Sulcal fundi are 3D curves that lie in the depths of the cerebral cortex and are often used as landmarks for downstream computations in brain imaging. We present a sequence of geometric algorithms which automatically extract the sulcal fundi from magnetic resonance images and represent them as smooth polygons lying on the cortical surface. First we compute a geometric depth measure for each point on the cortical surface, and based on this information we extract sulcal regions by checking the connectivity above a depth threshold. We then extract the endpoints of each fundus and delineate the fundus by thinning each connected region keeping the endpoints fixed. The curves thus defined are smoothed using weighted splines on the gray-matter surface to yield high-quality representations of the sulcal fundi.