4,471 research outputs found
Most Likely Separation of Intensity and Warping Effects in Image Registration
This paper introduces a class of mixed-effects models for joint modeling of
spatially correlated intensity variation and warping variation in 2D images.
Spatially correlated intensity variation and warp variation are modeled as
random effects, resulting in a nonlinear mixed-effects model that enables
simultaneous estimation of template and model parameters by optimization of the
likelihood function. We propose an algorithm for fitting the model which
alternates estimation of variance parameters and image registration. This
approach avoids the potential estimation bias in the template estimate that
arises when treating registration as a preprocessing step. We apply the model
to datasets of facial images and 2D brain magnetic resonance images to
illustrate the simultaneous estimation and prediction of intensity and warp
effects
Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse and Fragmented Functional Data
Mathematical and Physical Sciences: 3rd Place (The Ohio State University Edward F. Hayes Graduate Research Forum)In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense sampling and sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and estimating the individual underlying functions from discrete observations has thus far been mainly approached sequentially without formal uncertainty propagation, or in an application-specific manner by pooling information across subjects. We propose a unified Bayesian framework for simultaneous registration and estimation, which is flexible enough to accommodate inference on individual functions under general observation regimes. Our ability to do this relies on the specification of strongly informative prior models over the amplitude component of function variability. We provide two strategies for this critical choice: a data-driven approach that defines an empirical basis for the amplitude subspace based on available training data, and a shape-restricted approach when the relative location and number of local extrema is well-understood. The proposed methods build on the elastic functional data analysis framework to separately model amplitude and phase variability inherent in functional data. We emphasize the importance of uncertainty quantification and visualization of these two components as they provide complementary information about the estimated functions. We validate the proposed framework using simulation studies, and real applications to estimation of fractional anisotropy profiles based on diffusion tensor imaging measurements, growth velocity functions and bone mineral density curves.No embarg
A Statistical Model for Simultaneous Template Estimation, Bias Correction, and Registration of 3D Brain Images
Template estimation plays a crucial role in computational anatomy since it
provides reference frames for performing statistical analysis of the underlying
anatomical population variability. While building models for template
estimation, variability in sites and image acquisition protocols need to be
accounted for. To account for such variability, we propose a generative
template estimation model that makes simultaneous inference of both bias fields
in individual images, deformations for image registration, and variance
hyperparameters. In contrast, existing maximum a posterori based methods need
to rely on either bias-invariant similarity measures or robust image
normalization. Results on synthetic and real brain MRI images demonstrate the
capability of the model to capture heterogeneity in intensities and provide a
reliable template estimation from registration
Simultaneous inference for misaligned multivariate functional data
We consider inference for misaligned multivariate functional data that
represents the same underlying curve, but where the functional samples have
systematic differences in shape. In this paper we introduce a new class of
generally applicable models where warping effects are modeled through nonlinear
transformation of latent Gaussian variables and systematic shape differences
are modeled by Gaussian processes. To model cross-covariance between sample
coordinates we introduce a class of low-dimensional cross-covariance structures
suitable for modeling multivariate functional data. We present a method for
doing maximum-likelihood estimation in the models and apply the method to three
data sets. The first data set is from a motion tracking system where the
spatial positions of a large number of body-markers are tracked in
three-dimensions over time. The second data set consists of height and weight
measurements for Danish boys. The third data set consists of three-dimensional
spatial hand paths from a controlled obstacle-avoidance experiment. We use the
developed method to estimate the cross-covariance structure, and use a
classification setup to demonstrate that the method outperforms
state-of-the-art methods for handling misaligned curve data.Comment: 44 pages in total including tables and figures. Additional 9 pages of
supplementary material and reference
Joint Clustering and Registration of Functional Data
Curve registration and clustering are fundamental tools in the analysis of
functional data. While several methods have been developed and explored for
either task individually, limited work has been done to infer functional
clusters and register curves simultaneously. We propose a hierarchical model
for joint curve clustering and registration. Our proposal combines a Dirichlet
process mixture model for clustering of common shapes, with a reproducing
kernel representation of phase variability for registration. We show how
inference can be carried out applying standard posterior simulation algorithms
and compare our method to several alternatives in both engineered data and a
benchmark analysis of the Berkeley growth data. We conclude our investigation
with an application to time course gene expression
Modeling and inference of multisubject fMRI data
Functional magnetic resonance imaging (fMRI) is a
rapidly growing technique for studying the brain in
action. Since its creation [1], [2], cognitive scientists
have been using fMRI to understand how we remember,
manipulate, and act on information in our environment.
Working with magnetic resonance physicists, statisticians, and
engineers, these scientists are pushing the frontiers of knowledge
of how the human brain works.
The design and analysis of single-subject fMRI studies
has been well described. For example, [3], chapters 10
and 11 of [4], and chapters 11 and 14 of [5] all give accessible
overviews of fMRI methods for one subject. In contrast,
while the appropriate manner to analyze a group of
subjects has been the topic of several recent papers, we do
not feel it has been covered well in introductory texts and
review papers. Therefore, in this article, we bring together
old and new work on so-called group modeling of fMRI
data using a consistent notation to make the methods more
accessible and comparable
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
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