## surface shape analysis

The analysis of brain surface is a special case of studying structural properties of objects with closed surfaces. One basic approach for such a surface analysis is the decomposition of the x, y, and z coordinate functions of a given surface (e.g., the grey matter surface). Analogous to 2D Fourier transforms of images, linear combinations of basis functions, called **spherical harmonics**, can be used to deconstruct the surface into its frequency components. After finding a spherical parametrization of the surface (for instance, via conformal mapping), a spherical harmonic transform is applied to each coordinate function of the original surface mesh. The resulting **spherical harmonic coefficients** contain information about the spatial frequency components of the analyzed brain surface. One important question is how these harmonic representations can be used to analyze developmental and clinical differences related to cortical folding.