10,202 research outputs found
Bayesian Estimation of White Matter Atlas from High Angular Resolution Diffusion Imaging
We present a Bayesian probabilistic model to estimate the brain white matter
atlas from high angular resolution diffusion imaging (HARDI) data. This model
incorporates a shape prior of the white matter anatomy and the likelihood of
individual observed HARDI datasets. We first assume that the atlas is generated
from a known hyperatlas through a flow of diffeomorphisms and its shape prior
can be constructed based on the framework of large deformation diffeomorphic
metric mapping (LDDMM). LDDMM characterizes a nonlinear diffeomorphic shape
space in a linear space of initial momentum uniquely determining diffeomorphic
geodesic flows from the hyperatlas. Therefore, the shape prior of the HARDI
atlas can be modeled using a centered Gaussian random field (GRF) model of the
initial momentum. In order to construct the likelihood of observed HARDI
datasets, it is necessary to study the diffeomorphic transformation of
individual observations relative to the atlas and the probabilistic
distribution of orientation distribution functions (ODFs). To this end, we
construct the likelihood related to the transformation using the same
construction as discussed for the shape prior of the atlas. The probabilistic
distribution of ODFs is then constructed based on the ODF Riemannian manifold.
We assume that the observed ODFs are generated by an exponential map of random
tangent vectors at the deformed atlas ODF. Hence, the likelihood of the ODFs
can be modeled using a GRF of their tangent vectors in the ODF Riemannian
manifold. We solve for the maximum a posteriori using the
Expectation-Maximization algorithm and derive the corresponding update
equations. Finally, we illustrate the HARDI atlas constructed based on a
Chinese aging cohort of 94 adults and compare it with that generated by
averaging the coefficients of spherical harmonics of the ODF across subjects
Coverage and Field Estimation on Bounded Domains by Diffusive Swarms
In this paper, we consider stochastic coverage of bounded domains by a
diffusing swarm of robots that take local measurements of an underlying scalar
field. We introduce three control methodologies with diffusion, advection, and
reaction as independent control inputs. We analyze the diffusion-based control
strategy using standard operator semigroup-theoretic arguments. We show that
the diffusion coefficient can be chosen to be dependent only on the robots'
local measurements to ensure that the swarm density converges to a function
proportional to the scalar field. The boundedness of the domain precludes the
need to impose assumptions on decaying properties of the scalar field at
infinity. Moreover, exponential convergence of the swarm density to the
equilibrium follows from properties of the spectrum of the semigroup generator.
In addition, we use the proposed coverage method to construct a
time-inhomogenous diffusion process and apply the observability of the heat
equation to reconstruct the scalar field over the entire domain from
observations of the robots' random motion over a small subset of the domain. We
verify our results through simulations of the coverage scenario on a 2D domain
and the field estimation scenario on a 1D domain.Comment: To appear in the proceedings of the 55th IEEE Conference on Decision
and Control (CDC 2016
Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates
The study of cerebral anatomy in developing neonates is of great importance for
the understanding of brain development during the early period of life. This
dissertation therefore focuses on three challenges in the modelling of cerebral
anatomy in neonates during brain development. The methods that have been
developed all use Magnetic Resonance Images (MRI) as source data.
To facilitate study of vascular development in the neonatal period, a set of image
analysis algorithms are developed to automatically extract and model cerebral
vessel trees. The whole process consists of cerebral vessel tracking from
automatically placed seed points, vessel tree generation, and vasculature
registration and matching. These algorithms have been tested on clinical Time-of-
Flight (TOF) MR angiographic datasets.
To facilitate study of the neonatal cortex a complete cerebral cortex segmentation
and reconstruction pipeline has been developed. Segmentation of the neonatal
cortex is not effectively done by existing algorithms designed for the adult brain
because the contrast between grey and white matter is reversed. This causes pixels
containing tissue mixtures to be incorrectly labelled by conventional methods. The
neonatal cortical segmentation method that has been developed is based on a novel
expectation-maximization (EM) method with explicit correction for mislabelled
partial volume voxels. Based on the resulting cortical segmentation, an implicit
surface evolution technique is adopted for the reconstruction of the cortex in
neonates. The performance of the method is investigated by performing a detailed
landmark study.
To facilitate study of cortical development, a cortical surface registration algorithm
for aligning the cortical surface is developed. The method first inflates extracted
cortical surfaces and then performs a non-rigid surface registration using free-form
deformations (FFDs) to remove residual alignment. Validation experiments using
data labelled by an expert observer demonstrate that the method can capture local
changes and follow the growth of specific sulcus
Data-Driven Shape Analysis and Processing
Data-driven methods play an increasingly important role in discovering
geometric, structural, and semantic relationships between 3D shapes in
collections, and applying this analysis to support intelligent modeling,
editing, and visualization of geometric data. In contrast to traditional
approaches, a key feature of data-driven approaches is that they aggregate
information from a collection of shapes to improve the analysis and processing
of individual shapes. In addition, they are able to learn models that reason
about properties and relationships of shapes without relying on hard-coded
rules or explicitly programmed instructions. We provide an overview of the main
concepts and components of these techniques, and discuss their application to
shape classification, segmentation, matching, reconstruction, modeling and
exploration, as well as scene analysis and synthesis, through reviewing the
literature and relating the existing works with both qualitative and numerical
comparisons. We conclude our report with ideas that can inspire future research
in data-driven shape analysis and processing.Comment: 10 pages, 19 figure
Quantitative evaluation of 10 tractography algorithms on a realistic diffusion MR phantom.
International audienceAs it provides the only method for mapping white matter fibers in vivo, diffusion MRI tractography is gaining importance in clinical and neuroscience research. However, despite the increasing availability of different diffusion models and tractography algorithms, it remains unclear how to select the optimal fiber reconstruction method, given certain imaging parameters. Consequently, it is of utmost importance to have a quantitative comparison of these models and algorithms and a deeper understanding of the corresponding strengths and weaknesses. In this work, we use a common dataset with known ground truth and a reproducible methodology to quantitatively evaluate the performance of various diffusion models and tractography algorithms. To examine a wide range of methods, the dataset, but not the ground truth, was released to the public for evaluation in a contest, the "Fiber Cup". 10 fiber reconstruction methods were evaluated. The results provide evidence that: 1. For high SNR datasets, diffusion models such as (fiber) orientation distribution functions correctly model the underlying fiber distribution and can be used in conjunction with streamline tractography, and 2. For medium or low SNR datasets, a prior on the spatial smoothness of either the diffusion model or the fibers is recommended for correct modelling of the fiber distribution and proper tractography results. The phantom dataset, the ground truth fibers, the evaluation methodology and the results obtained so far will remain publicly available on: http://www.lnao.fr/spip.php?rubrique79 to serve as a comparison basis for existing or new tractography methods. New results can be submitted to [email protected] and updates will be published on the webpage
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