流形上扩散、核平滑和小波的统一热核回归及其在CT图像下颌骨生长建模中的应用
Unified heat kernel regression for diffusion, kernel smoothing and wavelets on manifolds and its application to mandible growth modeling in CT images.
作者信息
Chung Moo K, Qiu Anqi, Seo Seongho, Vorperian Houri K
机构信息
Department of Biostatistics and Medical Informatics, USA; Vocal Tract Development Laboratory, Waisman Center, University of Wisconsin, Madison, USA.
Department of Biomedical Engineering, National University of Singapore, Singapore.
出版信息
Med Image Anal. 2015 May;22(1):63-76. doi: 10.1016/j.media.2015.02.003. Epub 2015 Mar 2.
Abstract
We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel method is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, the method is applied to characterize the localized growth pattern of mandible surfaces obtained in CT images between ages 0 and 20 by regressing the length of displacement vectors with respect to a surface template.
摘要
我们提出了一种新颖的核回归框架，用于使用拉普拉斯 - 贝尔特拉米特征函数对标量曲面数据进行平滑处理。从由特征函数构建的热核出发，我们将一个新的双变量核回归框架表述为以热核为权重的加权特征函数展开。新的核方法在数学上等同于各向同性热扩散、核平滑以及最近流行的扩散小波。使用球谐函数在单位球面上对数值实现进行了验证。作为示例，通过将位移向量的长度相对于曲面模板进行回归，该方法被应用于表征在0到20岁之间的CT图像中获得的下颌骨表面的局部生长模式。
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