Abstract: Shape analysis plays an important role in brain mapping as it has the potential of computing informative biomarkers for the early diagnosis and tracking of neurological diseases. In this talk, I will present our recent work on 3D brain shape analysis using the eigenfunctions of the Laplace-Beltrami (LB) operator. The spectra of the LB operator provides an intrinsic way of characterizing 3D shapes. By computing the Reeb graph of LB eigenfunctions, we can construct robust skeletal features of 3D surfaces. Using global features extracted from the LB eigenfunctions, we can compute robust surface maps that enable the localized analysis of morphometric changes. Experimental results on the automated analysis of thousands of shapes will be presented.