Super-Resolution of Depth Maps Using Graph Regularization

We address single depth map super-resolution as an inverse problem and rely on a graph-based representation of depth maps to explore the use of the Laplacian matrix as a regularizer. The Laplacian matrix is well known in graph theory for encoding important properties of graph nodes and edges. We solve the corresponding optimization problem with the Alternating Direction Method of Multipliers (ADMM), an algorithm that has been widely used in recent years for solving complex problems by splitting them into smaller and simpler subproblems. By using the graph Laplacian as a regularizer within the ADMM algorithm, we promote smoothness and preserve structural details of the considered depth map. We showcase a comprehensive formulation of the ADMM algorithm and how the Laplacian matrix is integrated. Results show that our approach outperforms existing optimization-based solutions and ADMM-based methods that use machine learning techniques for regularization (Plug and Play priors).