Depth completion is a fundamental task for many applications such as autonomous vehicles, 3D cinema, 3D reconstruction, and others. Many approaches have been proposed to tackle this problem, from classical models (variational models, morphological models, etc.) to convolutional networks. Hybrid models consider the advantages of the convolutional networks to select features and the generalization capacities of the classical models to extrapolate data. A hybrid model that considers convolutional stages and an interpolator has been proposed in the literature. This model assumes an anisotropic metric g(ij) and the image domain (Omega), embedding the data in a Riemannian manifold M = (g(ij), Omega). The interpolation task is performed by solving a degenerated partial differential equation in this manifold M. The proposed metric g(ij) used in this manifold is fundamental to correctly estimate distances between points in the sparse depth data. In this paper, our contributions are two-fold: first, an empirical evaluation of a metric based on a Positive Definite Operator Metric to compare color pixels applied to the depth completion task, and second, a variation of the infinity Laplacian (also the biased infinity Laplacian), namely unbalanced infinity Laplacian (unbalanced biased infinity Laplacian). Both interpolators include a weight map that balances the contribution of different models in the interpolation process. Experimental results in the KITTI Depth Completion Suite dataset, which is publicly available, show that the use of the Positive Definite Metric Operator performs better than the other two models and also performs better than similar models in this dataset.