Morphometric Gaussian Process for Landmarking on Grey Matter Tetrahedral Models.

Area of Science:

• Computational neuroimaging
• Manifold learning
• Bayesian modeling

Background:

• High-dimensional manifold modeling enhances cortical morphometry but introduces computational challenges.
• Existing methods may overlook critical geometric features, leading to less significant analyses.
• Gaussian process regression offers dimensionality reduction but may not fully capture morphometric properties.

Purpose of the Study:

• To propose a novel Bayesian model, the morphometric Gaussian process (M-GP), for manifold learning on gray matter meshes.
• To develop an M-GP regression landmarking algorithm for non-linear dimensionality reduction in morphometry.
• To ensure that dimensionality reduction methods incorporate and preserve essential geometric information.

Main Methods:

• Developed a novel Bayesian model, M-GP, operating on gray matter tetrahedral meshes.
• Incorporated a scale-invariant wave kernel signature distance map for local geometric feature similarity.
• Utilized heat flow entropy to implicitly embed global curvature flow information.
• Implemented an M-GP regression landmarking algorithm for manifold learning.

Main Results:

• The M-GP model effectively encodes geometric information, ensuring morphometrically significant posterior predictive inference.
• Experimental evaluation on 518 gray matter meshes from an Alzheimer's disease cohort demonstrated the method's validity.
• The M-GP approach successfully selects a representative data subset from large-scale manifold data.

Conclusions:

• The proposed M-GP is theoretically and experimentally validated for selecting representative subsets from extensive manifold-valued data.
• This method offers a significant improvement over existing techniques by integrating geometric properties.
• The M-GP approach has broad applicability in large-scale or iterative computations for morphometry and medical data processing.