Reliable uncertainty quantification for 2D/3D anatomical landmark localization using multi-output conformal prediction

TL;DR

The paper tackles unreliable uncertainty quantification in automatic 2D/3D anatomical landmark localization by adopting conformal prediction to guarantee finite-sample coverage at $1-\alpha$. It introduces two multi-output CP methods, M-R2CCP and M-R2C2R, capable of producing flexible, non-convex prediction regions that better capture complex uncertainty structures. Extensive experiments on 2D and 3D datasets (ISBI, CHD, MML) show that these methods achieve higher validity and efficiency than existing multi-output CP approaches and outperform traditional uncertainty quantification techniques that rely on normality assumptions. The results hold promise for more trustworthy clinical decision support and broader multi-output regression applications beyond medical imaging.

Abstract

Automatic anatomical landmark localization in medical imaging requires not just accurate predictions but reliable uncertainty quantification for effective clinical decision support. Current uncertainty quantification approaches often fall short, particularly when combined with normality assumptions, systematically underestimating total predictive uncertainty. This paper introduces conformal prediction as a framework for reliable uncertainty quantification in anatomical landmark localization, addressing a critical gap in automatic landmark localization. We present two novel approaches guaranteeing finite-sample validity for multi-output prediction: Multi-output Regression-as-Classification Conformal Prediction (M-R2CCP) and its variant Multi-output Regression to Classification Conformal Prediction set to Region (M-R2C2R). Unlike conventional methods that produce axis-aligned hyperrectangular or ellipsoidal regions, our approaches generate flexible, non-convex prediction regions that better capture the underlying uncertainty structure of landmark predictions. Through extensive empirical evaluation across multiple 2D and 3D datasets, we demonstrate that our methods consistently outperform existing multi-output conformal prediction approaches in both validity and efficiency. This work represents a significant advancement in reliable uncertainty estimation for anatomical landmark localization, providing clinicians with trustworthy confidence measures for their diagnoses. While developed for medical imaging, these methods show promise for broader applications in multi-output regression problems.

Figures (10)

• Figure 1: Examples of prediction region produced by different multi-output conformal prediction approaches (2D).
• Figure 2: Examples of prediction region produced by different multi-output conformal prediction approaches (3D).
• Figure 3: Cephalogram example of conformal prediction regions.
• Figure 4: Box plot showing the empirical coverage of prediction regions for different landmarks (19 landmarks), evaluating various uncertainty quantification approaches at different confidence target levels on the ISBI 2015 (2D) dataset test set.
• Figure 5: Box plot showing the empirical coverage of prediction regions for different landmarks (14 landmarks), evaluating various uncertainty quantification approaches at different confidence target levels on the MML (3D) dataset test set.

Theorems & Definitions (12)

• Proposition 1
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• Proposition 2
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• Proposition 3
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• Proposition 3
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• Proposition 3
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