Weakly Supervised Bayesian Shape Modeling from Unsegmented Medical Images

TL;DR

This paper addresses the burden and bias of traditional SSM pipelines by introducing a weakly supervised BVIB-DeepSSM that predicts probabilistic PDMs from unsegmented medical images using point-cloud supervision. By replacing ground-truth PDM supervision with permutation-invariant Chamfer-distance losses and employing encoder-side dropout for epistemic uncertainty, the method achieves comparable accuracy and uncertainty calibration to fully supervised baselines while requiring far less annotation. The key contributions are the formulation of a weakly supervised BVIB objective with Chamfer-based NLL, a sampling strategy for uncertainty using encoder dropout, and extensive evaluation on left atrium and liver datasets demonstrating feasibility and robustness. The practical impact lies in making SSM construction from images more accessible for clinical research without sacrificing predictive reliability or uncertainty quantification.

Abstract

Anatomical shape analysis plays a pivotal role in clinical research and hypothesis testing, where the relationship between form and function is paramount. Correspondence-based statistical shape modeling (SSM) facilitates population-level morphometrics but requires a cumbersome, potentially bias-inducing construction pipeline. Recent advancements in deep learning have streamlined this process in inference by providing SSM prediction directly from unsegmented medical images. However, the proposed approaches are fully supervised and require utilizing a traditional SSM construction pipeline to create training data, thus inheriting the associated burdens and limitations. To address these challenges, we introduce a weakly supervised deep learning approach to predict SSM from images using point cloud supervision. Specifically, we propose reducing the supervision associated with the state-of-the-art fully Bayesian variational information bottleneck DeepSSM (BVIB-DeepSSM) model. BVIB-DeepSSM is an effective, principled framework for predicting probabilistic anatomical shapes from images with quantification of both aleatoric and epistemic uncertainties. Whereas the original BVIB-DeepSSM method requires strong supervision in the form of ground truth correspondence points, the proposed approach utilizes weak supervision via point cloud surface representations, which are more readily obtainable. Furthermore, the proposed approach learns correspondence in a completely data-driven manner without prior assumptions about the expected variability in shape cohort. Our experiments demonstrate that this approach yields similar accuracy and uncertainty estimation to the fully supervised scenario while substantially enhancing the feasibility of model training for SSM construction.

Figures (6)

• Figure 1: Overview of the differences between VIB-DeepSSM adams2022vib, BVIB-DeepSSM adams2023bvib, and the proposed weakly supervised variant of BVIB-DeepSSM with point cloud supervision.
• Figure 2: Results of VIB-DeepSSM and C-BVIB-DeepSSM with PDM-supervision and the proposed point cloud supervision on the left atrium and liver dataset. Box plots show the distribution of errors across the test set. The SSM metric plots show the values with various numbers of PCA modes, where the line type depicts the type of DeepSSM model. Lower values are better for all metrics with the exception of compactness.
• Figure 3: Modes of variation resulting from the predicted SSM on the test set with the BVIB-DeepSSM models from the top and anterior view. The mean shape is shown with the primary and secondary PCA modes of variation at $\pm 1.5$ standard deviations (SD). Correspondence points are displayed over meshes constructed from the points.
• Figure 4: Uncertainty calibration results. Scatter plots and corresponding Pearson R correlation coefficients demonstrate the point-wise correlation between the estimated uncertainty and P2S error across the test sets. The average P2S error and uncertainty values are also shown via heatmaps on a representative mesh, illustrating spatial correlation.
• Figure 5: Left atrium outlier test sets. The histogram plots the distribution of image and shape outlier degrees with example image slices and meshes. Box plots show the distribution of P2S error and uncertainty across the three test sets: inliers (blue), image outliers (yellow), and shape outliers (red).