Results 1  10
of
19
Spatiotemporal Atlas Estimation for Developmental Delay Detection in Longitudinal
"... Abstract. We propose a new methodology to analyze the anatomical variability of a set of longitudinal data (population scanned at several ages). This method accounts not only for the usual 3D anatomical variability (geometry of structures), but also for possible changes in the dynamics of evolution ..."
Abstract

Cited by 34 (18 self)
 Add to MetaCart
(Show Context)
Abstract. We propose a new methodology to analyze the anatomical variability of a set of longitudinal data (population scanned at several ages). This method accounts not only for the usual 3D anatomical variability (geometry of structures), but also for possible changes in the dynamics of evolution of the structures. It does not require that subjects are scanned the same number of times or at the same ages. First a regression model infers a continuous evolution of shapes from a set of observations of the same subject. Second, spatiotemporal registrations deform jointly (1) the geometry of the evolving structure via 3D deformations and (2) the dynamics of evolution via time change functions. Third, we infer from a population a prototype scenario of evolution and its 4D variability. Our method is used to analyze the morphological evolution of 2D profiles of hominids skulls and to analyze brain growth from amygdala of autistics, developmental delay and control children. 1 Methodology for Statistics on Longitudinal Data
Shape modeling and analysis with entropybased particle systems
 In Proceedings of the 20th International Conference on Information Processing in Medical Imaging
, 2007
"... Many important fields of basic research in medicine and biology routinely employ tools for the statistical analysis of collections of similar shapes. Biologists, for example, have long relied on homologous, anatomical landmarks as shape models to characterize the growth and development of species. I ..."
Abstract

Cited by 27 (14 self)
 Add to MetaCart
(Show Context)
Many important fields of basic research in medicine and biology routinely employ tools for the statistical analysis of collections of similar shapes. Biologists, for example, have long relied on homologous, anatomical landmarks as shape models to characterize the growth and development of species. Increasingly, however, researchers are exploring the use of more detailed models that are derived computationally from threedimensional images and surface descriptions. While computationallyderived models of shape are promising new tools for biomedical research, they also present some significant engineering challenges, which existing modeling methods have only begun to address. In this dissertation, I propose a new computational framework for statistical shape modeling that significantly advances the stateoftheart by overcoming many of the limitations of existing methods. The framework uses a particlesystem representation of shape, with a fast correspondencepoint optimization based on information content. The optimization balances the simplicity of the model (compactness) with the accuracy of the shape representations by using two commensurate entropy
Sparse approximation of currents for statistics on curves and surfaces
, 2008
"... ..."
(Show Context)
A hypothesis testing framework for highdimensional shape models
 in MICCAI Workshop on Mathematical Foundations of Computational Anatomy
"... Abstract. Statistical shape models are powerful tools for describing anatomical structures and are increasingly being used in a wide variety of clinical and biological contexts. One of the promising applications of this technology is the testing of hypotheses that entail shape differences, and visua ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
Abstract. Statistical shape models are powerful tools for describing anatomical structures and are increasingly being used in a wide variety of clinical and biological contexts. One of the promising applications of this technology is the testing of hypotheses that entail shape differences, and visualization of those differences between cohorts. Statistical testing of shapes, however, is difficult due the large numbers of degrees of freedom and challenge of obtaining sufficient numbers of subjects to ensure statistical power. To date, research in statistical shape modeling has focused mainly on the construction of representative models, and the field has not reached a consensus on the best approach to statistical hypothesis testing. This paper illustrates some problems inherent in the statistical analysis of highdimensional shape models, and suggests a systematic approach to hypothesis testing that avoids those problems. The proposed framework is based on research in the factor analysis statistics literature, with permutation testing in the PCA space of the model, and dimensionality reduction via a a simulationbased analysis. We also describe two methods for visualizing group mean differences, first by direct visualization of the linear discriminant implicit in the hypothesis test metric, and second, by visualizing strain tensors from a deformation computed between the group means. We illustrate the proposed analysis and visualization framework on several clinical and biological datasets. 1
Studying Brain Morphometry using Conformal Equivalence Class
"... Two surfaces are conformally equivalent if there exists a bijective anglepreserving map between them. The Teichmüller space for surfaces with the same topology is a finitedimensional manifold, where each point represents a conformal equivalence class, and the conformal map is homotopic to the iden ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
Two surfaces are conformally equivalent if there exists a bijective anglepreserving map between them. The Teichmüller space for surfaces with the same topology is a finitedimensional manifold, where each point represents a conformal equivalence class, and the conformal map is homotopic to the identity map. In this paper, we propose a novel method to apply conformal equivalence based shape index to study brain morphometry. The shape index is defined based on Teichmüller space coordinates. It is intrinsic, and invariant under conformal transformations, rigid motions and scaling. It is also simple to compute; no registration of surfaces is needed. Using the Yamabe flow method, we can conformally map a genuszero open boundary surface to the Poincaré disk. The shape indices that we compute are the lengths of a special set of geodesics under hyperbolic metric. By computing and studying this shape index and its statistical behavior, we can analyze differences in anatomical morphometry due to disease or development. Study on twin lateral ventricular surface data shows it may help detect generic influence on lateral ventricular shapes. In leaveoneout validation tests, we achieved 100 % accurate classification (versus only 68 % accuracy for volume measures) in distinguishing 11 HIV/AIDS individuals from 8 healthy control subjects, based on Teichmüller coordinates for lateral ventricular surfaces extracted from their 3D MRI scans.Our conformal invariants, the Teichmüller coordinates, successfully classified all lateral ventricular surfaces, showing their promise for analyzing anatomical surface morphometry. 1.
Shape Analysis with Conformal Invariants for Multiply Connected Domains and its Application to Analyzing Brain Morphology
"... All surfaces can be classified by the conformal equivalence relation. Conformal invariants, which are shape indices that can be defined intrinsically on a surface, may be used to identify which surfaces are conformally equivalent, and they can also be used to measure surface deformation. Here we pro ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
All surfaces can be classified by the conformal equivalence relation. Conformal invariants, which are shape indices that can be defined intrinsically on a surface, may be used to identify which surfaces are conformally equivalent, and they can also be used to measure surface deformation. Here we propose to compute a conformal invariant, or shape index, that is associated with the perimeter of the inner concentric circle in the hyperbolic parameter plane. With the surface Ricci flow method, we can conformally map a multiply connected domain to a multihole disk and this conformal map can preserve the values of the conformal invariant. Our algorithm provides a stable method to map the values of this shape index in the 2D (hyperbolic space) parameter domain. We also applied this new shape index for analyzing abnormalities in brain morphology in Alzheimer’s disease (AD) and Williams syndrome (WS). After cutting along various landmark curves on surface models of the cerebral cortex or hippocampus, we obtained multiple connected domains. We conformally projected the surfaces to hyperbolic plane with surface Ricci flow method, accurately computed the proposed conformal invariant for each selected landmark curve, and assembled these into a feature vector.We also detected group differences in brain structure based on multivariate analysis of the surface deformation tensors induced by these Ricci flow mappings. Experimental results with 3D MRI data from 80 subjects demonstrate that our method powerfully detects brain surface abnormalities when combined with a constrained harmonic map based surface registration method. 1.
Rotational flows for interpolation between sampled surfaces
 IEEE CVPR Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA
, 2008
"... We introduce a locally defined shapemaintaining method for interpolating between corresponding oriented samples (vertices) from a pair of surfaces. We have applied this method to interpolate synthetic data sets in two and three dimensions and to interpolate medially represented shape models of anat ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
We introduce a locally defined shapemaintaining method for interpolating between corresponding oriented samples (vertices) from a pair of surfaces. We have applied this method to interpolate synthetic data sets in two and three dimensions and to interpolate medially represented shape models of anatomical objects in three dimensions. In the plane, each oriented vertex follows a circular arc as if it was rotating to its destination. In three dimensions, each oriented vertex moves along a helical path that combines inplane rotation with translation along the axis of rotation. We show that our planar method provides shapemaintaining interpolations when the reference and target objects are similar. Moreover, the interpolations are size maintaining when the reference and target objects are congruent. In three dimensions, similar objects are interpolated by an affine transformation. We use measurements of the fractional anisotropy of such global affine transformations to demonstrate that our method is generally more shape preserving than the alternative of interpolating vertices along linear paths irrespective of changes in orientation. In both two and three dimensions we have experimental evidence that when nonshapepreserving deformations are applied to template shapes, the interpolation tends to be visually satisfying with each intermediate object appearing to belong to the same class of objects as the end points. 1.