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 proposed approach is entirely error-driven, convergence-proven, and does not need to specify a number of segments. The partitioning is guided by robust shape extractions based on RANSAC sampling and by a global graphical model which regularizes the segmented regions. The final decomposition is based on the minimum of the energy associated with this graphical model. Obtained segmentations on noisy mechanical meshes outperform other approaches in terms of region contour correctness 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, and remeshing.