Results 1 - 10
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88
Genus zero surface conformal mapping and its application to brain surface mapping
- IEEE Transactions on Medical Imaging
, 2004
"... Abstract—We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms for surfaces with or without boundaries (Gu and Yau, 2002), (Gu and Yau, 2003). For genus zero surfaces, our algorithm can find a unique mapping betwe ..."
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Cited by 188 (78 self)
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Abstract—We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms for surfaces with or without boundaries (Gu and Yau, 2002), (Gu and Yau, 2003). For genus zero surfaces, our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. In this paper, we apply the algorithm to the cortical surface matching problem. We use a mesh structure to represent the brain surface. Further constraints are added to ensure that the conformal map is unique. Empirical tests on magnetic resonance imaging (MRI) data show that the mappings preserve angular relationships, are stable in MRIs acquired at different times, and are robust to differences in data triangulation, and resolution. Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility. Index Terms—Brain mapping, conformal map, landmark matching, spherical harmonic transformation. I.
Mapping cortical change in Alzheimer’s disease, brain development, and schizophrenia
, 2004
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Boundary and Medial Shape Analysis of the Hippocampus in Schizophrenia
, 2004
"... Statistical shape analysis has become of increasing interest to the neuroimaging community due to its potential to precisely locate morphological changes and thus potentially discriminate between healthy and pathological structures. This paper describes a combined boundary and medial shape analysis ..."
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Cited by 64 (11 self)
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Statistical shape analysis has become of increasing interest to the neuroimaging community due to its potential to precisely locate morphological changes and thus potentially discriminate between healthy and pathological structures. This paper describes a combined boundary and medial shape analysis based on two different shape descriptions applied to a study of the hippocampus shape abnormalities in schizophrenia. The first shape description is the sampled boundary implied by the spherical harmonic SPHARM description. The second one is the medial shape description called M-rep. Both descriptions are sampled descriptions with inherent point correspondence. Their shape analysis is based on computing differences from an average template structure analyzed using standard group mean difference tests. The results of the global and local shape analysis in the presented hippocampus study exhibit the same patterns for the boundary and the medial analysis. The results strongly suggest that the normalized hippocampal shape of the schizophrenic group is different from the control group, most significantly as a deformation difference in the tail region.
Statistical Shape Analysis of Neuroanatomical Structures Based on Medial Models
- Medical Image Analysis (MEDIA
"... Knowledge about the biological variability of anatomical objects is essential for statistical shape analysis and discrimination between healthy and pathological structures. This paper describes a novel approach that incorporates the variability of an object population into the generation of a charac ..."
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Cited by 64 (13 self)
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Knowledge about the biological variability of anatomical objects is essential for statistical shape analysis and discrimination between healthy and pathological structures. This paper describes a novel approach that incorporates the variability of an object population into the generation of a characteristic 3D shape model. The proposed shape representation is a coarse-scale sampled medial description derived from a fine-scale spherical harmonics (SPHARM) boundary description. This medial description is composed of a net of medial samples (m-rep) with fixed graph properties. The medial model is computed automatically from a predefined shape space using pruned 3D Voronoi skeletons. A new method determines the stable medial branching topology from the shape space. An intrinsic coordinate system and an implicit correspondence between shapes is defined on the medial manifold. Several studies of biological structures clearly demonstrate that the novel representation has the promise to describe shape changes in a natural and intuitive way. A new medial shape similarity study of group di#erences between Monozygotic and Dizygotic twins in lateral ventricle shape demonstrates the meaningful and powerful representation of local and global form.
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.
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
Global medical shape analysis using the Laplace-Beltrami spectrum
- in Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI
, 2007
"... Abstract. This paper proposes to use the Laplace-Beltrami spectrum (LBS) as a global shape descriptor for medical shape analysis, allowing for shape comparisons using minimal shape preprocessing: no registration, mapping, or remeshing is necessary. The discriminatory power of the method is tested on ..."
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Cited by 23 (6 self)
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Abstract. This paper proposes to use the Laplace-Beltrami spectrum (LBS) as a global shape descriptor for medical shape analysis, allowing for shape comparisons using minimal shape preprocessing: no registration, mapping, or remeshing is necessary. The discriminatory power of the method is tested on a population of female caudate shapes of normal control subjects and of subjects with schizotypal personality disorder. 1
Tensor-based cortical surface morphometry via weighted spherical harmonic representation
- IEEE Transactions on Medical Imaging
, 2008
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Laplace-Beltrami Eigenvalues and Topological Features of Eigenfunctions for Statistical Shape Analysis
, 2009
"... This paper proposes the use of the surface-based Laplace-Beltrami and the volumetric Laplace eigenvalues and eigenfunctions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre- ..."
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Cited by 22 (3 self)
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This paper proposes the use of the surface-based Laplace-Beltrami and the volumetric Laplace eigenvalues and eigenfunctions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the 2D surface and 3D solid methods is demonstrated on a population of female caudate nuclei (a subcortical gray matter structure of the brain, involved in memory function, emotion processing, and learning) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the Laplace-Beltrami eigenvalues and eigenfunctions are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann vs. the Dirichlet spectra in 3D. Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable of localizing geometric properties and detecting shape differences by indirectly registering topological features such as critical points, level sets and integral lines of the gradient field across subjects. The use of these topological features of the Laplace-Beltrami eigenfunctions in 2D and 3D for statistical shape analysis is novel.
Statistical shape models for segmentation and structural analysis
- in Proceedings of IEEE International Symposium on Biomedical Imaging (ISBI
, 2004
"... Biomedical imaging of large patient populations, both cross-sectionally and longitudinally, is becoming a standard technique for noninvasive, in-vivo studies of the pathophysiology of diseases and for monitoring drug treatment. In radiation oncology, imaging and extraction of anatomical organ geomet ..."
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Cited by 18 (3 self)
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Biomedical imaging of large patient populations, both cross-sectionally and longitudinally, is becoming a standard technique for noninvasive, in-vivo studies of the pathophysiology of diseases and for monitoring drug treatment. In radiation oncology, imaging and extraction of anatomical organ geometry is a routine procedure for therapy planning an monitoring, and similar procedures are vital for surgical planning and image-guided therapy. Bottlenecks of today’s studies, often processed by labor-intensive manual region drawing, are the lack of efficient, reliable tools for threedimensional organ segmentation and for advanced morphologic characterization. This paper discusses current research and development focused towards building of statistical shape models, used for automatic model-based segmentation and for shape analysis and discrimination. We build statistical shape models which describe the geometric variability and image intensity characteristics of anatomical structures. New segmentations are obtained by model deformation driven by local image match forces and constrained by the training statistics. Two complimentary representations for 3D shape are discussed and compared, one based on global surface parametrization and a second one on medial manifold description. The discussion will be guided by presenting a most recent study to construct a statistical shape model of the caudate structure. 1.
