We present a monocular system that uses shape priors for improving the quality of estimated depth maps, specially in the region of an object of interest, when the environment presents complex conditions like changes in light, with low-textured, very reflective and translucent objects. A depth map is built by solving a non-convex optimization problem using the primal-dual algorithm and a coupling term. The energy functional consists of a photometric term for a set of images with common elements in the scene and a regularization term that allows smooth solutions. The camera is moved by hand and tracked using ORB-SLAM2. The resulting depth map is enhanced by integrating, with a novel variational formulation, depth data coming from the 3D model that best fits to observed data, optimized w.r.t. shape, pose and scale (shape prior). We also present an alternative algorithm that simultane ously builds a depth map and integrates a previously estimated shape prior. We quantify the improvements in accuracy and in noise reduction of the final depth map.