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Unified heat kernel regression for diffusion, kernel smoothing and wavelets on manifolds and its application to mandible growth modeling in CT images

https://doi.org/10.1016/j.media.2015.02.003

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Applications of random field theory to functional connectivity

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Detecting changes in nonisotropic images

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Detection of fMRI activation using Cortical Surface Mapping

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On the growth of the mandible

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Gender effects on cortical thickness and the influence of scaling

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Topological correction of brain surface meshes using spherical harmonics

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Analysis of fMRI Time-Series Revisited—Again

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Tests for Distributed, Nonfocal Brain Activations

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Unified Statistical Approach to Cortical Thickness Analysis

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Fast Difference Schemes for Edge Enhancing Beltrami Flow

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Applications of Random Fields in Human Brain Mapping

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Global Medical Shape Analysis Using the Laplace-Beltrami Spectrum

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Medical Image Computing and Computer-Assisted Intervention – MICCAI 2008

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Harmonic Surface Mapping with Laplace-Beltrami Eigenmaps

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Topological Correction of Brain Surface Meshes Using Spherical Harmonics

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Cortical Shape Analysis in the Laplace-Beltrami Feature Space

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Intra-Patient Supine-Prone Colon Registration in CT Colonography Using Shape Spectrum

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Heat Kernel Smoothing Using Laplace-Beltrami Eigenfunctions

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Heat Kernel Smoothing via Laplace-Beltrami Eigenfunctions and Its Application to Subcortical Structure Modeling

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Discrete Differential Geometry

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Convergence of the Cotangent Formula: An Overview

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Partial Differential Equations

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Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions

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Dento-facial development and growth

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Methods for fast morphological image transforms using bitmapped binary images

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Diffusion wavelets

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Diffusion wavelet packets

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Wavelet transform on manifolds: Old and new approaches

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Wavelets on graphs via spectral graph theory

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Evaluating the mandible with cone-beam computed tomography

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Laplace–Beltrami spectra as ‘Shape-DNA’ of surfaces and solids

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Laplace–Beltrami eigenvalues and topological features of eigenfunctions for statistical shape analysis

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Volumetric heat Kernel: Padé-Chebyshev approximation, convergence, and computation

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Nonstationary cluster-size inference with random field and permutation methods

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Unified univariate and multivariate random field theory

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Cortical thickness analysis examined through power analysis and a population simulation

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Unbiased diffeomorphic atlas construction for computational anatomy

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A curvature-based approach to estimate local gyrification on the cortical surface

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Reliability of MRI-derived measurements of human cerebral cortical thickness: The effects of field strength, scanner upgrade and manufacturer

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Increased local gyrification mapped in Williams syndrome

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Smoothing and cluster thresholding for cortical surface-based group analysis of fMRI data

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Diffeomorphic metric surface mapping in subregion of the superior temporal gyrus

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Spatial accuracy of fMRI activation influenced by volume- and surface-based spatial smoothing techniques

inferredcites →https://doi.org/10.1016/j.neuroimage.2008.01.013openalex-snapshot

Structure-specific statistical mapping of white matter tracts

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Detection of focal changes in human cortical thickness: Spherical wavelets versus Gaussian smoothing

inferredcites →https://doi.org/10.1016/j.neuroimage.2008.04.257openalex-snapshot

Multi-structure network shape analysis via normal surface momentum maps

inferredcites →https://doi.org/10.1016/j.neuroimage.2008.10.044openalex-snapshot

The emerging discipline of Computational Functional Anatomy

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Multi-manifold diffeomorphic metric mapping for aligning cortical hemispheric surfaces

inferredcites →https://doi.org/10.1016/j.neuroimage.2009.10.086openalex-snapshot

Multivariate tensor-based morphometry on surfaces: Application to mapping ventricular abnormalities in HIV/AIDS

inferredcites →https://doi.org/10.1016/j.neuroimage.2011.01.069openalex-snapshot

Locally Linear Diffeomorphic Metric Embedding (LLDME) for surface-based anatomical shape modeling

inferredcites →https://doi.org/10.1016/j.patcog.2011.03.006openalex-snapshot

Wavelet kernel learning

inferredcites →https://doi.org/10.1016/j.tripleo.2005.10.039openalex-snapshot

Assessment of bone segmentation quality of cone-beam CT versus multislice spiral CT: a pilot study

inferredcites →https://doi.org/10.1016/s0278-2391(97)90621-2openalex-snapshot

Essentials of facial growth

inferredcites →https://doi.org/10.1016/s1053-8119(01)91438-7openalex-snapshot

Diffusion smoothing on the cortical surface

inferredcites →https://doi.org/10.1016/s1361-8415(03)00031-8openalex-snapshot

A generic framework for the parcellation of the cortical surface into gyri using geodesic Voronoı diagrams

inferredcites →https://doi.org/10.1017/cbo9780511623783.002openalex-snapshot

The Laplacian on a Riemannian Manifold

inferredcites →https://doi.org/10.1017/cbo9780511809682openalex-snapshot

Kernel Methods for Pattern Analysis

inferredcites →https://doi.org/10.1043/0003-3219(1982)052<0325:gotmdp>2.0.co;2openalex-snapshot

Growth of the mandible during pubescence.

inferredcites →https://doi.org/10.1088/0031-9155/52/16/006openalex-snapshot

Evaluation of smoothing in an iterativelp-norm minimization algorithm for surface-based source localization of MEG

inferredcites →https://doi.org/10.1090/qam/1632326openalex-snapshot

Variational problems on flows of diffeomorphisms for image matching

inferredcites →https://doi.org/10.1097/00008505-199600540-00041openalex-snapshot

Essentials of Facial Growth

inferredcites →https://doi.org/10.1097/01.prs.0000169940.69315.9copenalex-snapshot

The Pediatric Mandible: I. A Primer on Growth and Development

inferredcites →https://doi.org/10.1109/34.56205openalex-snapshot

Scale-space and edge detection using anisotropic diffusion

inferredcites →https://doi.org/10.1109/34.824822openalex-snapshot

Medical image analysis: progress over two decades and the challenges ahead

inferredcites →https://doi.org/10.1109/42.896780openalex-snapshot

Surface-bounded growth modeling applied to human mandibles

inferredcites →https://doi.org/10.1109/83.661181openalex-snapshot

A general framework for low level vision

inferredcites →https://doi.org/10.1109/cvpr.2010.5539838openalex-snapshot

Scale-invariant heat kernel signatures for non-rigid shape recognition

inferredcites →https://doi.org/10.1109/iccv.1999.790423openalex-snapshot

Direction diffusion

inferredcites →https://doi.org/10.1109/isbi.2004.1398567openalex-snapshot

Diffusion smoothing on brain surface via finite element method

inferredcites →https://doi.org/10.1109/isbi.2007.356825openalex-snapshot

STATISTICAL SHAPE ANALYSIS OF BRAIN STRUCTURES USING SPHERICAL WAVELETS

inferredcites →https://doi.org/10.1109/isbi.2011.5872426openalex-snapshot

Laplace-Beltrami eigenfunction expansion of cortical manifolds

inferredcites →https://doi.org/10.1109/smi.2006.21openalex-snapshot

Laplace-Beltrami Eigenfunctions Towards an Algorithm That "Understands" Geometry

inferredcites →https://doi.org/10.1109/tip.2009.2016163openalex-snapshot

A Parameterization-Based Numerical Method for Isotropic and Anisotropic Diffusion Smoothing on Non-Flat Surfaces

inferredcites →https://doi.org/10.1109/tmi.2003.814781openalex-snapshot

A primal sketch of the cortex mean curvature: A morphogenesis based approach to study the variability of the folding patterns

inferredcites →https://doi.org/10.1109/tmi.2006.882143openalex-snapshot

Smooth functional and structural maps on the neocortex via orthonormal bases of the Laplace-Beltrami operator

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A Statistical Analysis of Brain Morphology Using Wild Bootstrapping

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Spectral Geometry Processing with Manifold Harmonics

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A Hierarchical Segmentation of Articulated Bodies

inferredcites →https://doi.org/10.1111/j.1467-8659.2009.01515.xopenalex-snapshot

A Concise and Provably Informative Multi‐Scale Signature Based on Heat Diffusion

inferredcites →https://doi.org/10.1111/j.1467-8659.2010.01655.xopenalex-snapshot

Spectral Mesh Processing

inferredcites →https://doi.org/10.1112/blms/14.1.59openalex-snapshot

THE GEOMETRY OF RANDOM FIELDS

inferredcites →https://doi.org/10.1117/12.877537openalex-snapshot

Mandible shape modeling using the second eigenfunction of the Laplace-Beltrami operator

inferredcites →https://doi.org/10.1137/1.9780898718980openalex-snapshot

The Geometry of Random Fields

inferredcites →https://doi.org/10.1137/1.9780898719628openalex-snapshot

ARPACK Users' Guide

inferredcites →https://doi.org/10.1137/s003614450036757xopenalex-snapshot

Strong Stability-Preserving High-Order Time Discretization Methods

inferredcites →https://doi.org/10.1145/1273496openalex-snapshot

Proceedings of the 24th international conference on Machine learning

inferredcites →https://doi.org/10.1145/1273496.1273584openalex-snapshot

Regression on manifolds using kernel dimension reduction

inferredcites →https://doi.org/10.1145/990002.990007openalex-snapshot

Removing excess topology from isosurfaces

inferredcites →https://doi.org/10.1191/0962280203sm340raopenalex-snapshot

Detecting activation in fMRI data

inferredcites →https://doi.org/10.1198/016214507000000815openalex-snapshot

Detecting Sparse Signals in Random Fields, With an Application to Brain Mapping

inferredcites →https://doi.org/10.1198/jasa.2003.s269openalex-snapshot

Learning With Kernels: Support Vector Machines, Regularization, Optimization, and Beyond

inferredcites →https://doi.org/10.1214/10-aoas337openalex-snapshot

Topological inference for EEG and MEG

inferredcites →https://doi.org/10.1214/aop/1023481118openalex-snapshot

Sharp explicit lower bounds of heat kernels

inferredcites →https://doi.org/10.1515/9783111302522-004openalex-snapshot

4 Partial differential equations

inferredcites →https://doi.org/10.20380/gi2001.03openalex-snapshot

Topological Noise Removal

inferredcites →https://doi.org/10.2307/2287334openalex-snapshot

The Geometry of Random Fields.

inferredcites →https://doi.org/10.2312/egst.20001029openalex-snapshot

Geometric Signal Processing on Polygonal Meshes

inferredcites →https://doi.org/10.2312/egst.20071052openalex-snapshot

Spectral Methods for Mesh Processing and Analysis

inferredcites →https://doi.org/10.3233/ida-2004-8602openalex-snapshot

A surface-based approach for classification of 3D neuroanatomic structures

inferredcites →https://doi.org/10.4171/owr/2009/02openalex-snapshot

Discrete Differential Geometry

inferredcites →https://doi.org/10.54294/owxzilopenalex-snapshot

Framework for the Statistical Shape Analysis of Brain Structures using SPHARM-PDM

inferredcites →https://doi.org/10.5555/1248547.1248632openalex-snapshot

Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples

inferredcites →https://doi.org/10.5555/1281991.1282022openalex-snapshot

Laplace-Beltrami eigenfunctions for deformation invariant shape representation

inferredcites →https://doi.org/10.7551/mitpress/4175.001.0001openalex-snapshot

Learning with Kernels

inferredcites →https://doi.org/10.82308/37914openalex-snapshot

Statistical morphometry in Neuroanatomy

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.2139/ssrn.4648197openalex-extracted

Reliable and Autonomy-Enabled Collaborative Medical Prediction System Using Distributed Learning

inferred← citeshttps://doi.org/10.1002/ar.24594openalex-snapshot

Growth and sexual dimorphism of the hyoid bone and its relationship to the mandible from birth to 19 years: A three‐dimensional computed tomography study

inferred← citeshttps://doi.org/10.1007/978-3-030-32251-9_6openalex-snapshot

Fast Polynomial Approximation to Heat Diffusion in Manifolds

inferred← citeshttps://doi.org/10.1007/978-3-030-32520-6_42openalex-snapshot

K-means Principal Geodesic Analysis on Riemannian Manifolds

inferred← citeshttps://doi.org/10.1007/978-3-030-33226-6_21openalex-snapshot

Mixture Probabilistic Principal Geodesic Analysis

inferred← citeshttps://doi.org/10.1007/978-3-030-33416-1_12openalex-snapshot

Heat Kernel Smoothing on Manifolds and Its Application to Hyoid Bone Growth Modeling

inferred← citeshttps://doi.org/10.1007/978-3-032-37595-7_17openalex-snapshot

Heat Kernel Textures the Geodesic Gaussians That Do Not Splat

inferred← citeshttps://doi.org/10.1007/978-3-319-66185-8_82openalex-snapshot

Online Statistical Inference for Large-Scale Binary Images

inferred← citeshttps://doi.org/10.1007/978-3-319-67159-8_16openalex-snapshot

Topological Network Analysis of Electroencephalographic Power Maps

inferred← citeshttps://doi.org/10.1007/s00521-021-06006-6openalex-snapshot

Revisiting convolutional neural network on graphs with polynomial approximations of Laplace–Beltrami spectral filtering

inferred← citeshttps://doi.org/10.1007/s10489-022-03492-6openalex-snapshot

Robust kernel ensemble regression in diversified kernel space with shared parameters

inferred← citeshttps://doi.org/10.1007/s11222-023-10288-2openalex-snapshot

Penalized model-based clustering of complex functional data

inferred← citeshttps://doi.org/10.1007/s11548-016-1451-yopenalex-snapshot

Planning of mandibular reconstructions based on statistical shape models

inferred← citeshttps://doi.org/10.1007/s11760-016-1013-3openalex-snapshot

Single image dehazing using kernel regression model and dark channel prior

inferred← citeshttps://doi.org/10.1016/j.archoralbio.2017.01.018openalex-snapshot

Characterizing mandibular growth using three-dimensional imaging techniques and anatomic landmarks

inferred← citeshttps://doi.org/10.1016/j.compbiomed.2024.108455openalex-snapshot

An open-source, three-dimensional growth model of the mandible

inferred← citeshttps://doi.org/10.1016/j.media.2021.102123openalex-snapshot

Tetrahedral spectral feature-Based bayesian manifold learning for grey matter morphometry: Findings from the Alzheimer’s disease neuroimaging initiative

inferred← citeshttps://doi.org/10.1016/j.neunet.2021.05.025openalex-snapshot

Fast mesh data augmentation via Chebyshev polynomial of spectral filtering

inferred← citeshttps://doi.org/10.1017/9781316882610openalex-snapshot

Brain Network Analysis

inferred← citeshttps://doi.org/10.1017/9781316882610.001openalex-snapshot

Preface

inferred← citeshttps://doi.org/10.1017/9781316882610.002openalex-snapshot

Statistical Preliminary

inferred← citeshttps://doi.org/10.1017/9781316882610.003openalex-snapshot

Brain Network Nodes and Edges

inferred← citeshttps://doi.org/10.1017/9781316882610.004openalex-snapshot

Graph Theory

inferred← citeshttps://doi.org/10.1017/9781316882610.005openalex-snapshot

Correlation Networks

inferred← citeshttps://doi.org/10.1017/9781316882610.006openalex-snapshot

Big Brain Network Data

inferred← citeshttps://doi.org/10.1017/9781316882610.007openalex-snapshot

Network Simulations

inferred← citeshttps://doi.org/10.1017/9781316882610.008openalex-snapshot

Persistent Homology

inferred← citeshttps://doi.org/10.1017/9781316882610.009openalex-snapshot

Diffusions on Graphs

inferred← citeshttps://doi.org/10.1017/9781316882610.010openalex-snapshot

Sparse Networks

inferred← citeshttps://doi.org/10.1017/9781316882610.011openalex-snapshot

Brain Network Distances

inferred← citeshttps://doi.org/10.1017/9781316882610.012openalex-snapshot

Combinatorial Inferences for Networks

inferred← citeshttps://doi.org/10.1017/9781316882610.013openalex-snapshot

Series Expansion of Connectivity Matrices

inferred← citeshttps://doi.org/10.1017/9781316882610.014openalex-snapshot

Dynamic Network Models

inferred← citeshttps://doi.org/10.1017/9781316882610.015openalex-snapshot

Bibliography

inferred← citeshttps://doi.org/10.1017/9781316882610.016openalex-snapshot

Index

inferred← citeshttps://doi.org/10.1021/acs.jcim.6c02173openalex-snapshot

DESPOT: Direction-Enhanced Scoring POTentials for Scoring of Protein–Ligand Interactions

inferred← citeshttps://doi.org/10.1038/s41598-021-98421-xopenalex-snapshot

A three-dimensional statistical shape model of the growing mandible

inferred← citeshttps://doi.org/10.1080/10618600.2026.2670661openalex-snapshot

Low-Rank Neural Regression Models for Spatial Data on Complex Domains

inferred← citeshttps://doi.org/10.1093/jrsssb/qkae023openalex-snapshot

Interpretable discriminant analysis for functional data supported on random nonlinear domains with an application to Alzheimer’s disease

inferred← citeshttps://doi.org/10.1097/rct.0000000000000669openalex-snapshot

A Novel Registration-Based Semiautomatic Mandible Segmentation Pipeline Using Computed Tomography Images to Study Mandibular Development

inferred← citeshttps://doi.org/10.1109/embc.2018.8513450openalex-snapshot

Discrete Heat Kernel Smoothing in Irregular Image Domains

inferred← citeshttps://doi.org/10.1109/icassp.2019.8682979openalex-snapshot

Kernel Regression for Graph Signal Prediction in Presence of Sparse Noise

inferred← citeshttps://doi.org/10.1109/tmi.2020.2967451openalex-snapshot

Fast Polynomial Approximation of Heat Kernel Convolution on Manifolds and Its Application to Brain Sulcal and Gyral Graph Pattern Analysis

inferred← citeshttps://doi.org/10.1109/tsipn.2019.2936358openalex-snapshot

Predicting Graph Signals Using Kernel Regression Where the Input Signal is Agnostic to a Graph

inferred← citeshttps://doi.org/10.1117/1.jei.25.4.043003openalex-snapshot

Single image dehazing algorithm using wavelet decomposition and fast kernel regression model

inferred← citeshttps://doi.org/10.1214/21-sts825openalex-snapshot

Diffusion Smoothing for Spatial Point Patterns

inferred← citeshttps://doi.org/10.3390/app10041223openalex-snapshot

Analysis of the Quantization Noise in Discrete Wavelet Transform Filters for 3D Medical Imaging

inferred← citeshttps://doi.org/10.3390/books978-3-0365-1475-8openalex-snapshot

Mathematics and Digital Signal Processing

inferred← citeshttps://doi.org/10.3390/diagnostics13061111openalex-snapshot

Noise Reduction Using Singular Value Decomposition with Jensen–Shannon Divergence for Coronary Computed Tomography Angiography

inferred← citeshttps://doi.org/10.3390/e24070951openalex-snapshot

Lossless Medical Image Compression by Using Difference Transform

inferred← citeshttps://doi.org/10.3390/s18072379openalex-snapshot

Fast Feature-Preserving Approach to Carpal Bone Surface Denoising

inferred← citeshttps://doi.org/10.48550/arxiv.2102.08623openalex-snapshot

Reviews: Topological Distances and Losses for Brain Networks

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