In this paper, we exploit spectral shape analysis techniques to detect brain morphological abnormalities. We propose a new shape descriptor able to encode morphometric properties of a brain image or region using diffusion geometry techniques based on the local Heat Kernel. Using this approach, it is possible to design a versatile signature, employed in this case to classify between normal subjects and patients affected by schizophrenia. Several diffusion strategies are assessed to verify the robustness of the proposed descriptor under different deformation variations. A dataset consisting of MRI scans from 30 patients and 30 control subjects is utilized to test the proposed approach, which achieves promising classification accuracies, up to 83.33%. This constitutes a drastic improvement in comparison with other shape description techniques.
