Sulcal fundi are 3D curves along the bottom of sulcal regions of the human cerebral cortex. In this paper, we propose a novel automatic method for extraction of sulcal fundi from triangulated cortical surface. Compared to existing methods, the proposed method can find accurate sulcal fundi using curvatures and curvature derivatives without manual interaction. Given a triangulated cortical surface, our method is composed of four steps: estimating curvatures and curvature derivatives for each vertex, detecting the sulcal fundi segments in each triangle, linking the sulcal fundi segments and combining of adjacent sulcal fundi, and connecting breaking sulcal fundi and smoothing using the fast marching method on the cortical surface. The proposed sulcal fundi extraction method is applied to ten normal brain inner cortical surfaces. We quantitatively validated the proposed method of sulcal fundi extraction using manually labeled sulcal fundi by experts as the ground truth.