 research outputs found
LNCS
We describe an algorithm for segmenting three-dimensional medical imaging data modeled as a continuous function on a 3-manifold. It is related to watershed algorithms developed in image processing but is closer to its mathematical roots, which are Morse theory and homological algebra. It allows for the implicit treatment of an underlying mesh, thus combining the structural integrity of its mathematical foundations with the computational efficiency of image processing
Failure Filtrations for Fenced Sensor Networks
In this paper we consider the question of sensor network coverage for a
2-dimensional domain. We seek to compute the probability that a set of sensors
fails to cover given only non-metric, local (who is talking to whom)
information and a probability distribution of failure of each node. This builds
on the work of de Silva and Ghrist who analyzed this problem in the
deterministic situation. We first show that a it is part of a slightly larger
class of problems which is #P-complete, and thus fast algorithms likely do not
exist unless PNP. We then give a deterministic algorithm which is feasible
in the case of a small set of sensors, and give a dynamic algorithm for an
arbitrary set of sensors failing over time which utilizes a new criterion for
coverage based on the one proposed by de Silva and Ghrist. These algorithms
build on the theory of topological persistence
Geometric Cross-Modal Comparison of Heterogeneous Sensor Data
In this work, we address the problem of cross-modal comparison of aerial data
streams. A variety of simulated automobile trajectories are sensed using two
different modalities: full-motion video, and radio-frequency (RF) signals
received by detectors at various locations. The information represented by the
two modalities is compared using self-similarity matrices (SSMs) corresponding
to time-ordered point clouds in feature spaces of each of these data sources;
we note that these feature spaces can be of entirely different scale and
dimensionality. Several metrics for comparing SSMs are explored, including a
cutting-edge time-warping technique that can simultaneously handle local time
warping and partial matches, while also controlling for the change in geometry
between feature spaces of the two modalities. We note that this technique is
quite general, and does not depend on the choice of modalities. In this
particular setting, we demonstrate that the cross-modal distance between SSMs
corresponding to the same trajectory type is smaller than the cross-modal
distance between SSMs corresponding to distinct trajectory types, and we
formalize this observation via precision-recall metrics in experiments.
Finally, we comment on promising implications of these ideas for future
integration into multiple-hypothesis tracking systems.Comment: 10 pages, 13 figures, Proceedings of IEEE Aeroconf 201
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