# Joint Graph-based Depth Refinement and Normal Estimation

arXiv: https://arxiv.org/abs/1912.01306 · HTML: https://mlsanity.com/paper/1912.01306/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2019.

## Built on by (most cited first, 12 of 12)

- [Guided Depth Super-Resolution by Deep Anisotropic Diffusion](https://mlsanity.com/paper/2211.11592/) (2022)
- [Learning Graph Regularisation for Guided Super-Resolution](https://mlsanity.com/paper/2203.14297/) (2022)
- [Leveraging Near-Field Lighting for Monocular Depth Estimation from Endoscopy Videos](https://mlsanity.com/paper/2403.17915/) (2024)
- [Augmenting Depth Estimation with Geospatial Context](https://mlsanity.com/paper/2109.09879/) (2021)
- [Digging Into Normal Incorporated Stereo Matching](https://mlsanity.com/paper/2402.18171/) (2024)
- [RPG360: Robust 360 Depth Estimation with Perspective Foundation Models and Graph Optimization](https://mlsanity.com/paper/2509.23991/) (2025)
- [Revisiting PatchMatch Multi-View Stereo for Urban 3D Reconstruction](https://mlsanity.com/paper/2207.08439/) (2022)
- [MoRe: Monocular Geometry Refinement via Graph Optimization for Cross-View Consistency](https://mlsanity.com/paper/2510.07119/) (2025)
- [Exploiting Multiple Priors for Neural 3D Indoor Reconstruction](https://mlsanity.com/paper/2309.07021/) (2023)
- [Consistent Time-of-Flight Depth Denoising via Graph-Informed Geometric Attention](https://mlsanity.com/paper/2506.23542/) (2025)
- [Learnable Fractional Reaction-Diffusion Dynamics for Under-Display ToF Imaging and Beyond](https://mlsanity.com/paper/2511.01704/) (2025)
- [Towards Robust Time-of-Flight Depth Denoising with Confidence-Aware Diffusion Model](https://mlsanity.com/paper/2503.19448/) (2025)

## Abstract (arXiv)

Depth estimation is an essential component in understanding the 3D geometry of a scene, with numerous applications in urban and indoor settings. These scenes are characterized by a prevalence of human made structures, which in most of the cases, are either inherently piece-wise planar, or can be approximated as such. In these settings, we devise a novel depth refinement framework that aims at recovering the underlying piece-wise planarity of the inverse depth map. We formulate this task as an optimization problem involving a data fidelity term that minimizes the distance to the input inverse depth map, as well as a regularization that enforces a piece-wise planar solution. As for the regularization term, we model the inverse depth map as a weighted graph between pixels. The proposed regularization is designed to estimate a plane automatically at each pixel, without any need for an a priori estimation of the scene planes, and at the same time it encourages similar pixels to be assigned to the same plane. The resulting optimization problem is efficiently solved with ADAM algorithm. Experiments show that our method leads to a significant improvement in depth refinement, both visually and numerically, with respect to state-of-the-art algorithms on Middlebury, KITTI and ETH3D multi-view stereo datasets.