How to analyze complex shapes, such as of the highly folded surface of the brain? This talk will show how spectral representations of shapes can benefit neuroimaging. Here, we exploit spectral coordinates derived from the eigenfunctions of the graph Laplacian. Methodologically, we address the inherent instability of spectral shape decompositions. This change of paradigm, exploiting spectral representations, enables an intrinsic processing of brain surfaces. Brain surface matching will be shown as an example.