We present here a method that aims at defining a surface-based coordinate system on the cortical surface. Such a system is needed for both cortical localization and intersubject matching in the framework of neuroimaging. We propose an automatic parameterization based on the spherical topology of the grey/white matter interface of each hemisphere and on the use of naturally organized and reproducible anatomical features. From those markers used as initial constraints, the coordinate system is propagated via a PDE solved on the cortical surface.