# Depth Image Inpainting: Improving Low Rank Matrix Completion with Low Gradient Regularization

arXiv: https://arxiv.org/abs/1604.05817 · HTML: https://mlsanity.com/paper/1604.05817/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2016.

## Built on by (most cited first, 11 of 11)

- [Bayesian Deep Basis Fitting for Depth Completion with Uncertainty](https://mlsanity.com/paper/2103.15254/) (2021)
- [JPGNet: Joint Predictive Filtering and Generative Network for Image Inpainting](https://mlsanity.com/paper/2107.04281/) (2021)
- [Simple, Fast, and Flexible Framework for Matrix Completion with Infinite Width Neural Networks](https://mlsanity.com/paper/2108.00131/) (2021)
- [Point Cloud Scene Completion with Joint Color and Semantic Estimation from Single RGB-D Image](https://mlsanity.com/paper/2210.05891/) (2022)
- [Bayesian Low-rank Matrix Completion with Dual-graph Embedding: Prior Analysis and Tuning-free Inference](https://mlsanity.com/paper/2203.10044/) (2022)
- [DeepDR: Deep Structure-Aware RGB-D Inpainting for Diminished Reality](https://mlsanity.com/paper/2312.00532/) (2023)
- [Raformer: Redundancy-Aware Transformer for Video Wire Inpainting](https://mlsanity.com/paper/2404.15802/) (2024)
- [Contextual Attention Mechanism, SRGAN Based Inpainting System for Eliminating Interruptions from Images](https://mlsanity.com/paper/2204.02591/) (2022)
- [Graph-Based Matrix Completion Applied to Weather Data](https://mlsanity.com/paper/2306.08627/) (2023)
- [Evaluating Gaussian Grasp Maps for Generative Grasping Models](https://mlsanity.com/paper/2206.00432/) (2022)
- [Global Convergence Analysis of Vanilla Gradient Descent for Asymmetric Matrix Completion](https://mlsanity.com/paper/2508.09685/) (2025)

## Abstract (arXiv)

We consider the case of inpainting single depth images. Without corresponding color images, previous or next frames, depth image inpainting is quite challenging. One natural solution is to regard the image as a matrix and adopt the low rank regularization just as inpainting color images. However, the low rank assumption does not make full use of the properties of depth images. A shallow observation may inspire us to penalize the non-zero gradients by sparse gradient regularization. However, statistics show that though most pixels have zero gradients, there is still a non-ignorable part of pixels whose gradients are equal to 1. Based on this specific property of depth images , we propose a low gradient regularization method in which we reduce the penalty for gradient 1 while penalizing the non-zero gradients to allow for gradual depth changes. The proposed low gradient regularization is integrated with the low rank regularization into the low rank low gradient approach for depth image inpainting. We compare our proposed low gradient regularization with sparse gradient regularization. The experimental results show the effectiveness of our proposed approach.