11,035 research outputs found
Feature Lines for Illustrating Medical Surface Models: Mathematical Background and Survey
This paper provides a tutorial and survey for a specific kind of illustrative
visualization technique: feature lines. We examine different feature line
methods. For this, we provide the differential geometry behind these concepts
and adapt this mathematical field to the discrete differential geometry. All
discrete differential geometry terms are explained for triangulated surface
meshes. These utilities serve as basis for the feature line methods. We provide
the reader with all knowledge to re-implement every feature line method.
Furthermore, we summarize the methods and suggest a guideline for which kind of
surface which feature line algorithm is best suited. Our work is motivated by,
but not restricted to, medical and biological surface models.Comment: 33 page
The Filament Sensor for Near Real-Time Detection of Cytoskeletal Fiber Structures
A reliable extraction of filament data from microscopic images is of high
interest in the analysis of acto-myosin structures as early morphological
markers in mechanically guided differentiation of human mesenchymal stem cells
and the understanding of the underlying fiber arrangement processes. In this
paper, we propose the filament sensor (FS), a fast and robust processing
sequence which detects and records location, orientation, length and width for
each single filament of an image, and thus allows for the above described
analysis. The extraction of these features has previously not been possible
with existing methods. We evaluate the performance of the proposed FS in terms
of accuracy and speed in comparison to three existing methods with respect to
their limited output. Further, we provide a benchmark dataset of real cell
images along with filaments manually marked by a human expert as well as
simulated benchmark images. The FS clearly outperforms existing methods in
terms of computational runtime and filament extraction accuracy. The
implementation of the FS and the benchmark database are available as open
source.Comment: 32 pages, 21 figure
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
PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures
Persistence diagrams, the most common descriptors of Topological Data
Analysis, encode topological properties of data and have already proved pivotal
in many different applications of data science. However, since the (metric)
space of persistence diagrams is not Hilbert, they end up being difficult
inputs for most Machine Learning techniques. To address this concern, several
vectorization methods have been put forward that embed persistence diagrams
into either finite-dimensional Euclidean space or (implicit) infinite
dimensional Hilbert space with kernels. In this work, we focus on persistence
diagrams built on top of graphs. Relying on extended persistence theory and the
so-called heat kernel signature, we show how graphs can be encoded by
(extended) persistence diagrams in a provably stable way. We then propose a
general and versatile framework for learning vectorizations of persistence
diagrams, which encompasses most of the vectorization techniques used in the
literature. We finally showcase the experimental strength of our setup by
achieving competitive scores on classification tasks on real-life graph
datasets
Metaplex networks: influence of the exo-endo structure of complex systems on diffusion
In a complex system the interplay between the internal structure of its
entities and their interconnection may play a fundamental role in the global
functioning of the system. Here, we define the concept of metaplex, which
describes such trade-off between internal structure of entities and their
interconnections. We then define a dynamical system on a metaplex and study
diffusive processes on them. We provide analytical and computational evidences
about the role played by the size of the nodes, the location of the internal
coupling areas, and the strength and range of the coupling between the nodes on
the global dynamics of metaplexes. Finally, we extend our analysis to two
real-world metaplexes: a landscape and a brain metaplex. We corroborate that
the internal structure of the nodes in a metaplex may dominate the global
dynamics (brain metaplex) or play a regulatory role (landscape metaplex) to the
influence of the interconnection between nodes.Comment: 28 pages, 19 figure
Constraints on higher-dimensional gravity from the cosmic shear three-point correlation function
With the developments of large galaxy surveys or cosmic shear surveys it is
now possible to map the dark matter distribution at truly cosmological scales.
Detailed examinations of the statistical properties of the dark matter
distribution reveal the detail of the large-scale structure growth of the
Universe. In particular it is shown here that the behavior of the density field
bi-spectrum is sensitive to departure from normal gravity in a way which
depends only weakly on the background evolution. The cosmic shear bispectrum
appears to be particularly sensitive to changes in the Poisson equation: we
show that the current cosmic shear data can already be used to infer
constraints on the scale of a possible higher-dimensional gravity, above 2
h^{-1}Mpc.Comment: 5 pages, 3 figures, submitted to PR
Sparse reduced-rank regression for imaging genetics studies: models and applications
We present a novel statistical technique; the sparse reduced rank regression (sRRR) model
which is a strategy for multivariate modelling of high-dimensional imaging responses and
genetic predictors. By adopting penalisation techniques, the model is able to enforce sparsity
in the regression coefficients, identifying subsets of genetic markers that best explain
the variability observed in subsets of the phenotypes. To properly exploit the rich structure
present in each of the imaging and genetics domains, we additionally propose the use of
several structured penalties within the sRRR model. Using simulation procedures that accurately
reflect realistic imaging genetics data, we present detailed evaluations of the sRRR
method in comparison with the more traditional univariate linear modelling approach. In
all settings considered, we show that sRRR possesses better power to detect the deleterious
genetic variants. Moreover, using a simple genetic model, we demonstrate the potential
benefits, in terms of statistical power, of carrying out voxel-wise searches as opposed to
extracting averages over regions of interest in the brain. Since this entails the use of phenotypic
vectors of enormous dimensionality, we suggest the use of a sparse classification
model as a de-noising step, prior to the imaging genetics study. Finally, we present the
application of a data re-sampling technique within the sRRR model for model selection.
Using this approach we are able to rank the genetic markers in order of importance of association
to the phenotypes, and similarly rank the phenotypes in order of importance to
the genetic markers. In the very end, we illustrate the application perspective of the proposed
statistical models in three real imaging genetics datasets and highlight some potential
associations
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