Hosseinbor Ameer Pasha, Kim Won Hwa, Adluru Nagesh, Acharya Amit, Vorperian Houri K, Chung Moo K
Med Image Comput Comput Assist Interv. 2014;17(Pt 3):65-72. doi: 10.1007/978-3-319-10443-0_9.
Recently, the HyperSPHARM algorithm was proposed to parameterize multiple disjoint objects in a holistic manner using the 4D hyperspherical harmonics. The HyperSPHARM coefficients are global; they cannot be used to directly infer localized variations in signal. In this paper, we present a unified wavelet framework that links Hyper-SPHARM to the diffusion wavelet transform. Specifically, we will show that the HyperSPHARM basis forms a subset of a wavelet-based multiscale representation of surface-based signals. This wavelet, termed the hyperspherical diffusion wavelet, is a consequence of the equivalence of isotropic heat diffusion smoothing and the diffusion wavelet transform on the hypersphere. Our framework allows for the statistical inference of highly localized anatomical changes, which we demonstrate in the first-ever developmental study on the hyoid bone investigating gender and age effects. We also show that the hyperspherical wavelet successfully picks up group-wise differences that are barely detectable using SPHARM.
最近，提出了HyperSPHARM算法，以使用4D超球谐函数以整体方式对多个不相交的对象进行参数化。HyperSPHARM系数是全局的；它们不能用于直接推断信号中的局部变化。在本文中，我们提出了一个统一的小波框架，将Hyper-SPHARM与扩散小波变换联系起来。具体来说，我们将表明HyperSPHARM基构成了基于表面信号的基于小波的多尺度表示的一个子集。这种小波，称为超球扩散小波，是超球面上各向同性热扩散平滑和扩散小波变换等价的结果。我们的框架允许对高度局部化的解剖变化进行统计推断，我们在有史以来第一项关于舌骨的发育研究中研究了性别和年龄效应，证明了这一点。我们还表明，超球小波成功地捕捉到了使用SPHARM几乎无法检测到的组间差异。
