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Leveraging the Mahalanobis Distance to enhance Unsupervised Brain MRI Anomaly Detection

Finn Behrendt, Debayan Bhattacharya, Robin Mieling, Lennart Maack, Julia Krüger, Roland Opfer, Alexander Schlaefer

TL;DR

This work tackles the challenge of unsupervised brain MRI anomaly detection by addressing false positives arising from imperfect reconstructions in reconstruction-based methods. It introduces case-specific pseudo-healthy distributions generated by conditioned diffusion models and refines pixel-level anomaly scoring with the Mahalanobis distance, leveraging inter-pixel covariance across multiple reconstructions. The approach yields substantial improvements in AUPRC across BRATS21, ATLAS, MSLUB, and WMH datasets, with notable gains when using full covariance (sMHD) over diagonal covariance or mean reconstructions. By demonstrating the value of per-image probabilistic healthy references and covariance-aware scoring, the method enhances segmentation reliability and provides a practical path toward more accurate, unsupervised brain anomaly detection.

Abstract

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.

Leveraging the Mahalanobis Distance to enhance Unsupervised Brain MRI Anomaly Detection

TL;DR

This work tackles the challenge of unsupervised brain MRI anomaly detection by addressing false positives arising from imperfect reconstructions in reconstruction-based methods. It introduces case-specific pseudo-healthy distributions generated by conditioned diffusion models and refines pixel-level anomaly scoring with the Mahalanobis distance, leveraging inter-pixel covariance across multiple reconstructions. The approach yields substantial improvements in AUPRC across BRATS21, ATLAS, MSLUB, and WMH datasets, with notable gains when using full covariance (sMHD) over diagonal covariance or mean reconstructions. By demonstrating the value of per-image probabilistic healthy references and covariance-aware scoring, the method enhances segmentation reliability and provides a practical path toward more accurate, unsupervised brain anomaly detection.

Abstract

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.
Paper Structure (11 sections, 6 equations, 1 figure, 1 table)

This paper contains 11 sections, 6 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Recent Work
  3. Methods
  4. Generating Pseudo-healthy Distributions with DDPMs
  5. Anomaly Scoring using Pseudo-Healthy Distributions and Mahalanobis Distance
  6. Data
  7. Implementation Details
  8. Results
  9. Discussion and Conclusion
  10. Acknowledgments.
  11. Disclosure of Interests.

Figures (1)

  • Figure 1: (a): Top row: input, reconstruction, S$_{mean}$ (SSIM), MHD, sMHD and the final anomaly map are shown for an exemplary image taken from the BRATS data set. Bottom row: the ground truth (green) and binarized segmentation maps (white) are shown. Note that the threshold for the segmentation maps is derived by optimizing the Dice score, based on the ground truth. (b): The correlation of one pixel (green arrow) with all other pixels, derived from $\Sigma_{full}$ is visualized as a heatmap.