ArticleIEEE transactions on medical imaging2020
Fast Polynomial Approximation of Heat Kernel Convolution on Manifolds and Its Application to Brain Sulcal and Gyral Graph Pattern Analysis.
Article in IEEE transactions on medical imaging, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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Who cites it
13 citing papers in PubMed, 25 citations in OpenAlex.
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- HKD-MGIN: a physics informed graph neural network using heat kernel diffusion for mapping adolescent functional brain connectivity.Machine learning for computational science and engineering · 2025Article
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- Estimating Outlier-Immunized Common Harmonic Waves for Brain Network Analyses on the Stiefel Manifold.IEEE journal of biomedical and health informatics · 2023Article
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- Characterizing the propagation pathway of neuropathological events of Alzheimer's disease using harmonic wavelet analysis.Medical image analysis · 2022Article
- Discussion of 'Event history and topological data analysis'.Biometrika · 2021Article
- Fast mesh data augmentation via Chebyshev polynomial of spectral filtering.Neural networks : the official journal of the International Neural Network Society · 2021Article
- Cortical Surface-Informed Volumetric Spatial Smoothing of fMRI Data via Graph Signal Processing.Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference · 2021Article
- Revisiting convolutional neural network on graphs with polynomial approximations of Laplace-Beltrami spectral filtering.Neural computing & applications · 2021Article
- Tetrahedral spectral feature-Based bayesian manifold learning for grey matter morphometry: Findings from the Alzheimer's disease neuroimaging initiative.Medical image analysis · 2021Article
- Labeling lateral prefrontal sulci using spherical data augmentation and context-aware training.NeuroImage · 2021Article
- Convolutional Bayesian Models for Anatomical Landmarking on Multi-Dimensional Shapes.Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention · 2020Article
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Authors and funding
4 authors at 3 institutions in 2 countries.
Funding
Abstract
Heat diffusion has been widely used in brain imaging for surface fairing, mesh regularization and cortical data smoothing. Motivated by diffusion wavelets and convolutional neural networks on graphs, we present a new fast and accurate numerical scheme to solve heat diffusion on surface meshes. This is achieved by approximating the heat kernel convolution using high degree orthogonal polynomials in the spectral domain. We also derive the closed-form expression of the spectral decomposition of the Laplace-Beltrami operator and use it to solve heat diffusion on a manifold for the first time. The proposed fast polynomial approximation scheme avoids solving for the eigenfunctions of the Laplace-Beltrami operator, which is computationally costly for large mesh size, and the numerical instability associated with the finite element method based diffusion solvers. The proposed method is applied in localizing the male and female differences in cortical sulcal and gyral graph patterns obtained from MRI in an innovative way. The MATLAB code is available at http://www.stat.wisc.edu/~mchung/chebyshev.
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