Heat Kernel Smoothing on Human Cortex Extracted from Magnetic Resonance Images

Gaussian kernel smoothing has been widely used in 3D whole brain imaging analysis as a way to increase signal-to-noise ratio. Gaussian kernel is isotropic in Euclidian space. However, data obtained on the convoluted brain cortex fails to be isotropic in the Euclidean sense. On the curved surface, a straight line between two points is not the shortest distance so one may incorrectly assign less weights to closer observations. In this paper, we will present how to correctly formulate isotropic smoothing for data on the human cortical surface that was extracted from the magnetic resonance images. As an illustration, we show how to detect the regions of abnormal cortical pattern in 16 autistic children that utilizes the new technique.