The objective of this paper is to extract concave and convex feature regions via segmenting surface mesh of a mechanical part whose surface geometry exhibits drastic variations and concave-convex features are equally important when modeling. Referring to the original approach based on the minima rule (MR) in cognitive science, we have created a revised minima rule (RMR) and presented an improved approach based on RMR in the paper. Using the logarithmic function in terms of the minimum curvatures that are normalized by the expectation and the standard deviation on the vertices of the mesh, we determined the solution formulas for the feature vertices according to RMR. Because only a small range of the threshold parameters was selected from in the determined formulas, an iterative process was implemented to realize the automatic selection of thresholds. Finally according to the obtained feature vertices, the feature edges and facets were obtained by growing neighbors. The improved approach overcomes the inherent inadequacies of the original approach for our objective in the paper, realizes full automation without setting parameters, and obtains better results compared with the latest conventional approaches. We demonstrated the feasibility and superiority of our approach by performing certain experimental comparisons.