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Is Hyperbolic Space All You Need for Medical Anomaly Detection?

Alvaro Gonzalez-Jimenez, Simone Lionetti, Ludovic Amruthalingam, Philippe Gottfrois, Fabian Gröger, Marc Pouly, Alexander A. Navarini

TL;DR

Is Hyperbolic Space All You Need for Medical Anomaly Detection? investigates whether hyperbolic geometry can better capture hierarchical relationships in medical image representations for anomaly detection and localization. The authors propose a framework that synthesizes anomalies, extracts multi layer features from a frozen backbone, maps Euclidean features to hyperbolic space with the Lorentz model, and classifies via a hyperplane in hyperbolic space using a confidence weighted aggregation. Empirical results on BMAD benchmarks show consistent gains in image level AUROC over Euclidean baselines, with strong few shot performance and robustness to parameter variations. The work suggests hyperbolic embeddings offer a data efficient and scalable alternative for clinical anomaly detection and localization, with potential for deployment in resource constrained settings.

Abstract

Medical anomaly detection has emerged as a promising solution to challenges in data availability and labeling constraints. Traditional methods extract features from different layers of pre-trained networks in Euclidean space; however, Euclidean representations fail to effectively capture the hierarchical relationships within these features, leading to suboptimal anomaly detection performance. We propose a novel yet simple approach that projects feature representations into hyperbolic space, aggregates them based on confidence levels, and classifies samples as healthy or anomalous. Our experiments demonstrate that hyperbolic space consistently outperforms Euclidean-based frameworks, achieving higher AUROC scores at both image and pixel levels across multiple medical benchmark datasets. Additionally, we show that hyperbolic space exhibits resilience to parameter variations and excels in few-shot scenarios, where healthy images are scarce. These findings underscore the potential of hyperbolic space as a powerful alternative for medical anomaly detection. The project website can be found at https://hyperbolic-anomalies.github.io

Is Hyperbolic Space All You Need for Medical Anomaly Detection?

TL;DR

Is Hyperbolic Space All You Need for Medical Anomaly Detection? investigates whether hyperbolic geometry can better capture hierarchical relationships in medical image representations for anomaly detection and localization. The authors propose a framework that synthesizes anomalies, extracts multi layer features from a frozen backbone, maps Euclidean features to hyperbolic space with the Lorentz model, and classifies via a hyperplane in hyperbolic space using a confidence weighted aggregation. Empirical results on BMAD benchmarks show consistent gains in image level AUROC over Euclidean baselines, with strong few shot performance and robustness to parameter variations. The work suggests hyperbolic embeddings offer a data efficient and scalable alternative for clinical anomaly detection and localization, with potential for deployment in resource constrained settings.

Abstract

Medical anomaly detection has emerged as a promising solution to challenges in data availability and labeling constraints. Traditional methods extract features from different layers of pre-trained networks in Euclidean space; however, Euclidean representations fail to effectively capture the hierarchical relationships within these features, leading to suboptimal anomaly detection performance. We propose a novel yet simple approach that projects feature representations into hyperbolic space, aggregates them based on confidence levels, and classifies samples as healthy or anomalous. Our experiments demonstrate that hyperbolic space consistently outperforms Euclidean-based frameworks, achieving higher AUROC scores at both image and pixel levels across multiple medical benchmark datasets. Additionally, we show that hyperbolic space exhibits resilience to parameter variations and excels in few-shot scenarios, where healthy images are scarce. These findings underscore the potential of hyperbolic space as a powerful alternative for medical anomaly detection. The project website can be found at https://hyperbolic-anomalies.github.io

Paper Structure

This paper contains 14 sections, 6 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Synthesis Anomalies
  4. Feature Extraction
  5. Euclidean to Hyperbolic Features
  6. Hyperbolic Classifier
  7. Experiments
  8. Datasets
  9. Experimental Setup
  10. Results
  11. Ablation Study on Model Parameters
  12. Few-Shot Anomaly Detection and Localization
  13. Conclusions
  14. Disclosure of Interests.

Figures (3)

  • Figure 1: Overview of the anomaly localization methodology in the hyperbolic space, from medical anomaly synthesis to classification.
  • Figure 2: Ablation study on key components of our hyperbolic framework: fixed curvature, patch size variations, and hyperbolic layer dimensionality.
  • Figure 3: Few-shot evaluation with varying normal image counts $\brk[c]{1,3,5,10,25}$. Our hyperbolic model outperforms PaDiM and PatchCore in scarce data scenarios. Error bands are obtained with five different random seeds, without changing the training set.