While 3D reconstruction is a well-established and widely explored research topic, semantic 3D reconstruction has only recently witnessed an increasing share of attention from the Computer Vision community. Semantic annotations allow in fact to enforce strong class-dependent priors, as planarity for ground and walls, which can be exploited to refine the reconstruction often resulting in non-trivial performance improvements... State-of-the art methods propose volumetric approaches to fuse RGB image data with semantic labels; even if successful, they do not scale well and fail to output high resolution meshes. In this paper we propose a novel method to refine both the geometry and the semantic labeling of a given mesh. We refine the mesh geometry by applying a variational method that optimizes a composite energy made of a state-of-the-art pairwise photo-metric term and a single-view term that models the semantic consistency between the labels of the 3D mesh and those of the segmented images. We also update the semantic labeling through a novel Markov Random Field (MRF) formulation that, together with the classical data and smoothness terms, takes into account class-specific priors estimated directly from the annotated mesh. This is in contrast to state-of-the-art methods that are typically based on handcrafted or learned priors. We are the first, jointly with the very recent and seminal work of [M. Blaha et al arXiv:1706.08336, 2017], to propose the use of semantics inside a mesh refinement framework. Differently from [M. Blaha et al arXiv:1706.08336, 2017], which adopts a more classical pairwise comparison to estimate the flow of the mesh, we apply a single-view comparison between the semantically annotated image and the current 3D mesh labels; this improves the robustness in case of noisy segmentations. (read more)