Graph Laplacian for Image Anomaly Detection

TL;DR

This paper introduces a graph-based method utilizing the graph Fourier transform for image anomaly detection, addressing limitations of the Reed-Xiaoli detector and improving performance on hyperspectral and medical images.

Contribution

A novel graph Laplacian-based approach for image anomaly detection that overcomes RXD's limitations and enhances detection performance with reduced computational cost.

Findings

Significant performance improvements over state-of-the-art algorithms.

Effective handling of spatial information in anomaly detection.

Reduced computational complexity compared to traditional methods.

Abstract

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.