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.

翻译：医学影像中的自动解剖标志点定位不仅需要精确预测，更需可靠的不确定性量化以提供有效的临床决策支持。现有不确定性量化方法常存在不足，尤其在结合正态性假设时，会系统性地低估总体预测不确定性。本文引入共形预测作为解剖标志点定位中可靠不确定性量化的框架，填补了自动标志点定位领域的关键空白。我们提出两种保证多输出预测有限样本有效性的创新方法：多输出回归即分类共形预测（M-R2CCP）及其变体——面向区域的多输出回归至分类共形预测（M-R2C2R）。与传统方法生成轴对齐超矩形或椭球区域不同，我们的方法能生成灵活的非凸预测区域，更好地捕捉标志点预测的底层不确定性结构。通过对多个二维和三维数据集的广泛实证评估，我们证明该方法在有效性和效率上均持续优于现有多输出共形预测方法。这项研究标志着解剖标志点定位可靠不确定性估计的重要进展，为临床医生提供了可信的诊断置信度度量。虽然针对医学影像开发，这些方法在多输出回归问题中展现出更广泛的应用前景。