Mathematics, Computation and Geometry of Data

Volume 2 (2022)

Number 2

A novel geometric model for Alzheimer’s disease diagnosis based on Laplace–Beltrami spectrum and texture analysis

Pages: 89 – 115



Zhehao Xu (The Chinese University of Hong Kong)

Lok Ming Lui (The Chinese University of Hong Kong)


This paper proposes a new model for the early diagnosis of Alzheimer’s Disease (AD), which can distinguish between normal control subjects (NC) and AD subjects as well as between early mild cognitive impairment subjects (EMCI) and late mild cognitive impairment subjects (LMCI). Surface geometry characteristics of the hippocampus and amygdala are quantified by LB spectrum using the finite element method. Besides, we extract labels on which certain measures are statistically significant. In addition, texture analysis is performed on the amygdala and hippocampus to identify subtle changes in deep white matter. Afterwards, a two-sample t-test with a bagging strategy is applied to filter out non-significant features, followed by a multiple comparison correction. Finally, we use different methods for further feature selection and compare the accuracy of the support vector machine trained with features selected by different approaches. The proposed algorithm achieves the best result of 93.33% accuracy on the AD-NC classification tasks with 311 samples and 80.00% accuracy in the EMCI-LMCI classification tasks with 383 samples. From the finally selected features and achieved accuracy, we may deduce that changes in the hippocampus, amygdala, and certain regions of the cortex play an important role in the early diagnosis of AD.


Alzheimer’s disease, mild cognitive impairment, Laplace–Beltrami spectrum, texture analysis, medical image analysis

Received 18 July 2022

Published 21 March 2023