Fast Polynomial Approximation of Heat Kernel Convolution on Manifolds and Its Application to Brain Sulcal and Gyral Graph Pattern Analysis.
Fast Polynomial Approximation of Heat Kernel Convolution on Manifolds and Its Application to Brain Sulcal and Gyral Graph Pattern Analysis.
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DOI：
10.1109/tmi.2020.2967451
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发表时间：
2020-06
影响因子：
10.6
通讯作者：
Chung MK
中科院分区：
文献类型：
--
作者：
Huang SG;Lyu I;Qiu A;Chung MK
热扩散技术在脑成像中被广泛应用于曲面光顺、网格正则化和皮层数据平滑等方面。基于图上的扩散小波和卷积神经网络，我们提出了一种新的快速精确的数值方法来求解表面网格上的热扩散问题。这是通过在谱域中使用高次正交多项式来近似热核卷积来实现的。我们还导出了Laplace-Beltrami算子谱分解的封闭形式表达式，并首次将其用于求解流形上的热扩散问题。所提出的快速多项式逼近方案避免了求解Laplace-Beltrami算子的本征函数，这对于大网格尺寸来说是计算昂贵的，并且避免了与基于有限元法的扩散求解器相关联的数值不稳定性。所提出的方法是应用于本地化的男性和女性的差异，从MRI获得的大脑皮层沟回图形模式的创新方式。MATLAB代码可在http://www.stat.wisc.edu/mchung/chebyshev上获得。
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.
用于提取皮质沟底的自动化管道。
影响因子：
10.9
作者：
Li, Gang;Guo, Lei;Nie, Jingxin;Liu, Tianming
通讯作者：
Liu, Tianming