26,505 research outputs found
The Topology ToolKit
This system paper presents the Topology ToolKit (TTK), a software platform
designed for topological data analysis in scientific visualization. TTK
provides a unified, generic, efficient, and robust implementation of key
algorithms for the topological analysis of scalar data, including: critical
points, integral lines, persistence diagrams, persistence curves, merge trees,
contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots,
Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due
to a tight integration with ParaView. It is also easily accessible to
developers through a variety of bindings (Python, VTK/C++) for fast prototyping
or through direct, dependence-free, C++, to ease integration into pre-existing
complex systems. While developing TTK, we faced several algorithmic and
software engineering challenges, which we document in this paper. In
particular, we present an algorithm for the construction of a discrete gradient
that complies to the critical points extracted in the piecewise-linear setting.
This algorithm guarantees a combinatorial consistency across the topological
abstractions supported by TTK, and importantly, a unified implementation of
topological data simplification for multi-scale exploration and analysis. We
also present a cached triangulation data structure, that supports time
efficient and generic traversals, which self-adjusts its memory usage on demand
for input simplicial meshes and which implicitly emulates a triangulation for
regular grids with no memory overhead. Finally, we describe an original
software architecture, which guarantees memory efficient and direct accesses to
TTK features, while still allowing for researchers powerful and easy bindings
and extensions. TTK is open source (BSD license) and its code, online
documentation and video tutorials are available on TTK's website
Analysis of the contour structural irregularity of skin lesions using wavelet decomposition
The boundary irregularity of skin lesions is of clinical significance for the early detection of
malignant melanomas and to distinguish them from other lesions such as benign moles. The
structural components of the contour are of particular importance. To extract the structure from
the contour, wavelet decomposition was used as these components tend to locate in the lower
frequency sub-bands. Lesion contours were modeled as signatures with scale normalization to
give position and frequency resolution invariance. Energy distributions among different wavelet
sub-bands were then analyzed to extract those with significant levels and differences to enable
maximum discrimination.
Based on the coefficients in the significant sub-bands, structural components from the original
contours were modeled, and a set of statistical and geometric irregularity descriptors researched
that were applied at each of the significant sub-bands. The effectiveness of the descriptors was
measured using the Hausdorff distance between sets of data from melanoma and mole contours.
The best descriptor outputs were input to a back projection neural network to construct a
combined classifier system. Experimental results showed that thirteen features from four
sub-bands produced the best discrimination between sets of melanomas and moles, and that a
small training set of nine melanomas and nine moles was optimum
Task-based Augmented Contour Trees with Fibonacci Heaps
This paper presents a new algorithm for the fast, shared memory, multi-core
computation of augmented contour trees on triangulations. In contrast to most
existing parallel algorithms our technique computes augmented trees, enabling
the full extent of contour tree based applications including data segmentation.
Our approach completely revisits the traditional, sequential contour tree
algorithm to re-formulate all the steps of the computation as a set of
independent local tasks. This includes a new computation procedure based on
Fibonacci heaps for the join and split trees, two intermediate data structures
used to compute the contour tree, whose constructions are efficiently carried
out concurrently thanks to the dynamic scheduling of task parallelism. We also
introduce a new parallel algorithm for the combination of these two trees into
the output global contour tree. Overall, this results in superior time
performance in practice, both in sequential and in parallel thanks to the
OpenMP task runtime. We report performance numbers that compare our approach to
reference sequential and multi-threaded implementations for the computation of
augmented merge and contour trees. These experiments demonstrate the run-time
efficiency of our approach and its scalability on common workstations. We
demonstrate the utility of our approach in data segmentation applications
Director Field Model of the Primary Visual Cortex for Contour Detection
We aim to build the simplest possible model capable of detecting long, noisy
contours in a cluttered visual scene. For this, we model the neural dynamics in
the primate primary visual cortex in terms of a continuous director field that
describes the average rate and the average orientational preference of active
neurons at a particular point in the cortex. We then use a linear-nonlinear
dynamical model with long range connectivity patterns to enforce long-range
statistical context present in the analyzed images. The resulting model has
substantially fewer degrees of freedom than traditional models, and yet it can
distinguish large contiguous objects from the background clutter by suppressing
the clutter and by filling-in occluded elements of object contours. This
results in high-precision, high-recall detection of large objects in cluttered
scenes. Parenthetically, our model has a direct correspondence with the Landau
- de Gennes theory of nematic liquid crystal in two dimensions.Comment: 9 pages, 7 figure
NonAbelian Vortices, Large Winding Limits and Aharonov-Bohm Effects
Remarkable simplification arises from considering vortex equations in the
large winding limit. This was recently used in [1] to display all sorts of
vortex zeromodes, the orientational, translational, fermionic as well as
semi-local, and to relate them to the apparently distinct phenomena of the
Nielsen-Olesen-Ambjorn magnetic instabilities. Here we extend these analyses to
more general types of BPS nonAbelian vortices, taking as a prototype a system
with gauged U(1) x SU(N) x SU(N) symmetry where the VEV of charged scalar
fields in the bifundamental representation breaks the symmetry to SU(N)_{l+r} .
The presence of the massless SU(N)_{l+r} gauge fields in 4D bulk introduces all
sorts of non-local, topological phenomena such as the nonAbelian Aharonov-Bohm
effects, which in the theory with global SU(N)_r group (g_r=0) are washed away
by the strongly fluctuating orientational zeromodes in the worldsheet. Physics
changes qualitatively at the moment the right gauge coupling constant g_r is
turned on.Comment: 31 pages, 4 figure
- âŠ