Alzheimer's disease (AD) is a progressive neurodegenerative disorder that causes brain regions to undergo structural changes. Shape descriptors are useful in reflecting the morphological alterations of brain structures in AD conditions compared to volume based measures. In this work, moment based shape descriptors are used to classify control, mild cognitive impairment (MCI) and AD subjects. Lattice Boltzmann criterion-based hybrid level set method (LSM) is used to delineate lateral ventricles. Legendre and United moments are extracted from the segmented binary images and are statistically analysed using Statistical Package for Social Science (SPSS). The performance of significant moments in the shape analysis is validated using machine learning algorithm. Results demonstrate that, level set is able to delineate ventricles and found to have high similarity index with ground truth. The area under curve (AUC) values for Legendre moment is found to be 1.0, 0.75 and 1.0 for Control-MCI, MCI-AD and Control-AD subjects. Rather, the AUC for United moment is found to be 0.98, 0.76 and 0.98 for Control-MCI, MCI-AD and Control-AD subjects respectively. Further, machine learning algorithm could classify Control from AD subjects with high accuracy of 99.25% using Legendre moments and hence the study seems to be clinically significant. © The Institution of Engineering and Technology 2019