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The Uncertainty Principle

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

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Related Experiment Video

Updated: Feb 2, 2026

2D and 3D Echocardiography in the Axolotl Ambystoma Mexicanum

2D and 3D Echocardiography in the Axolotl Ambystoma Mexicanum

Published on: November 29, 2018

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

Jef Jonkers¹, Frank Coopman², Luc Duchateau²

¹Department of Electronics and Information Systems, IDLab, Ghent University, Belgium.

Medical Image Analysis

|January 31, 2026

Summary

This summary is machine-generated.

This study introduces conformal prediction for reliable uncertainty quantification in anatomical landmark localization. Novel methods generate flexible prediction regions, outperforming existing approaches for trustworthy clinical decision support.

Keywords:

Conformal prediction Landmark localization Multi-output conformal prediction Prediction region Uncertainty quantification

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Area of Science:

Medical Imaging
Machine Learning
Uncertainty Quantification

Background:

Accurate anatomical landmark localization in medical imaging needs reliable uncertainty quantification for clinical decisions.
Current methods often underestimate uncertainty, especially with normality assumptions.

Purpose of the Study:

Introduce conformal prediction for robust uncertainty quantification in anatomical landmark localization.
Address limitations of existing uncertainty estimation techniques in medical imaging.

Main Methods:

Developed two novel multi-output conformal prediction methods: multi-output regression-as-classification conformal prediction (M-R2CCP) and multi-output regression to classification conformal prediction set to region (M-R2C2R).
These methods guarantee finite-sample validity and produce flexible, non-convex prediction regions.

Main Results:

Empirical evaluations on 2D and 3D datasets show superior performance compared to existing multi-output conformal prediction approaches.
Demonstrated improved validity and efficiency in uncertainty estimation for landmark localization.

Conclusions:

The proposed conformal prediction framework offers significant advancements in reliable uncertainty estimation for anatomical landmark localization.
Provides clinicians with trustworthy confidence measures, with potential for broader multi-output regression applications.