We present a method for automatically finding curves representing the sulcal fundi on the human brain cortex. A flattened map of the cortical surface is used as the reference space in which the curves are modeled. The map is also used to transfer planar curves back to the cortical surface to extract sulcal fundal curves. Instead of modeling the curves by densely sampled landmark points, as it is done in the traditional active shape models, we model sulcal curves by a small number of anchor points that correspond to salient features, such as end points or points of intersections. The full sulcal curves connecting the anchor points are reconstructed by an extension of the fast marching method. Each anchor point carries a wavelet based attribute vector whose goal is to provide a distinctive morphological signature for the anchor point. This allows us to efficiently solve the problem in a low-dimensional space. Moreover, because each anchor point has this signature, and because anchor points are chosen to be salient features, the cost function defined in this low-dimensional space is presumed to have few local minima. Experimental results show that the sulcal curves extracted using the automatic method agrees well with the manually drawn sulcal curves.