# Leveraging the Mahalanobis Distance to enhance Unsupervised Brain MRI Anomaly Detection

arXiv: https://arxiv.org/abs/2407.12474 · HTML: https://mlsanity.com/paper/2407.12474/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 17 Jul 2024.

## Builds on (most cited first, 19 of 19)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic Classification](https://mlsanity.com/paper/2107.02314/) (2021)
- [DRAEM -- A discriminatively trained reconstruction embedding for surface anomaly detection](https://mlsanity.com/paper/2108.07610/) (2021)
- [Anomaly Detection via Reverse Distillation from One-Class Embedding](https://mlsanity.com/paper/2201.10703/) (2022)
- [An overview of deep learning in medical imaging focusing on MRI](https://mlsanity.com/paper/1811.10052/) (2018)
- [Standardized Assessment of Automatic Segmentation of White Matter Hyperintensities and Results of the WMH Segmentation Challenge](https://mlsanity.com/paper/1904.00682/) (2019)
- [Fast Unsupervised Brain Anomaly Detection and Segmentation with Diffusion Models](https://mlsanity.com/paper/2206.03461/) (2022)
- [Context-encoding Variational Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/1812.05941/) (2018)
- [Patched Diffusion Models for Unsupervised Anomaly Detection in Brain MRI](https://mlsanity.com/paper/2303.03758/) (2023)
- [Detecting Outliers with Poisson Image Interpolation](https://mlsanity.com/paper/2107.02622/) (2021)
- [Unsupervised Pathology Detection: A Deep Dive Into the State of the Art](https://mlsanity.com/paper/2303.00609/) (2023)
- [Unsupervised Anomaly Localization with Structural Feature-Autoencoders](https://mlsanity.com/paper/2208.10992/) (2022)
- [Reversing the Abnormal: Pseudo-Healthy Generative Networks for Anomaly Detection](https://mlsanity.com/paper/2303.08452/) (2023)
- [Guided Reconstruction with Conditioned Diffusion Models for Unsupervised Anomaly Detection in Brain MRIs](https://mlsanity.com/paper/2312.04215/) (2023)
- [On the Pitfalls of Using the Residual Error as Anomaly Score](https://mlsanity.com/paper/2202.03826/) (2022)
- [Limitations of Out-of-Distribution Detection in 3D Medical Image Segmentation](https://mlsanity.com/paper/2306.13528/) (2023)
- [Simple statistical methods for unsupervised brain anomaly detection on MRI are competitive to deep learning methods](https://mlsanity.com/paper/2011.12735/) (2020)

## Built on by (most cited first, 10 of 10)

- [MAD-AD: Masked Diffusion for Unsupervised Brain Anomaly Detection](https://mlsanity.com/paper/2502.16943/) (2025)
- [REFLECT: Rectified Flows for Efficient Brain Anomaly Correction Transport](https://mlsanity.com/paper/2508.02889/) (2025)
- [Lightweight Model Attribution and Detection of Synthetic Speech via Audio Residual Fingerprints](https://mlsanity.com/paper/2411.14013/) (2024)
- [OCSVM-Guided Representation Learning for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2507.21164/) (2025)
- [Diffusing the Blind Spot: Uterine MRI Synthesis with Diffusion Models](https://mlsanity.com/paper/2508.07903/) (2025)
- [U2AD: Uncertainty-based Unsupervised Anomaly Detection Framework for Detecting T2 Hyperintensity in MRI Spinal Cord](https://mlsanity.com/paper/2503.13400/) (2025)
- [MIAS-SAM: Medical Image Anomaly Segmentation without thresholding](https://mlsanity.com/paper/2505.22762/) (2025)
- [Knowledge-Guided Brain Tumor Segmentation via Synchronized Visual-Semantic-Topological Prior Fusion](https://mlsanity.com/paper/2507.08574/) (2025)
- [Out-of-Distribution Detection in Medical Imaging via Diffusion Trajectories](https://mlsanity.com/paper/2507.23411/) (2025)
- [MTL-MAD: Multi-Task Learners are Effective Medical Anomaly Detectors](https://mlsanity.com/paper/2605.05891/) (2026)

## Abstract (arXiv)

Unsupervised Anomaly Detection (UAD) methods rely on healthy data distributions to identify anomalies as outliers. In brain MRI, a common approach is reconstruction-based UAD, where generative models reconstruct healthy brain MRIs, and anomalies are detected as deviations between input and reconstruction. However, this method is sensitive to imperfect reconstructions, leading to false positives that impede the segmentation. To address this limitation, we construct multiple reconstructions with probabilistic diffusion models. We then analyze the resulting distribution of these reconstructions using the Mahalanobis distance to identify anomalies as outliers. By leveraging information about normal variations and covariance of individual pixels within this distribution, we effectively refine anomaly scoring, leading to improved segmentation. Our experimental results demonstrate substantial performance improvements across various data sets. Specifically, compared to relying solely on single reconstructions, our approach achieves relative improvements of 15.9%, 35.4%, 48.0%, and 4.7% in terms of AUPRC for the BRATS21, ATLAS, MSLUB and WMH data sets, respectively.