In this paper, we describe an algorithm called Fast Marching Watersheds that segments a triangle mesh into visual parts. This computer vision algorithm leverages a human vision theory known as the minima rule. Our implementation computes the principal curvatures and principal directions at each vertex of a mesh, and then our hill-climbing watershed algorithm identifies regions bounded by contours of negative curvature minima. These regions fit the definition of visual parts according to the minima rule. We present evaluation analysis and experimental results for the proposed algorithm.