Fan Yonghui, Leporé Natasha, Wang Yalin
School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, 699 S Mill Ave, Tempe, USA.
CIBORG Lab, Department of Radiology, Children's Hospital Los Angeles, 4650 Sunset Blvd. MS #81, Los Angeles, USA.
Proc SPIE Int Soc Opt Eng. 2020 Jan 3;11330. doi: 10.1117/12.2542492.
High-dimensional manifold modeling increases the precision and performance of cortical morphometry analysis by densely sampling on the grey matters. But this also brings redundant information and increased computational burden. Gaussian process regression has been used to tackle this problem by learning a mapping to a low-dimensional subspace. However, current methods may not take relevant morphometric properties, usually measured by geometric features, into account, and as a result, may generate morphometrically insignificant selections. In this paper, we propose a morphometric Gaussian process (M-GP) as a novel Bayesian model on the gray matter tetrahedral meshes. We also implement an M-GP regression landmarking algorithm as a manifold learning method for non-linear dimensionality reduction. The definition of M-GP involves a scale-invariant wave kernel signature distance map measuring the local similarities of geometric features, and a heat flow entropy which implicitly embeds the global curvature flow. With such a design, the prior knowledge fully encodes the geometric information so that a posterior predictive inference is morphometrically significant. In experiments, we use 518 grey matter tetrahedral meshes generated from structural magnetic resonance images of a publicly available Alzheimer's disease imaging cohort to empirically and numerically evaluate our method. The results verify that our method is theoretically and experimentally valid in selecting a representative subset from the original massive data. Our work may benefit any studies involving large-scale or iterative computations on extensive manifold-valued data, including morphometry analyses and general medical data processing.
高维流形建模通过在灰质上进行密集采样提高了皮质形态计量分析的精度和性能。但这也带来了冗余信息和计算负担的增加。高斯过程回归已被用于通过学习到低维子空间的映射来解决这个问题。然而，当前的方法可能没有考虑到通常由几何特征测量的相关形态计量属性，因此可能会产生形态计量上无意义的选择。在本文中，我们提出了形态计量高斯过程（M-GP）作为灰质四面体网格上的一种新型贝叶斯模型。我们还实现了一种M-GP回归地标算法作为一种用于非线性降维的流形学习方法。M-GP的定义涉及一个测量几何特征局部相似性的尺度不变波核特征距离图，以及一个隐含嵌入全局曲率流的热流熵。通过这样的设计，先验知识充分编码了几何信息，使得后验预测推理在形态计量上具有意义。在实验中，我们使用从一个公开可用的阿尔茨海默病成像队列的结构磁共振图像生成的518个灰质四面体网格，从经验和数值上评估我们的方法。结果验证了我们的方法在从原始海量数据中选择代表性子集方面在理论和实验上都是有效的。我们的工作可能会使任何涉及对大量流形值数据进行大规模或迭代计算的研究受益，包括形态计量分析和一般医学数据处理。
