Brain Morphometry Analysis with Surface Foliation Theory

TL;DR

This paper introduces a novel, automatic brain surface morphometry method based on surface foliation theory, utilizing intrinsic geometric features for classifying Alzheimer's disease from healthy controls.

Contribution

It is the first to apply surface foliation theory to brain morphometry, providing a rigorous, geometric, and automatic analysis framework with new intrinsic features.

Findings

Effective classification of Alzheimer's disease using the proposed features.

Features are intrinsic and geometrically meaningful.

Method demonstrates high efficiency and efficacy in experiments.

Abstract

Brain morphometry study plays a fundamental role in neuroimaging research. In this work, we propose a novel method for brain surface morphometry analysis based on surface foliation theory. Given brain cortical surfaces with automatically extracted landmark curves, we first construct finite foliations on surfaces. A set of admissible curves and a height parameter for each loop are provided by users. The admissible curves cut the surface into a set of pairs of pants. A pants decomposition graph is then constructed. Strebel differential is obtained by computing a unique harmonic map from surface to pants decomposition graph. The critical trajectories of Strebel differential decompose the surface into topological cylinders. After conformally mapping those topological cylinders to standard cylinders, parameters of standard cylinders (height, circumference) are intrinsic geometric features of the original cortical surfaces and thus can be used for morphometry analysis purpose. In this work, we propose a set of novel surface features rooted in surface foliation theory. To the best of our knowledge, this is the first work to make use of surface foliation theory for brain morphometry analysis. The features we computed are intrinsic and informative. The proposed method is rigorous, geometric, and automatic. Experimental results on classifying brain cortical surfaces between patients with Alzheimer's disease and healthy control subjects demonstrate the efficiency and efficacy of our method.