Studying morphological changes of subcortical structures often predicate neurodevelopmental and neurodegenerative diseases, such as Alzheimer's disease and schizophrenia. Hence, methods for quantifying morphological variations in the brain anatomy, including groupwise shape analyses, are becoming increasingly important for studying neurological disorders. In this paper, a novel groupwise shape analysis approach is proposed to detect regional morphological alterations in subcortical structures between two study groups, e.g., healthy and pathological subjects. The proposed scheme extracts smoothed triangulated surface meshes from segmented binary maps, and establishes reliable point-to-point correspondences among the population of surfaces using a spectral matching method. Mean curvature features are incorporated in the matching process, in order to increase the accuracy of the established surface correspondence. The mean shapes are created as the geometric mean of all surfaces in each group, and a distance map between these shapes is used to characterize the morphological changes between the two study groups. The resulting distance map is further analyzed to check for statistically significant differences between two populations. The performance of the proposed framework is evaluated on two separate subcortical structures (hippocampus and putamen). Furthermore, the proposed methodology is validated in a clinical application for detecting abnormal subcortical shape variations in Alzheimer's disease. Experimental results show that the proposed method is comparable to state-of-the-art algorithms, has less computational cost, and is more sensitive to small morphological variations in patients with neuropathologies. 
Statistical shape analysis of subcortical structures using spectral matching