3,502 research outputs found
Bayesian Atlas Estimation for the Variability Analysis of Shape Complexes
International audienceIn this paper we propose a Bayesian framework for multi-object atlas estimation based on the metric of currents which permits to deal with both curves and surfaces without relying on point correspondence. This approach aims to study brain morphometry as a whole and not as a set of different components, focusing mainly on the shape and relative position of different anatomical structures which is fundamental in neuro-anatomical studies. We propose a generic algorithm to estimate templates of sets of curves (fiber bundles) and closed surfaces (sub-cortical structures) which have the same " form " (topology) of the shapes present in the population. This atlas construction method is based on a Bayesian framework which brings to two main improvements with respect to previous shape based methods. First, it allows to estimate from the data set a parameter specific to each object which was previously fixed by the user: the trade-off between data-term and regularity of deformations. In a multi-object analysis these parameters balance the contributions of the different objects and the need for an automatic estimation is even more crucial. Second, the covariance matrix of the deformation parameters is estimated during the atlas construction in a way which is less sensitive to the outliers of the population
Interpretable statistics for complex modelling: quantile and topological learning
As the complexity of our data increased exponentially in the last decades, so has our
need for interpretable features. This thesis revolves around two paradigms to approach
this quest for insights.
In the first part we focus on parametric models, where the problem of interpretability
can be seen as a “parametrization selection”. We introduce a quantile-centric
parametrization and we show the advantages of our proposal in the context of regression,
where it allows to bridge the gap between classical generalized linear (mixed)
models and increasingly popular quantile methods.
The second part of the thesis, concerned with topological learning, tackles the
problem from a non-parametric perspective. As topology can be thought of as a way
of characterizing data in terms of their connectivity structure, it allows to represent
complex and possibly high dimensional through few features, such as the number of
connected components, loops and voids. We illustrate how the emerging branch of
statistics devoted to recovering topological structures in the data, Topological Data
Analysis, can be exploited both for exploratory and inferential purposes with a special
emphasis on kernels that preserve the topological information in the data.
Finally, we show with an application how these two approaches can borrow strength
from one another in the identification and description of brain activity through fMRI
data from the ABIDE project
A Geometric Approach to Pairwise Bayesian Alignment of Functional Data Using Importance Sampling
We present a Bayesian model for pairwise nonlinear registration of functional
data. We use the Riemannian geometry of the space of warping functions to
define appropriate prior distributions and sample from the posterior using
importance sampling. A simple square-root transformation is used to simplify
the geometry of the space of warping functions, which allows for computation of
sample statistics, such as the mean and median, and a fast implementation of a
-means clustering algorithm. These tools allow for efficient posterior
inference, where multiple modes of the posterior distribution corresponding to
multiple plausible alignments of the given functions are found. We also show
pointwise credible intervals to assess the uncertainty of the alignment
in different clusters. We validate this model using simulations and present
multiple examples on real data from different application domains including
biometrics and medicine
Doctor of Philosophy in Computing
dissertationAn important area of medical imaging research is studying anatomical diffeomorphic shape changes and detecting their relationship to disease processes. For example, neurodegenerative disorders change the shape of the brain, thus identifying differences between the healthy control subjects and patients affected by these diseases can help with understanding the disease processes. Previous research proposed a variety of mathematical approaches for statistical analysis of geometrical brain structure in three-dimensional (3D) medical imaging, including atlas building, brain variability quantification, regression, etc. The critical component in these statistical models is that the geometrical structure is represented by transformations rather than the actual image data. Despite the fact that such statistical models effectively provide a way for analyzing shape variation, none of them have a truly probabilistic interpretation. This dissertation contributes a novel Bayesian framework of statistical shape analysis for generic manifold data and its application to shape variability and brain magnetic resonance imaging (MRI). After we carefully define the distributions on manifolds, we then build Bayesian models for analyzing the intrinsic variability of manifold data, involving the mean point, principal modes, and parameter estimation. Because there is no closed-form solution for Bayesian inference of these models on manifolds, we develop a Markov Chain Monte Carlo method to sample the hidden variables from the distribution. The main advantages of these Bayesian approaches are that they provide parameter estimation and automatic dimensionality reduction for analyzing generic manifold-valued data, such as diffeomorphisms. Modeling the mean point of a group of images in a Bayesian manner allows for learning the regularity parameter from data directly rather than having to set it manually, which eliminates the effort of cross validation for parameter selection. In population studies, our Bayesian model of principal modes analysis (1) automatically extracts a low-dimensional, second-order statistics of manifold data variability and (2) gives a better geometric data fit than nonprobabilistic models. To make this Bayesian framework computationally more efficient for high-dimensional diffeomorphisms, this dissertation presents an algorithm, FLASH (finite-dimensional Lie algebras for shooting), that hugely speeds up the diffeomorphic image registration. Instead of formulating diffeomorphisms in a continuous variational problem, Flash defines a completely new discrete reparameterization of diffeomorphisms in a low-dimensional bandlimited velocity space, which results in the Bayesian inference via sampling on the space of diffeomorphisms being more feasible in time. Our entire Bayesian framework in this dissertation is used for statistical analysis of shape data and brain MRIs. It has the potential to improve hypothesis testing, classification, and mixture models
Fast Optimal Transport Averaging of Neuroimaging Data
Knowing how the Human brain is anatomically and functionally organized at the
level of a group of healthy individuals or patients is the primary goal of
neuroimaging research. Yet computing an average of brain imaging data defined
over a voxel grid or a triangulation remains a challenge. Data are large, the
geometry of the brain is complex and the between subjects variability leads to
spatially or temporally non-overlapping effects of interest. To address the
problem of variability, data are commonly smoothed before group linear
averaging. In this work we build on ideas originally introduced by Kantorovich
to propose a new algorithm that can average efficiently non-normalized data
defined over arbitrary discrete domains using transportation metrics. We show
how Kantorovich means can be linked to Wasserstein barycenters in order to take
advantage of an entropic smoothing approach. It leads to a smooth convex
optimization problem and an algorithm with strong convergence guarantees. We
illustrate the versatility of this tool and its empirical behavior on
functional neuroimaging data, functional MRI and magnetoencephalography (MEG)
source estimates, defined on voxel grids and triangulations of the folded
cortical surface.Comment: Information Processing in Medical Imaging (IPMI), Jun 2015, Isle of
Skye, United Kingdom. Springer, 201
Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms
We propose a method to learn a distribution of shape trajectories from
longitudinal data, i.e. the collection of individual objects repeatedly
observed at multiple time-points. The method allows to compute an average
spatiotemporal trajectory of shape changes at the group level, and the
individual variations of this trajectory both in terms of geometry and time
dynamics. First, we formulate a non-linear mixed-effects statistical model as
the combination of a generic statistical model for manifold-valued longitudinal
data, a deformation model defining shape trajectories via the action of a
finite-dimensional set of diffeomorphisms with a manifold structure, and an
efficient numerical scheme to compute parallel transport on this manifold.
Second, we introduce a MCMC-SAEM algorithm with a specific approach to shape
sampling, an adaptive scheme for proposal variances, and a log-likelihood
tempering strategy to estimate our model. Third, we validate our algorithm on
2D simulated data, and then estimate a scenario of alteration of the shape of
the hippocampus 3D brain structure during the course of Alzheimer's disease.
The method shows for instance that hippocampal atrophy progresses more quickly
in female subjects, and occurs earlier in APOE4 mutation carriers. We finally
illustrate the potential of our method for classifying pathological
trajectories versus normal ageing
Quantifying atrial anatomy uncertainty from clinical data and its impact on electro-physiology simulation predictions
Patient-specific computational models of structure and function are increasingly being used to diagnose disease and predict how a patient will respond to therapy. Models of anatomy are often derived after segmentation of clinical images or from mapping systems which are affected by image artefacts, resolution and contrast. Quantifying the impact of uncertain anatomy on model predictions is important, as models are increasingly used in clinical practice where decisions need to be made regardless of image quality. We use a Bayesian probabilistic approach to estimate the anatomy and to quantify the uncertainty about the shape of the left atrium derived from Cardiac Magnetic Resonance images. We show that we can quantify uncertain shape, encode uncertainty about the left atrial shape due to imaging artefacts, and quantify the effect of uncertain shape on simulations of left atrial activation times
Influence of Environment and Mitochondrial Heritage on the Ecological Characteristics of Fish in a Hybrid Zone
Ecological characteristics (growth, morphology, reproduction) arise from the interaction between environmental factors and genetics. Genetic analysis of individuals' life history traits might be used to improve our understanding of mechanisms that form and maintain a hybrid zone.A fish hybrid zone was used to characterize the process of natural selection. Data were collected during two reproductive periods (2001 and 2002) and 1117 individuals (nase, Chondrostama nasus nasus, sofie C. toxostoma toxostoma and hybrids) were sampled. Reproductive dates of the two parental species overlapped at sympatric sites. The nase had an earlier reproductive period than the sofie; males had longer reproductive periods for both species. Hybridisation between female nase and male sofie was the most likely. Hybrids had a reproductive period similar to the inherited parental mitochondrial type. Growth and reproductive information from different environments has been synthesised following a bayesian approach of the von Bertalanffy model. Hybrid life history traits appear to link with maternal heritage. Hybrid size from the age of two and size at first maturity appeared to be closer to the size of the maternal origin species (nase or sofie). Median growth rates for hybrids were similar and intermediate between those of the parental species. We observed variable life history traits for hybrids and pure forms in the different parts of the hybrid zone. Geometrical analysis of the hybrid fish shape gave evidence of two main morphologies with a link to maternal heritage.Selective mating seemed to be the underlying process which, with mitochondrial heritage, could explain the evolution of the studied hybrid zone. More generally, we showed the importance of studies on hybrid zones and specifically the study of individuals' ecological characteristics, to improve our understanding of speciation
Computational Anatomy for Multi-Organ Analysis in Medical Imaging: A Review
The medical image analysis field has traditionally been focused on the
development of organ-, and disease-specific methods. Recently, the interest in
the development of more 20 comprehensive computational anatomical models has
grown, leading to the creation of multi-organ models. Multi-organ approaches,
unlike traditional organ-specific strategies, incorporate inter-organ relations
into the model, thus leading to a more accurate representation of the complex
human anatomy. Inter-organ relations are not only spatial, but also functional
and physiological. Over the years, the strategies 25 proposed to efficiently
model multi-organ structures have evolved from the simple global modeling, to
more sophisticated approaches such as sequential, hierarchical, or machine
learning-based models. In this paper, we present a review of the state of the
art on multi-organ analysis and associated computation anatomy methodology. The
manuscript follows a methodology-based classification of the different
techniques 30 available for the analysis of multi-organs and multi-anatomical
structures, from techniques using point distribution models to the most recent
deep learning-based approaches. With more than 300 papers included in this
review, we reflect on the trends and challenges of the field of computational
anatomy, the particularities of each anatomical region, and the potential of
multi-organ analysis to increase the impact of 35 medical imaging applications
on the future of healthcare.Comment: Paper under revie
Coupled non-parametric shape and moment-based inter-shape pose priors for multiple basal ganglia structure segmentation
This paper presents a new active contour-based, statistical method for simultaneous volumetric segmentation of multiple subcortical structures in the brain. In biological tissues, such as the human brain, neighboring structures exhibit co-dependencies which can aid in segmentation, if properly analyzed and modeled. Motivated by this observation, we formulate the segmentation problem as a maximum a posteriori estimation problem, in which we incorporate statistical prior models on the shapes and inter-shape (relative) poses of the structures of interest. This provides a principled mechanism to bring high level information about the shapes and the relationships of anatomical structures into the segmentation problem. For learning the prior densities we use a nonparametric multivariate kernel density estimation framework. We combine these priors with data in a variational framework and develop an active contour-based iterative segmentation algorithm.
We test our method on the problem of volumetric segmentation of basal ganglia structures in magnetic resonance (MR) images.
We present a set of 2D and 3D experiments as well as a quantitative performance analysis. In addition, we perform a comparison to several existent segmentation methods and demonstrate the improvements provided by our approach in terms of segmentation accuracy
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