This paper presents a method for segmenting noisy 2-manifold meshes based on a decomposition into local shape primitives maximizing global coherence. This technique works by partitioning the input mesh into regions which can be approximated by a simple geometrical primitive such as a plane, a sphere or a cylinder. The partitioning is guided by robust shape extractions based on RANSAC sampling and the final decision to keep a 3D model into the final decomposition is based on a global graphical model which involves spatial and label cost priors. Obtained segmentations on noisy mesh models outperform other approaches in terms of region contour smoothness and consistency with mechanical object decomposition. Applications of this work are reverse engineering, mesh structure analysis, mesh feature enhancement, noise removal, mesh compression, piecewise approximation of mesh geometry (points, normals, curvatures), and remeshing.