# Depth-Aided Color Image Inpainting in Quaternion Domain

arXiv: https://arxiv.org/abs/2503.16818 · HTML: https://mlsanity.com/paper/2503.16818/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Builds on (most cited first, 9 of 9)

- [High Quality Monocular Depth Estimation via Transfer Learning](https://mlsanity.com/paper/1812.11941/) (2018)
- [Boosting Monocular Depth Estimation Models to High-Resolution via Content-Adaptive Multi-Resolution Merging](https://mlsanity.com/paper/2105.14021/) (2021)
- [Weighted Schatten p-Norm Minimization for Image Denoising and Background Subtraction](https://mlsanity.com/paper/1512.01003/) (2015)
- [Bilinear Factor Matrix Norm Minimization for Robust PCA: Algorithms and Applications](https://mlsanity.com/paper/1810.05186/) (2018)
- [Color image recovery using low-rank quaternion matrix completion algorithm](https://mlsanity.com/paper/1909.06567/) (2019)
- [Robust PCA via Nonconvex Rank Approximation](https://mlsanity.com/paper/1511.05261/) (2015)
- [LogDet Rank Minimization with Application to Subspace Clustering](https://mlsanity.com/paper/1507.00908/) (2015)
- [Quaternion Matrix Completion Using Untrained Quaternion Convolutional Neural Network for Color Image Inpainting](https://mlsanity.com/paper/2305.00416/) (2023)
- [Quaternion higher-order singular value decomposition and its applications in color image processing](https://mlsanity.com/paper/2101.00364/) (2021)

## Abstract (arXiv)

In this paper, we propose a depth-aided color image inpainting method in the quaternion domain, called depth-aided low-rank quaternion matrix completion (D-LRQMC). In conventional quaternion-based inpainting techniques, the color image is expressed as a quaternion matrix by using the three imaginary parts as the color channels, whereas the real part is set to zero and has no information. Our approach incorporates depth information as the real part of the quaternion representations, leveraging the correlation between color and depth to improve the result of inpainting. In the proposed method, we first restore the observed image with the conventional LRQMC and estimate the depth of the restored result. We then incorporate the estimated depth into the real part of the observed image and perform LRQMC again. Simulation results demonstrate that the proposed D-LRQMC can improve restoration accuracy and visual quality for various images compared to the conventional LRQMC. These results suggest the effectiveness of the depth information for color image processing in quaternion domain.