The mesh-LBP: a framework for extracting local binary patterns from discrete manifolds, In this paper, we present a novel and original framework, which we dubbed mesh-local binary pattern (LBP), for computing local binary-like-patterns on a triangular-mesh manifold. This framework can be adapted to all the LBP variants employed in 2D image analysis. As such, it allows extending the related techniques to mesh surfaces. After describing the foundations, the construction and the main features of the mesh-LBP, we derive its possible variants and show how they can extend most of the 2D-LBP variants to the mesh manifold. In the experiments, we give evidence of the presence of the uniformity aspect in the mesh-LBP, similar to the one noticed in the 2D-LBP. We also report repeatability experiments that confirm, in particular, the rotation-invariance of mesh-LBP descriptors. Furthermore, we analyze the potential of mesh-LBP for the task of 3D texture classification of triangular-mesh surfaces collected from public data sets. Comparison with state-of-the-art surface descriptors, as well as with 2D-LBP counterparts applied on depth images, also evidences the effectiveness of the proposed framework. Finally, we illustrate the robustness of the mesh-LBP with respect to the class of mesh irregularity typical to 3D surface-digitizer scans.