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.

深度补全旨在通过 RGB 图像引导从稀疏深度测量中估计密集深度图像。然而，之前的方法没有充分考虑稀疏输入的保真度，导致稀疏输入的不一致以及对输入损坏的鲁棒性较差。在本文中，我们提出了用于深度补全的深度展开加权图拉普拉斯正则化（WGLR），它通过在网络设计中强制输入约束来增强输入保真度和噪声鲁棒性。具体来说，我们假设图拉普拉斯正则化作为深度完成优化的先验，并通过将深度图解释为连续流形的离散对应物来导出 WGLR 解决方案，从而能够在连续域中进行分析并强制输入一致性。基于其各向异性扩散解释，我们将 WGLR 解决方案展开为迭代过滤以实现高效实现。此外，我们将展开的 WGLR 集成到深度学习框架中，以开发高性能且可解释的网络，该网络以分层方式扩散深度，以确保全局平滑性，同时保留视觉上显着的细节。实验结果表明，所提出的方案提高了深度测量的一致性以及深度补全输入损坏的鲁棒性，在 NYUv2、KITTI-DC 和 TetrasRGBD 数据集上优于竞争方案。