Statistical Analysis on Brain Surfaces

[1]  A M Dale,et al.  Measuring the thickness of the human cerebral cortex from magnetic resonance images. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Trevor J. Hastie,et al.  Exact Covariance Thresholding into Connected Components for Large-Scale Graphical Lasso , 2011, J. Mach. Learn. Res..

[3]  K. Worsley,et al.  Diffusion smoothing on the cortical surface , 2001, NeuroImage.

[4]  Michael I. Jordan,et al.  Regression on manifolds using kernel dimension reduction , 2007, ICML '07.

[5]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  Guido Gerig,et al.  Elastic model-based segmentation of 3-D neuroradiological data sets , 1999, IEEE Transactions on Medical Imaging.

[7]  Paul M. Thompson,et al.  A curvature-based approach to estimate local gyrification on the cortical surface , 2006, NeuroImage.

[8]  Michael I. Miller,et al.  Multi-structure network shape analysis via normal surface momentum maps , 2008, NeuroImage.

[9]  J. Marron,et al.  SCALE SPACE VIEW OF CURVE ESTIMATION , 2000 .

[10]  MORPHOMETRIC ANALYSIS OF GENETIC VARIATION IN HIPPOCAMPAL SHAPE IN MILD COGNITIVE IMPAIRMENT : ROLE OF AN IL-6 PROMOTER POLYMORPHISM , 2006 .

[11]  Anqi Qiu,et al.  Locally Linear Diffeomorphic Metric Embedding (LLDME) for surface-based anatomical shape modeling , 2011, NeuroImage.

[12]  R. Woods,et al.  Gender effects on cortical thickness and the influence of scaling , 2006, Human brain mapping.

[13]  D Le Bihan,et al.  Detection of fMRI activation using Cortical Surface Mapping , 2001, Human brain mapping.

[14]  Jagath C. Rajapakse,et al.  Development of the human corpus callosum during childhood and adolescence: A longitudinal MRI study , 1999, Progress in Neuro-Psychopharmacology and Biological Psychiatry.

[15]  Christos Davatzikos,et al.  Using a deformable surface model to obtain a shape representation of the cortex , 1996, IEEE Trans. Medical Imaging.

[16]  G. Wahba.  Spline models for observational data , 1990 .

[17]  Michael I. Miller,et al.  Diffeomorphic metric surface mapping in subregion of the superior temporal gyrus , 2007, NeuroImage.

[18]  Brian B. Avants,et al.  Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neurodegenerative brain , 2008, Medical Image Anal..

[19]  Jae-Hun Kim,et al.  Spatial accuracy of fMRI activation influenced by volume- and surface-based spatial smoothing techniques , 2007, NeuroImage.

[20]  Moo K. Chung,et al.  Large-Scale Modeling of Parametric Surfaces Using Spherical Harmonics , 2006, Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06).

[21]  Moo K. Chung,et al.  Statistical and Computational Methods in Brain Image Analysis , 2013 .

[22]  A. Toga,et al.  Detection and mapping of abnormal brain structure with a probabilistic atlas of cortical surfaces. , 1997, Journal of computer assisted tomography.

[23]  Ross T. Whitaker,et al.  Dimensionality reduction and principal surfaces via Kernel Map Manifolds , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[24]  Karl J. Friston,et al.  A Voxel-Based Morphometric Study of Ageing in 465 Normal Adult Human Brains , 2001, NeuroImage.

[25]  Michael E. Taylor,et al.  Differential Geometry I , 1994 .

[26]  Paul M. Thompson,et al.  Genus zero surface conformal mapping and its application to brain surface mapping , 2004, IEEE Transactions on Medical Imaging.

[27]  Bruno Lévy,et al.  Spectral Mesh Processing , 2009, SIGGRAPH '10.

[28]  G. Molenberghs,et al.  Models for Discrete Longitudinal Data , 2005 .

[29]  P. Thomas Fletcher,et al.  Principal geodesic analysis for the study of nonlinear statistics of shape , 2004, IEEE Transactions on Medical Imaging.

[30]  Yang Song,et al.  Surface-based Tbm Boosts Power to Detect Disease Effects on the Brain: an N = 804 Adni Study ☆ and the Alzheimer's Disease Neuroimaging Initiative , 2022 .

[31]  Douglas W. Jones,et al.  Shape analysis of brain ventricles using SPHARM , 2001, Proceedings IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA 2001).

[32]  Martha Elizabeth Shenton,et al.  Laplace-Beltrami eigenvalues and topological features of eigenfunctions for statistical shape analysis , 2009, Comput. Aided Des..

[33]  Florian Yger,et al.  Wavelet kernel learning , 2011, Pattern Recognit..

[34]  Kenneth Stephenson,et al.  Cortical cartography using the discrete conformal approach of circle packings , 2004, NeuroImage.

[35]  Alexandre d'Aspremont,et al.  Model Selection Through Sparse Max Likelihood Estimation Model Selection Through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data , 2022 .

[36]  T M Mayhew,et al.  The cerebrum and cerebellum of the fixed human brain: efficient and unbiased estimates of volumes and cortical surface areas. , 1989, Journal of anatomy.

[37]  Hao Zhang,et al.  Spectral Methods for Mesh Processing and Analysis , 2007, Eurographics.

[38]  A. Yaglom.  Correlation Theory of Stationary and Related Random Functions I: Basic Results , 1987 .

[39]  Martin Styner,et al.  Framework for the Statistical Shape Analysis of Brain Structures using SPHARM-PDM. , 2006, The insight journal.

[40]  Kwang Suk Park,et al.  Evaluation of smoothing in an iterative lp-norm minimization algorithm for surface-based source localization of MEG , 2007, Physics in medicine and biology.

[41]  K. Worsley,et al.  Unified univariate and multivariate random field theory , 2004, NeuroImage.

[42]  Anne Gelb,et al.  The resolution of the Gibbs phenomenon for spherical harmonics , 1997, Math. Comput..

[43]  Martin Reuter,et al.  Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions , 2010, International Journal of Computer Vision.

[44]  S. Rosenberg.  The Laplacian on a Riemannian Manifold: The Construction of the Heat Kernel , 1997 .

[45]  Guillén Fernández,et al.  The right hippocampus participates in short-term memory maintenance of object–location associations , 2006, NeuroImage.

[46]  Alan C. Evans,et al.  A nonparametric method for automatic correction of intensity nonuniformity in MRI data , 1998, IEEE Transactions on Medical Imaging.

[47]  Jing Li,et al.  Learning brain connectivity of Alzheimer's disease by sparse inverse covariance estimation , 2010, NeuroImage.

[48]  Feng-Yu Wang,et al.  Sharp explicit lower bounds of heat kernels , 1997 .

[49]  K. Worsley,et al.  Local Maxima and the Expected Euler Characteristic of Excursion Sets of χ 2, F and t Fields , 1994, Advances in Applied Probability.

[50]  S. Edland,et al.  Mixed effect models of longitudinal Alzheimer's disease data: a cautionary note. , 2000, Statistics in medicine.

[51]  Thomas E. Nichols,et al.  Thresholding of Statistical Maps in Functional Neuroimaging Using the False Discovery Rate , 2002, NeuroImage.

[52]  Anthony Widjaja,et al.  Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond , 2003, IEEE Transactions on Neural Networks.

[53]  Kim M. Dalton,et al.  Encoding Cortical Surface by Spherical Harmonics , 2008 .

[54]  A. Dale,et al.  High‐resolution intersubject averaging and a coordinate system for the cortical surface , 1999, Human brain mapping.

[55]  Moo K. Chung,et al.  Heat Kernel Smoothing Using Laplace-Beltrami Eigenfunctions , 2010, MICCAI.

[56]  GelbAnne.  The resolution of the Gibbs phenomenon for spherical harmonics , 1997 .

[57]  Arthur W. Toga,et al.  Harmonic Surface Mapping with Laplace-Beltrami Eigenmaps , 2008, MICCAI.

[58]  U. Grenander,et al.  Statistical methods in computational anatomy , 1997, Statistical methods in medical research.

[59]  Alexandre d'Aspremont,et al.  Convex optimization techniques for fitting sparse Gaussian graphical models , 2006, ICML.

[60]  Luiz Velho,et al.  A Hierarchical Segmentation of Articulated Bodies , 2008, Comput. Graph. Forum.

[61]  Paul M. Thompson,et al.  A Parameterization-Based Numerical Method for Isotropic and Anisotropic Diffusion Smoothing on Non-Flat Surfaces , 2009, IEEE Transactions on Image Processing.

[62]  Benoit M. Dawant,et al.  Neural-network-based segmentation of multi-modal medical images: a comparative and prospective study , 1993, IEEE Trans. Medical Imaging.

[63]  Paul M. Thompson,et al.  Multivariate Statistics of the Jacobian Matrices in Tensor Based Morphometry and Their Application to HIV/AIDS , 2006, MICCAI.

[64]  Alan C. Evans,et al.  Structural maturation of neural pathways in children and adolescents: in vivo study. , 1999, Science.

[65]  G. Arfken.  Mathematical Methods for Physicists , 1967 .

[66]  Michael I. Miller,et al.  Differential geometry of the cortical surface , 1995, Optics & Photonics.

[67]  K. Worsley,et al.  THE DETECTION OF LOCAL SHAPE CHANGES VIA THE GEOMETRY OF HOTELLING’S T 2 FIELDS 1 , 1999 .

[68]  Karl J. Friston,et al.  A unified statistical approach for determining significant signals in images of cerebral activation , 1996, Human brain mapping.

[69]  R. Tibshirani,et al.  Sparse inverse covariance estimation with the graphical lasso. , 2008, Biostatistics.

[70]  Arthur W. Toga,et al.  Cortical Shape Analysis in the Laplace-Beltrami Feature Space , 2009, MICCAI.

[71]  Yvonne Freeh,et al.  An R and S–PLUS Companion to Applied Regression , 2004 .

[72]  Anders M. Dale,et al.  Cortical Surface-Based Analysis I. Segmentation and Surface Reconstruction , 1999, NeuroImage.

[73]  Leonidas J. Guibas,et al.  A concise and provably informative multi-scale signature based on heat diffusion , 2009 .

[74]  Richard J Davidson,et al.  Hippocampal morphometry in depressed patients and control subjects: relations to anxiety symptoms , 2001, Biological Psychiatry.

[75]  Edward R. Dougherty,et al.  Random processes for image and signal processing , 1998, SPIE / IEEE series on imaging science and engineering.

[76]  Moo K. Chung,et al.  Computational Neuroanatomy: The Methods , 2012 .

[77]  Marko Subasic,et al.  Level Set Methods and Fast Marching Methods , 2003 .

[78]  E. Dubois,et al.  Digital picture processing , 1985, Proceedings of the IEEE.

[79]  H. Späth,et al.  Fitting affine and orthogonal transformations between two sets of points , 2004 .

[80]  Michael I. Miller,et al.  A stochastic model for studying the laminar structure of cortex from MRI , 2005, IEEE Transactions on Medical Imaging.

[81]  Jianrong Xu,et al.  Intra-Patient Supine-Prone Colon Registration in CT Colonography Using Shape Spectrum , 2010, MICCAI.

[82]  Florian Steinke,et al.  Non-parametric Regression Between Manifolds , 2008, NIPS.

[83]  Iasonas Kokkinos,et al.  Scale-invariant heat kernel signatures for non-rigid shape recognition , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[84]  Ayse Pinar Saygin,et al.  Smoothing and cluster thresholding for cortical surface-based group analysis of fMRI data , 2006, NeuroImage.

[85]  Lewis D. Griffin.  The intrinsic geometry of the cerebral cortex. , 1994, Journal of theoretical biology.

[86]  Alan C. Evans,et al.  Detecting changes in nonisotropic images , 1999, Human brain mapping.

[87]  Martha Elizabeth Shenton,et al.  Global Medical Shape Analysis Using the Laplace-Beltrami Spectrum , 2007, MICCAI.

[88]  Guido Gerig,et al.  Parametrization of Closed Surfaces for 3-D Shape Description , 1995, Comput. Vis. Image Underst..

[89]  D. Bates,et al.  Mixed-Effects Models in S and S-PLUS , 2001 .

[90]  Mikhail Belkin,et al.  Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples , 2006, J. Mach. Learn. Res..

[91]  K. Worsley,et al.  Random fields of multivariate test statistics, with applications to shape analysis , 2008, 0803.1708.

[92]  KJ Worsley,et al.  SurfStat: A Matlab toolbox for the statistical analysis of univariate and multivariate surface and volumetric data using linear mixed effects models and random field theory , 2009, NeuroImage.

[93]  Alan C. Evans,et al.  Automated 3-D Extraction of Inner and Outer Surfaces of Cerebral Cortex from MRI , 2000, NeuroImage.

[94]  Isabelle Bloch,et al.  A primal sketch of the cortex mean curvature: a morphogenesis based approach to study the variability of the folding patterns , 2003, IEEE Transactions on Medical Imaging.

[95]  R. Adler,et al.  Random Fields and Geometry , 2007 .

[96]  Paul M. Thompson,et al.  Increased local gyrification mapped in Williams syndrome , 2006, NeuroImage.

[97]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[98]  A Bartesaghi,et al.  A system for the generation of curves on 3D brain images , 2001, Human brain mapping.

[99]  Jorge L. Bernal-Rusiel,et al.  Detection of focal changes in human cortical thickness: Spherical wavelets versus Gaussian smoothing , 2008, NeuroImage.

[100]  Karl J. Friston,et al.  Statistical parametric maps in functional imaging: A general linear approach , 1994 .

[101]  Richard M. Leahy,et al.  Optimization method for creating semi-isometric flat maps of the cerebral cortex , 2000, Medical Imaging: Image Processing.

[102]  S. Kiebel,et al.  Detecting Structural Changes in Whole Brain Based on Nonlinear Deformations—Application to Schizophrenia Research , 1999, NeuroImage.

[103]  Ross T. Whitaker,et al.  Geometric surface smoothing via anisotropic diffusion of normals , 2002, IEEE Visualization, 2002. VIS 2002..

[104]  Alan C. Evans,et al.  Anatomical standardization of the human brain in euclidean 3-space and on the cortical 2-manifold , 2004 .

[105]  Alan C. Evans,et al.  GROWTH PATTERNS IN THE DEVELOPING HUMAN BRAIN DETECTED USING CONTINUUM-MECHANICAL TENSOR MAPPING , 1999 .

[106]  K. Strimmer,et al.  Statistical Applications in Genetics and Molecular Biology A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics , 2011 .

[107]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[108]  Michael I. Miller,et al.  Smooth functional and structural maps on the neocortex via orthonormal bases of the Laplace-Beltrami operator , 2006, IEEE Transactions on Medical Imaging.

[109]  A. Toga,et al.  A SURFACE-BASED TECHNIQUE FOR WARPING 3-DIMENSIONAL IMAGES OF THE BRAIN , 2000 .

[110]  Thomas E. Nichols,et al.  Nonparametric permutation tests for functional neuroimaging: A primer with examples , 2002, Human brain mapping.

[111]  Hongtu Zhu,et al.  A Statistical Analysis of Brain Morphology Using Wild Bootstrapping , 2007, IEEE Transactions on Medical Imaging.

[112]  Michael I. Miller,et al.  The emerging discipline of Computational Functional Anatomy , 2009, NeuroImage.

[113]  Vasken Kollokian,et al.  Performance analysis of automatic techniques for tissue classification in magnetic resonance images of the human brain , 1996 .

[114]  Moo K. Chung,et al.  Unified Statistical Approach to Cortical Thickness Analysis , 2005, IPMI.

[115]  Bruno Lévy,et al.  Laplace-Beltrami Eigenfunctions Towards an Algorithm That "Understands" Geometry , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

[116]  Christos Davatzikos,et al.  Spatial Transformation and Registration of Brain Images Using Elastically Deformable Models , 1997, Comput. Vis. Image Underst..

[117]  Anja Vogler,et al.  An Introduction to Multivariate Statistical Analysis , 2004 .

[118]  Moo K. Chung,et al.  The 4D Hyperspherical Diffusion Wavelet: A New Method for the Detection of Localized Anatomical Variation , 2014, MICCAI.

[119]  P. Thomas Fletcher,et al.  Population Shape Regression from Random Design Data , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[120]  Ron Kikinis,et al.  On the Laplace-Beltrami operator and brain surface flattening , 1999, IEEE Transactions on Medical Imaging.

[121]  I. Aharon,et al.  Three‐dimensional mapping of cortical thickness using Laplace's Equation , 2000, Human brain mapping.

[122]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[123]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2003, ICTAI.

[124]  W. Boothby.  An introduction to differentiable manifolds and Riemannian geometry , 1975 .

[125]  Y. Benjamini,et al.  THE CONTROL OF THE FALSE DISCOVERY RATE IN MULTIPLE TESTING UNDER DEPENDENCY , 2001 .

[126]  Michael I. Miller,et al.  Dynamic Programming Generation of Curves on Brain Surfaces , 1998, IEEE Trans. Pattern Anal. Mach. Intell..