Uncertainty Quantification in Machine Learning Based Segmentation: A Post-Hoc Approach for Left Ventricle Volume Estimation in MRI

TL;DR

The paper tackles uncertain LV volume estimation from Cardiac MRI segmentations by proposing a post-hoc uncertainty framework that couples Itô stochastic differential equation dynamics for inner slices with a hierarchical gamma jump model for outer slices. This segmentation-agnostic approach uses a compact parameter set and a likelihood-based fitting procedure, including moment-matching surrogates for SDE transitions, and is validated on the M&Ms and ACDC datasets, demonstrating better uncertainty calibration and robustness to vendor/protocol shifts. The work yields a practical, data-efficient method to produce bias-free, non-negative uncertainty estimates that reflect real-world variability, enabling clinicians to identify unreliable predictions and compare segmentation methods across centers. Overall, this framework advances reliable automated LV volume estimation by providing quantified uncertainty without retraining segmentation models, thereby supporting safer clinical decision-making.

Abstract

Recent studies have confirmed cardiovascular diseases remain responsible for highest death toll amongst non-communicable diseases. Accurate left ventricular (LV) volume estimation is critical for valid diagnosis and management of various cardiovascular conditions, but poses significant challenge due to inherent uncertainties associated with segmentation algorithms in magnetic resonance imaging (MRI). Recent machine learning advancements, particularly U-Net-like convolutional networks, have facilitated automated segmentation for medical images, but struggles under certain pathologies and/or different scanner vendors and imaging protocols. This study proposes a novel methodology for post-hoc uncertainty estimation in LV volume prediction using Itô stochastic differential equations (SDEs) to model path-wise behavior for the prediction error. The model describes the area of the left ventricle along the heart's long axis. The method is agnostic to the underlying segmentation algorithm, facilitating its use with various existing and future segmentation technologies. The proposed approach provides a mechanism for quantifying uncertainty, enabling medical professionals to intervene for unreliable predictions. This is of utmost importance in critical applications such as medical diagnosis, where prediction accuracy and reliability can directly impact patient outcomes. The method is also robust to dataset changes, enabling application for medical centers with limited access to labeled data. Our findings highlight the proposed uncertainty estimation methodology's potential to enhance automated segmentation robustness and generalizability, paving the way for more reliable and accurate LV volume estimation in clinical settings as well as opening new avenues for uncertainty quantification in biomedical image segmentation, providing promising directions for future research.

Figures (12)

• Figure 1: Proposed approach to model left ventricle (LV) volume from short-axis cardiac MRI (the example image is from the ACDC Dataset Acdc_2018). (1) An arbitrary algorithm, segments the left ventricle. (2) Our method creates a distributional volume prediction from deterministic segmentations.
• Figure 1: Left ventricle area absolute error and predicted standard deviation (from \ref{['eq:model_RV_naive']}); outer and inner slices are shown as orange and blue, respectively
• Figure 1: Deterministic predictions of the left ventricle area for all slices in the dataset. The chosen threshold for zero predictions is shown in red. This is necessary as the neural network never predicts exactly zero.
• Figure 1: Comparison of the different model-based and empirical cumulative density functions of the deviation from the neural network prediction. Green shows the deviation of the expert labels from the neural network predictions. Light green shows the KS confidence band, based on the DKW-inequality, which includes the true cdf with a probability of 95%. Orange shows the cdf of our model and blue the cdf of the benchmark model, utilizing the five prediction of the neural network ensemble. To obtain the cdfs the LV volume of each heart is predicted 10,000 times. The benchmark model utilizes the predictions of all five neural networks from the nnU-Net.
• Figure 1: Fitted parameters for different data subsets. The full dataset is divided ten times into three parts, providing 30 datasets, with always three being disjoint. Values are shown with the likelihood calculated from the full dataset.

Theorems & Definitions (2)

• Theorem 3.1
• Proof 1