Deep Unrolled Weighted Graph Laplacian Regularization for Depth Completion

Depth completion aims to estimate dense depth images from sparse depth measurements with RGB image guidance. However, previous approaches have not fully considered sparse input fidelity, resulting in inconsistency with sparse input and poor robustness to input corruption. In this paper, we propose the deep unrolled Weighted Graph Laplacian Regularization (WGLR) for depth completion which enhances input fidelity and noise robustness by enforcing input constraints in the network design. Specifically, we assume graph Laplacian regularization as the prior for depth completion optimization and derive the WGLR solution by interpreting the depth map as the discrete counterpart of continuous manifold, enabling analysis in continuous domain and enforcing input consistency. Based on its anisotropic diffusion interpretation, we unroll the WGLR solution into iterative filtering for efficient implementation. Furthermore, we integrate the unrolled WGLR into deep learning framework to develop high-performance yet interpretable network, which diffuses the depth in a hierarchical manner to ensure global smoothness while preserving visually salient details. Experimental results demonstrate that the proposed scheme improves consistency with depth measurements and robustness to input corruption for depth completion, outperforming competing schemes on the NYUv2, KITTI-DC and TetrasRGBD datasets.