Ricci flow-based brain surface covariance descriptors for diagnosing Alzheimer's disease

TL;DR

This paper suggests a pipeline to extract novel covariance-based descriptors from the cortical surface using the Ricci energy optimization, and focuses on using the Gaussian radial basis function to apply manifold-based classification to the 3D shape problem.

Abstract

Automated feature extraction from MRI brain scans and diagnosis of Alzheimer's disease are ongoing challenges. With advances in 3D imaging technology, 3D data acquisition is becoming more viable and efficient than its 2D counterpart. Rather than using feature-based vectors, in this paper, for the first time, we suggest a pipeline to extract novel covariance-based descriptors from the cortical surface using the Ricci energy optimization. The covariance descriptors are components of the nonlinear manifold of symmetric positive-definite matrices, thus we focus on using the Gaussian radial basis function to apply manifold-based classification to the 3D shape problem. Applying this novel signature to the analysis of abnormal cortical brain morphometry allows for diagnosing Alzheimer's disease. Experimental studies performed on about two hundred 3D MRI brain models, gathered from Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate the effectiveness of our descriptors in achieving remarkable classification accuracy.

Figures (13)

• Figure 1: Block diagram of the proposed method in this paper.
• Figure 2: Discrete conformal mapping using circle packing.
• Figure 3: (a): The local area around a vertex in the first stage (3-dimensional), (b): The local area around a vertex in the last stage (2-dimensional) of Ricci energy optimization.
• Figure 4: Heat kernel distribution on a hippocampal region of the cerebral cortex in t=1 (left) and t=10 (right).
• Figure 5: Illustration of the functional areas of the left hemisphere of the cerebral cortex.