Learning Anatomical Variability: Statistical Shape Models for Vertebral Joint Pose Estimation

Abstract

Abstract Medical image registration, encompassing both rigid and non-rigid transformations, plays a fundamental role in medical image analysis. Applications such as therapy planning, longitudinal disease analyses, and model-based segmentation benefit from the use of registration. While rigid registration suffices for applications like bone imaging, where motion is constrained by joints and bone stiffness, non-rigid registration becomes necessary to accommodate tissue deformation from interventions, temporal changes, and substantial anatomical variability across individuals. However, non-rigid registration comes at the cost of overfitting, implying the potential loss of anatomical plausibility. This work presents a hybrid framework that combines Statistical Shape Models (SSM) and Active Shape Models (ASM) with kernel-based Principal Components Analysis (kPCA) to derive statistics of vertebral joint poses, setting a foundation to constrain joint pose changes in a registration setup. Using Computed Tomography (CT)-derived vertebral meshes, the pipeline generates mesh correspondence via Coherent Point Drift (CPD), shape variability using SSM and ASM, and estimates orientation through Principal Component Analysis (PCA)-based coordinate frames. The resulting model captures non-linear anatomical variation while maintaining geometric consistency across samples. Experimental results demonstrate that the proposed approach can reconstruct vertebral shapes with mean reconstruction errors of 7.55±2.25 mm, while robustly estimating intervertebral orientations and distances. The study highlights the feasibility of extracting anatomical priors with the possibility of integration into non-rigid registration frameworks to improve both accuracy and biomechanical realism.