Cortical Surface Reconstruction via Unified Reeb Analysis of Geometric and Topological Outliers in Magnetic Resonance Images

In this paper we present a novel system for the automated reconstruction of cortical surfaces from T1-weighted magnetic resonance images. At the core of our system is a unified Reeb analysis framework for the detection and removal of geometric and topological outliers on tissue boundaries. Using intrinsic Reeb analysis, our system can pinpoint the location of spurious branches and topological outliers, and correct them with localized filtering using information from both image intensity distributions and geometric regularity. In this system, we have also developed enhanced tissue classification with Hessian features for improved robustness to image inhomogeneity, and adaptive interpolation to achieve sub-voxel accuracy in reconstructed surfaces. By integrating these novel developments, we have a system that can automatically reconstruct cortical surfaces with improved quality and dramatically reduced computational cost as compared with the popular FreeSurfer software. In our experiments, we demonstrate on 40 simulated MR images and the MR images of 200 subjects from two databases: the Alzheimer's Disease Neuroimaging Initiative (ADNI) and International Consortium of Brain Mapping (ICBM), the robustness of our method in large scale studies. In comparisons with FreeSurfer, we show that our system is able to generate surfaces that better represent cortical anatomy and produce thickness features with higher statistical power in population studies.

I. Introduction

Cortical surface reconstruction from magnetic resonance (MR) images is a critical problem in brain mapping which provides the geometric foundation for measuring cortical morphometry and tissue integrity. While many sophisticated algorithms were developed for its solution [1]–[11], significant challenges remain in improving the accuracy, robustness, and speed of cortical reconstruction. In this work, we develop a novel system for the automated reconstruction of cortical surfaces from T1-weighted MR images based on intrinsic analysis of geometry and topology using the Reeb graph of Laplace–Beltrami (LB) eigenfunctions. We demonstrate that our system can robustly reconstruct high quality cortical surfaces on large scale data sets.