# Graph Laplacian for Image Anomaly Detection

arXiv: https://arxiv.org/abs/1802.09843 · HTML: https://mlsanity.com/paper/1802.09843/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2018.

## Built on by (most cited first, 5 of 5)

- [Hyperspectral Anomaly Detection Fused Unified Nonconvex Tensor Ring Factors Regularization](https://mlsanity.com/paper/2505.17881/) (2025)
- [Turbo-GoDec: Exploiting the Cluster Sparsity Prior for Hyperspectral Anomaly Detection](https://mlsanity.com/paper/2601.12337/) (2026)
- [Utilizing the Score of Data Distribution for Hyperspectral Anomaly Detection](https://mlsanity.com/paper/2601.12379/) (2026)
- [Anomaly as Non-Conformity via Training-Free Graph Laplacian Energy Minimization](https://mlsanity.com/paper/2605.28428/) (2026)
- [A Novel Unified Extended Matrix for Graph Signal Processing: Theory and Application](https://mlsanity.com/paper/2508.16633/) (2025)

## Abstract (arXiv)

Reed-Xiaoli detector (RXD) is recognized as the benchmark algorithm for image anomaly detection; however, it presents known limitations, namely the dependence over the image following a multivariate Gaussian model, the estimation and inversion of a high-dimensional covariance matrix, and the inability to effectively include spatial awareness in its evaluation. In this work, a novel graph-based solution to the image anomaly detection problem is proposed; leveraging the graph Fourier transform, we are able to overcome some of RXD's limitations while reducing computational cost at the same time. Tests over both hyperspectral and medical images, using both synthetic and real anomalies, prove the proposed technique is able to obtain significant gains over performance by other algorithms in the state of the art.