# Moving Object Detection under Discontinuous Change in Illumination Using Tensor Low-Rank and Invariant Sparse Decomposition

arXiv: https://arxiv.org/abs/1904.03175 · HTML: https://mlsanity.com/paper/1904.03175/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2019.

## Built on by (most cited first, 8 of 8)

- [SVDinsTN: A Tensor Network Paradigm for Efficient Structure Search from Regularized Modeling Perspective](https://mlsanity.com/paper/2305.14912/) (2023)
- [Polarimetric Monocular Dense Mapping Using Relative Deep Depth Prior](https://mlsanity.com/paper/2102.05212/) (2021)
- [Domain-Aware Tensor Network Structure Search](https://mlsanity.com/paper/2505.23537/) (2025)
- [Learning Spatial-Temporal Regularized Tensor Sparse RPCA for Background Subtraction](https://mlsanity.com/paper/2309.15576/) (2023)
- [Towards LLM-guided Efficient and Interpretable Multi-linear Tensor Network Rank Selection](https://mlsanity.com/paper/2410.10728/) (2024)
- [Perception Over Time: Temporal Dynamics for Robust Image Understanding](https://mlsanity.com/paper/2203.06254/) (2022)
- [Deep Polarimetric HDR Reconstruction](https://mlsanity.com/paper/2203.14190/) (2022)
- [Highlight Specular Reflection Separation based on Tensor Low-rank and Sparse Decomposition Using Polarimetric Cues](https://mlsanity.com/paper/2207.03543/) (2022)

## Abstract (arXiv)

Although low-rank and sparse decomposition based methods have been successfully applied to the problem of moving object detection using structured sparsity-inducing norms, they are still vulnerable to significant illumination changes that arise in certain applications. We are interested in moving object detection in applications involving time-lapse image sequences for which current methods mistakenly group moving objects and illumination changes into foreground. Our method relies on the multilinear (tensor) data low-rank and sparse decomposition framework to address the weaknesses of existing methods. The key to our proposed method is to create first a set of prior maps that can characterize the changes in the image sequence due to illumination. We show that they can be detected by a k-support norm. To deal with concurrent, two types of changes, we employ two regularization terms, one for detecting moving objects and the other for accounting for illumination changes, in the tensor low-rank and sparse decomposition formulation. Through comprehensive experiments using challenging datasets, we show that our method demonstrates a remarkable ability to detect moving objects under discontinuous change in illumination, and outperforms the state-of-the-art solutions to this challenging problem.