1,027 research outputs found
Analysis of Amoeba Active Contours
Subject of this paper is the theoretical analysis of structure-adaptive
median filter algorithms that approximate curvature-based PDEs for image
filtering and segmentation. These so-called morphological amoeba filters are
based on a concept introduced by Lerallut et al. They achieve similar results
as the well-known geodesic active contour and self-snakes PDEs. In the present
work, the PDE approximated by amoeba active contours is derived for a general
geometric situation and general amoeba metric. This PDE is structurally similar
but not identical to the geodesic active contour equation. It reproduces the
previous PDE approximation results for amoeba median filters as special cases.
Furthermore, modifications of the basic amoeba active contour algorithm are
analysed that are related to the morphological force terms frequently used with
geodesic active contours. Experiments demonstrate the basic behaviour of amoeba
active contours and its similarity to geodesic active contours.Comment: Revised version with several improvements for clarity, slightly
extended experiments and discussion. Accepted for publication in Journal of
Mathematical Imaging and Visio
Deep Neural Network and Data Augmentation Methodology for off-axis iris segmentation in wearable headsets
A data augmentation methodology is presented and applied to generate a large
dataset of off-axis iris regions and train a low-complexity deep neural
network. Although of low complexity the resulting network achieves a high level
of accuracy in iris region segmentation for challenging off-axis eye-patches.
Interestingly, this network is also shown to achieve high levels of performance
for regular, frontal, segmentation of iris regions, comparing favorably with
state-of-the-art techniques of significantly higher complexity. Due to its
lower complexity, this network is well suited for deployment in embedded
applications such as augmented and mixed reality headsets
Phase transitions during fruiting body formation in Myxococcus xanthus
The formation of a collectively moving group benefits individuals within a
population in a variety of ways such as ultra-sensitivity to perturbation,
collective modes of feeding, and protection from environmental stress. While
some collective groups use a single organizing principle, others can
dynamically shift the behavior of the group by modifying the interaction rules
at the individual level. The surface-dwelling bacterium Myxococcus xanthus
forms dynamic collective groups both to feed on prey and to aggregate during
times of starvation. The latter behavior, termed fruiting-body formation,
involves a complex, coordinated series of density changes that ultimately lead
to three-dimensional aggregates comprising hundreds of thousands of cells and
spores. This multi-step developmental process most likely involves several
different single-celled behaviors as the population condenses from a loose,
two-dimensional sheet to a three-dimensional mound. Here, we use
high-resolution microscopy and computer vision software to spatiotemporally
track the motion of thousands of individuals during the initial stages of
fruiting body formation. We find that a combination of cell-contact-mediated
alignment and internal timing mechanisms drive a phase transition from
exploratory flocking, in which cell groups move rapidly and coherently over
long distances, to a reversal-mediated localization into streams, which act as
slow-spreading, quasi-one-dimensional nematic fluids. These observations lead
us to an active liquid crystal description of the myxobacterial development
cycle.Comment: 16 pages, 5 figure
Deformable Simplicial Complexes
In this dissertation we present a novel method for deformable interface tracking in 2D and 3D|deformable simplicial complexes (DSC). Deformable interfaces are used in several applications, such as fluid simulation, image analysis, reconstruction or structural optimization. In the DSC method, the interface (curve in 2D; surface in 3D) is represented explicitly as a piecewise linear curve or surface. However, the domain is also subject to discretization: triangulation in 2D; tetrahedralization in 3D. This way, the interface can be alternatively represented as a set of edges/triangles separating triangles/tetrahedra marked as outside from those marked as inside. Such an approach allows for robust topological adaptivity. Among other advantages of the deformable simplicial complexes there are: space adaptivity, ability to handle and preserve sharp features, possibility for topology control. We demonstrate those strengths in several applications. In particular, a novel, DSC-based fluid dynamics solver has been developed during the PhD project. A special feature of this solver is that due to the fact that DSC maintains an explicit interface representation, surface tension is more easily dealt with. One particular advantage of DSC is the fact that as an alternative to topology adaptivity, topology control is also possible. This is exploited in the construction of cut loci on tori where a front expands from a single point on a torus and stops when it self-intersects
Active Mean Fields for Probabilistic Image Segmentation: Connections with Chan-Vese and Rudin-Osher-Fatemi Models
Segmentation is a fundamental task for extracting semantically meaningful
regions from an image. The goal of segmentation algorithms is to accurately
assign object labels to each image location. However, image-noise, shortcomings
of algorithms, and image ambiguities cause uncertainty in label assignment.
Estimating the uncertainty in label assignment is important in multiple
application domains, such as segmenting tumors from medical images for
radiation treatment planning. One way to estimate these uncertainties is
through the computation of posteriors of Bayesian models, which is
computationally prohibitive for many practical applications. On the other hand,
most computationally efficient methods fail to estimate label uncertainty. We
therefore propose in this paper the Active Mean Fields (AMF) approach, a
technique based on Bayesian modeling that uses a mean-field approximation to
efficiently compute a segmentation and its corresponding uncertainty. Based on
a variational formulation, the resulting convex model combines any
label-likelihood measure with a prior on the length of the segmentation
boundary. A specific implementation of that model is the Chan-Vese segmentation
model (CV), in which the binary segmentation task is defined by a Gaussian
likelihood and a prior regularizing the length of the segmentation boundary.
Furthermore, the Euler-Lagrange equations derived from the AMF model are
equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image
denoising. Solutions to the AMF model can thus be implemented by directly
utilizing highly-efficient ROF solvers on log-likelihood ratio fields. We
qualitatively assess the approach on synthetic data as well as on real natural
and medical images. For a quantitative evaluation, we apply our approach to the
icgbench dataset
Tops and Writhing DNA
The torsional elasticity of semiflexible polymers like DNA is of biological
significance. A mathematical treatment of this problem was begun by Fuller
using the relation between link, twist and writhe, but progress has been
hindered by the non-local nature of the writhe. This stands in the way of an
analytic statistical mechanical treatment, which takes into account thermal
fluctuations, in computing the partition function. In this paper we use the
well known analogy with the dynamics of tops to show that when subjected to
stretch and twist, the polymer configurations which dominate the partition
function admit a local writhe formulation in the spirit of Fuller and thus
provide an underlying justification for the use of Fuller's "local writhe
expression" which leads to considerable mathematical simplification in solving
theoretical models of DNA and elucidating their predictions. Our result
facilitates comparison of the theoretical models with single molecule
micromanipulation experiments and computer simulations.Comment: 17 pages two figure
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