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Framework for the statistical shape analysis of brain structures using spharm-pdm
- In Insight Journal, Special Edition on the Open Science Workshop at MICCAI
, 2006
"... Abstract — Shape analysis has become of increasing interest to the neuroimaging community due to its potential to precisely locate morphological changes between healthy and pathological structures. This manuscript presents a comprehensive set of tools for the computation of 3D structural statistical ..."
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Cited by 59 (7 self)
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Abstract — Shape analysis has become of increasing interest to the neuroimaging community due to its potential to precisely locate morphological changes between healthy and pathological structures. This manuscript presents a comprehensive set of tools for the computation of 3D structural statistical shape analysis. It has been applied in several studies on brain morphometry, but can potentially be employed in other 3D shape problems. Its main limitations is the necessity of spherical topology. The input of the proposed shape analysis is a set of binary segmentation of a single brain structure, such as the hippocampus or caudate. These segmentations are converted into a corresponding spherical harmonic description (SPHARM), which is then sampled into a triangulated surfaces (SPHARM-PDM). After alignment, differences between groups of surfaces are computed using the Hotelling T 2 two sample metric. Statistical p-values, both raw and corrected for multiple comparisons, result in significance maps. Additional visualization of the group tests are provided via mean difference magnitude and vector maps, as well as maps of the group covariance information. The correction for multiple comparisons is performed via two separate methods that each have a distinct view of the problem. The first one aims to control the family-wise error rate (FWER) or false-positives via the extrema histogram of non-parametric permutations. The second method controls the false discovery rate and results in a less conservative estimate of the false-negatives. I.
Hippocampal shape analysis using medial surfaces
- NeuroImage
, 2005
"... Abstract. Within the medial temporal lobe, significant attention has been paid to the analysis of the hippocampus (HC) in MR images because of its intimate connection to memory, emotion and learning. Volume changes in the HC have been recorded in conjunction with Alzheimer’s disease, post-traumatic ..."
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Cited by 28 (1 self)
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Abstract. Within the medial temporal lobe, significant attention has been paid to the analysis of the hippocampus (HC) in MR images because of its intimate connection to memory, emotion and learning. Volume changes in the HC have been recorded in conjunction with Alzheimer’s disease, post-traumatic stress disorder and depression. Recent studies have also found a significant reduction in HC volume that is related to gender; it is found in men but not women. In this paper we demonstrate a shape analysis of the HC and employ it to investigate gender differences in normal subjects. For each subject we extract the dominant medial sheet of the HC, find the plane defined by its two principal eigen vectors and then express the medial surface radius as a height function over this plane. This allows us to statistically quantify the relationship between several independent variables and local object width. 1
Multiscale 3-d shape representation and segmentation using spherical wavelets
- Trans. on Medical Imaging
, 2006
"... Abstract—This paper presents a novel multiscale shape representation and segmentation algorithm based on the spherical wavelet transform. This work is motivated by the need to compactly and accurately encode variations at multiple scales in the shape representation in order to drive the segmentation ..."
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Cited by 28 (3 self)
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Abstract—This paper presents a novel multiscale shape representation and segmentation algorithm based on the spherical wavelet transform. This work is motivated by the need to compactly and accurately encode variations at multiple scales in the shape representation in order to drive the segmentation and shape analysis of deep brain structures, such as the caudate nucleus or the hippocampus. Our proposed shape representation can be optimized to compactly encode shape variations in a population at the needed scale and spatial locations, enabling the construction of more descriptive, nonglobal, nonuniform shape probability priors to be included in the segmentation and shape analysis framework. In particular, this representation addresses the shortcomings of techniques that learn a global shape prior at a single scale of analysis and cannot represent fine, local variations in a population of shapes in the presence of a limited dataset.
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 ..."
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Cited by 27 (14 self)
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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 three-dimensional images and surface descriptions. While computationally-derived 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 state-of-the-art by overcoming many of the limitations of existing methods. The framework uses a particle-system representation of shape, with a fast correspondence-point 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
Automated Mapping of Hippocampal Atrophy in 1-Year Repeat MRI Data from 490 Subjects with Alzheimer’s Disease, Mild Cognitive Impairment, and Elderly Controls
, 2008
"... doi:10.1016/j.neuroimage.2008.10.043 ..."
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Brain surface conformal parameterization using riemann surface structure
- IEEE Trans. Med. Imaging
, 2007
"... Abstract—In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a s ..."
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Cited by 25 (17 self)
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Abstract—In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is diagonal, the modified
Statistical Shape Analysis of Multi-Object Complexes
"... An important goal of statistical shape analysis is the discrimination between populations of objects, exploring group differences in morphology not explained by standard volumetric analysis. Certain applications additionally require analysis of objects in their embedding context by joint statistical ..."
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Cited by 19 (4 self)
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An important goal of statistical shape analysis is the discrimination between populations of objects, exploring group differences in morphology not explained by standard volumetric analysis. Certain applications additionally require analysis of objects in their embedding context by joint statistical analysis of sets of interrelated objects. In this paper, we present a framework for discriminant analysis of populations of 3-D multi-object sets. In view of the driving medical applications, a skeletal object parametrization of shape is chosen since it naturally encodes thickening, bending and twisting. In a multi-object setting, we not only consider a joint analysis of sets of shapes but also must take into account differences in pose. Statistics on features of medial descriptions and pose parameters, which include rotational frames and distances, uses a Riemannian symmetric space instead of the standard Euclidean metric. Our choice of discriminant method is the distance weighted discriminant (DWD) because of its generalization ability in high dimensional, low sample size settings. Joint analysis of 10 subcortical brain structures in a pediatric autism study demonstrates that multi-object analysis of shape results in a better group discrimination than pose, and that the combination of pose and shape performs better than shape alone. Finally, given a discriminating axis of shape and pose, we can visualize the differences between the populations. 1.
Entropy-based particle systems for shape correspondence
- In proc. of MICCAI Workshop Mathematical Foundations of Computational Anatomy
, 2006
"... Abstract. This paper presents a new method for constructing statistical representations of ensembles of similar shapes. The proposed method relies on an optimal distribution of a large set of surface point correspondences, rather than the manipulation of a specific surface parameterization. The opti ..."
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Cited by 18 (3 self)
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Abstract. This paper presents a new method for constructing statistical representations of ensembles of similar shapes. The proposed method relies on an optimal distribution of a large set of surface point correspondences, rather than the manipulation of a specific surface parameterization. The optimal configuration is defined as one in which the entropy or information content of each shape is balanced against the entropy of the ensemble of shapes. The correspondences are modeled as sets of dynamic particles that are manipulated using a gradient descent on the entropies of the shapes and the ensemble, but constrained to lie on a set of implicit surfaces. The proposed, particle-based method for finding correspondences requires very little preprocessing of data or parameter tuning, and therefore makes the problem of shape analysis more practical for a wider range of problems. This paper presents the formulation and several synthetic and real shape examples in two and three dimensions. 1
Multiscale 3D Shape Analysis using Spherical
- in MICCAI, 2005, LNCS 3750
, 2005
"... Shape priors attempt to represent biological variations within a population. When variations are global, Principal Component Analysis (PCA) can be used to learn major modes of variation, even from a limited training set. However, when significant local variations exist, PCA typically cannot repr ..."
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Cited by 16 (4 self)
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Shape priors attempt to represent biological variations within a population. When variations are global, Principal Component Analysis (PCA) can be used to learn major modes of variation, even from a limited training set. However, when significant local variations exist, PCA typically cannot represent such variations from a small training set. To address this issue, we present a novel algorithm that learns shape variations from data at multiple scales and locations using spherical wavelets and spectral graph partitioning. Our results show that when the training set is small, our algorithm significantly improves the approximation of shapes in a testing set over PCA, which tends to oversmooth data.
