School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ, USA.
School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ, USA; School of Information and Electrical Engineering, Ludong University, Yantai, China.
Med Image Anal. 2021 Aug;72:102123. doi: 10.1016/j.media.2021.102123. Epub 2021 Jun 8.
Structural and anatomical analyses of magnetic resonance imaging (MRI) data often require a reconstruction of the three-dimensional anatomy to a statistical shape model. Our prior work demonstrated the usefulness of tetrahedral spectral features for grey matter morphometry. However, most of the current methods provide a large number of descriptive shape features, but lack an unsupervised scheme to automatically extract a concise set of features with clear biological interpretations and that also carries strong statistical power. Here we introduce a new tetrahedral spectral feature-based Bayesian manifold learning framework for effective statistical analysis of grey matter morphology. We start by solving the technical issue of generating tetrahedral meshes which preserve the details of the grey matter geometry. We then derive explicit weak-form tetrahedral discretizations of the Hamiltonian operator (HO) and the Laplace-Beltrami operator (LBO). Next, the Schrödinger's equation is solved for constructing the scale-invariant wave kernel signature (SIWKS) as the shape descriptor. By solving the heat equation and utilizing the SIWKS, we design a morphometric Gaussian process (M-GP) regression framework and an active learning strategy to select landmarks as concrete shape descriptors. We evaluate the proposed system on publicly available data from the Alzheimers Disease Neuroimaging Initiative (ADNI), using subjects structural MRI covering the range from cognitively unimpaired (CU) to full blown Alzheimer's disease (AD). Our analyses suggest that the SIWKS and M-GP compare favorably with seven other baseline algorithms to obtain grey matter morphometry-based diagnoses. Our work may inspire more tetrahedral spectral feature-based Bayesian learning research in medical image analysis.
磁共振成像（MRI）数据的结构和解剖分析通常需要将三维解剖结构重建到统计形状模型中。我们之前的工作证明了四面体谱特征在灰质形态计量学中的有用性。然而，目前大多数方法提供了大量的描述性形状特征，但缺乏一种无监督的方案来自动提取一组具有清晰生物学解释且具有强大统计能力的简洁特征。在这里，我们引入了一种新的基于四面体谱特征的贝叶斯流形学习框架，用于有效地分析灰质形态。我们首先解决了生成保留灰质几何细节的四面体网格的技术问题。然后，我们推导出哈密顿算子（HO）和拉普拉斯-贝尔特拉米算子（LBO）的显式弱形式四面体离散化。接下来，通过求解薛定谔方程来构建作为形状描述符的标度不变波核特征（SIWKS）。通过求解热方程并利用 SIWKS，我们设计了形态高斯过程（M-GP）回归框架和主动学习策略来选择地标作为具体的形状描述符。我们使用来自阿尔茨海默病神经影像学倡议（ADNI）的公开数据评估了所提出的系统，使用涵盖认知正常（CU）到完全阿尔茨海默病（AD）的受试者结构 MRI。我们的分析表明，SIWKS 和 M-GP 与其他七种基线算法相比，在获得基于灰质形态计量学的诊断方面表现出色。我们的工作可能会激发更多基于四面体谱特征的贝叶斯学习在医学图像分析中的研究。
