Diffusion Smoothing on the Cortical Surface

Moo K. Chung , Keith J. Worsley , Jonathan Taylor , Jim Ramsay , Steve Robbins , Alan C. Evans Department of Mathematics and Statistics Montreal Neurological Institute Department of Psychology, McGill University Abstract Gaussian kernel smoothing has been widely used in either 2D flat or 3D volume images, but it does not work on the curved cortical surface. However, by reformulating Gaussian kernel smoothing as a solution to a diffusion equation on a 2D manifold, we can generalize it to the cortical surface. This generalization is called diffusion smoothing and has been used in analysis of fMRI data on the cortical surface [1] and detecting cortical surface-area growth [3]. We give an exact mathematical formulation for the diffusion smoothing on triangulated cortical surfaces so that this technique can be used for any surface-based functional and structural analysis. As an illustration, we smooth the mean curvatures on the outer cortical surfaces to show how the the smoothing actually incorporates the geodesic curvature information of the surface.