This paper presents a dense monocular mapping algorithm that improves the accuracy of the state-of-the-art variational and multiview stereo methods by incorporating scene priors into its formulation. Most of the improvement of our proposal is in low-textured image regions and for low-parallax camera motions; two typical failure cases of multiview mapping. The specific priors we model are the planarity of homogeneous color regions, the repeating geometric primitives of the scene--that can be learned from data--and the Manhattan structure of indoor rooms. We evaluate the performance of our method in our own sequences and in the publicly available NYU dataset, emphasizing its strengths and weaknesses in different cases.