Implicitly Explicit: Segmenting Vertebrae with Deep Implicit Statistical Shape Models

Convolutional- or transformer-based neural networks have become a de facto standard for semantic image segmentation. While networks trained on volumetric medical images achieve state-of-the-art performance, their predictions may lack anatomical plausibility because the shape of target structures is only implicitly learned with no underlying constraints. Statistical shape models offer an interpretable alternative, as they ensure anatomical consistency, produce high-quality surfaces, and minimize outlier predictions by enforcing the segmented shapes to resemble the distribution of training shapes. This study revisits the innovative concept of deep implicit statistical shape models (DISSMs) that leverage the idea of the signed distance function for their construction. We propose a strategy that enhances DISSMs by controlling their overfitting, evaluating the quality of the learned latent space, and estimating the upper-bound performance of pose estimation. The proposed enhanced DISSMs were trained on 580, validated on 130 and applied to segment 210 lumbar vertebrae in publicly available computed tomography spine images, yielding a Dice coefficient of 87.2 +/- 2.9% and 95th percentile Hausdorff distance of 2.81 +/- 0.99 mm. Although not reaching the performance of conventional deep learning semantic segmentation, this novel approach offers an efficient detection of segmentation outliers by quantifying the resulting shape plausibility, hence providing additional insight into the interpretability of deep segmentation models.