Abstract. We present here a method that aims at producing representations of functional brain data on the cortical surface from functional MRI volumes. Such representations are required for subsequent corticalbased functional analysis. We propose a projection technique based on the definition, around each node of the grey/white matter interface mesh, of convolution kernels whose shape and distribution rely on the geometry of the local anatomy. For one anatomy, a set of convolution kernels is computed that can be used to project any functional data registered with this anatomy. The method is presented together with experiments on synthetic data and real statistical t-maps.