We present a method to jointly refine the geometry and semantic segmentation of 3D surface meshes. Our method alternates between updating the shape and the semantic labels. In the geometry refinement step, the mesh is deformed with variational energy minimization, such that it simultaneously maximizes photo-consistency and the compatibility of the semantic segmentations across a set of calibrated images. Label-specific shape priors account for interactions between the geometry and the semantic labels in 3D. In the semantic segmentation step, the labels on the mesh are updated with MRF inference, such that they are compatible with the semantic segmentations in the input images. Also, this step includes prior assumptions about the surface shape of different semantic classes. The priors induce a tight coupling, where semantic information influences the shape update and vice versa. Specifically, we introduce priors that favor (i) adaptive smoothing, depending on the class label; (ii) straightness of class boundaries; and (iii) semantic labels that are consistent with the surface orientation. The novel mesh-based reconstruction is evaluated in a series of experiments with real and synthetic data. We compare both to state-of-the-art, voxel-based semantic 3D reconstruction, and to purely geometric mesh refinement, and demonstrate that the proposed scheme yields improved 3D geometry as well as an improved semantic segmentation.

We propose an adaptive multi-resolution formulation of semantic 3D reconstruction. Given a set of images of a scene, semantic 3D reconstruction aims to densely reconstruct both the 3D shape of the scene and a segmentation into semantic object classes. Jointly reasoning about shape and class allows one to take into account class-specific shape priors (e.g., building walls should be smooth and vertical, and vice versa smooth, vertical surfaces are likely to be building walls), leading to improved reconstruction results. So far, semantic 3D reconstruction methods have been limited to small scenes and low resolution, because of their large memory footprint and computational cost. To scale them up to large scenes, we propose a hierarchical scheme which refines the reconstruction only in regions that are likely to contain a surface, exploiting the fact that both high spatial resolution and high numerical precision are only required in those regions. Our scheme amounts to solving a sequence of convex optimizations while progressively removing constraints, in such a way that the energy, in each iteration, is the tightest possible approximation of the underlying energy at full resolution. In our experiments the method saves up to 98% memory and 95% computation time, without any loss of accuracy.