1,056 research outputs found
Self-similar solutions for the LSW model with encounters
The LSW model with encounters has been suggested by Lifshitz and Slyozov as a
regularization of their classical mean-field model for domain coarsening to
obtain universal self-similar long-time behavior. We rigorously establish that
an exponentially decaying self-similar solution to this model exist, and show
that this solutions is isolated in a certain function space. Our proof relies
on setting up a suitable fixed-point problem in an appropriate function space
and careful asymptotic estimates of the solution to a corresponding homogeneous
problem.Comment: 22 page
On a thermodynamically consistent modification of the Becker-Doering equations
Recently, Dreyer and Duderstadt have proposed a modification of the
Becker--Doering cluster equations which now have a nonconvex Lyapunov function.
We start with existence and uniqueness results for the modified equations. Next
we derive an explicit criterion for the existence of equilibrium states and
solve the minimization problem for the Lyapunov function. Finally, we discuss
the long time behavior in the case that equilibrium solutions do exist
Self-similar solutions with fat tails for Smoluchowski's coagulation equation with locally bounded kernels
The existence of self-similar solutions with fat tails for Smoluchowski's
coagulation equation has so far only been established for the solvable and the
diagonal kernel. In this paper we prove the existence of such self-similar
solutions for continuous kernels that are homogeneous of degree and satisfy . More precisely,
for any we establish the existence of a continuous weak
self-similar profile with decay as
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
Fast Predictive Simple Geodesic Regression
Deformable image registration and regression are important tasks in medical
image analysis. However, they are computationally expensive, especially when
analyzing large-scale datasets that contain thousands of images. Hence, cluster
computing is typically used, making the approaches dependent on such
computational infrastructure. Even larger computational resources are required
as study sizes increase. This limits the use of deformable image registration
and regression for clinical applications and as component algorithms for other
image analysis approaches. We therefore propose using a fast predictive
approach to perform image registrations. In particular, we employ these fast
registration predictions to approximate a simplified geodesic regression model
to capture longitudinal brain changes. The resulting method is orders of
magnitude faster than the standard optimization-based regression model and
hence facilitates large-scale analysis on a single graphics processing unit
(GPU). We evaluate our results on 3D brain magnetic resonance images (MRI) from
the ADNI datasets.Comment: 19 pages, 10 figures, 13 table
Multiple Instance Learning for Heterogeneous Images: Training a CNN for Histopathology
Multiple instance (MI) learning with a convolutional neural network enables
end-to-end training in the presence of weak image-level labels. We propose a
new method for aggregating predictions from smaller regions of the image into
an image-level classification by using the quantile function. The quantile
function provides a more complete description of the heterogeneity within each
image, improving image-level classification. We also adapt image augmentation
to the MI framework by randomly selecting cropped regions on which to apply MI
aggregation during each epoch of training. This provides a mechanism to study
the importance of MI learning. We validate our method on five different
classification tasks for breast tumor histology and provide a visualization
method for interpreting local image classifications that could lead to future
insights into tumor heterogeneity
Regression uncertainty on the Grassmannian
Trends in longitudinal or cross-sectional studies over time are often captured through regression models. In their simplest manifestation, these regression models are formulated in ℝn. However, in the context of imaging studies, the objects of interest which are to be regressed are frequently best modeled as elements of a Riemannian manifold. Regression on such spaces can be accomplished through geodesic regression. This paper develops an approach to compute confidence intervals for geodesic regression models. The approach is general, but illustrated and specifically developed for the Grassmann manifold, which allows us, e.g., to regress shapes or linear dynamical systems. Extensions to other manifolds can be obtained in a similar manner. We demonstrate our approach for regression with 2D/3D shapes using synthetic and real data
MultisegPipeline: Automatic tissue segmentation of brain MR images with subject-specific atlases
Automated segmentation and labeling of individual brain anatomical regions is challenging due to individual structural variability. Although, atlas-based segmentation has shown its potential for both tissue and structure segmentation, the inherent natural variability as well as disease-related changes in MR appearance is often inappropriately represented by a single atlas image. In order to have a more accurate representation, several atlases may be used for the segmentation task in a given neuroimaging study. In this paper, we present the MultisegPipeline, it uses multiple atlases that have been visually inspected and capture the expected variability in a neonatal population. The MultisegPipeline transfers the labeled regions from each atlas to the target image using deformable registration (ANTs or QuickSilver is available for this task). Additionally, the set of labels are merged using a label fusion technique that reduces the errors produced by the registration. The final output is a single label map that combines the results produced by all atlases into a consensus solution. In our study, the MultisegPipeline is used to segment brain MR images from 31 infants, a leave-one-out strategy was used to test our framework. The average dice score coefficient was 0.89
On thermodynamically consistent Stefan problems with variable surface energy
A thermodynamically consistent two-phase Stefan problem with
temperature-dependent surface tension and with or without kinetic undercooling
is studied. It is shown that these problems generate local semiflows in
well-defined state manifolds. If a solution does not exhibit singularities, it
is proved that it exists globally in time and converges towards an equilibrium
of the problem. In addition, stability and instability of equilibria is
studied. In particular, it is shown that multiple spheres of the same radius
are unstable if surface heat capacity is small; however, if kinetic
undercooling is absent, they are stable if surface heat capacity is
sufficiently large.Comment: To appear in Arch. Ration. Mech. Anal. The final publication is
available at Springer via http://dx.doi.org/10.1007/s00205-015-0938-y. arXiv
admin note: substantial text overlap with arXiv:1101.376
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