Statistical shape modeling and Gaussian process-based reconstruction of the lumbar spine from partial data: a proof-of-concept study

Background: Accurate three-dimensional representations of lumbar vertebral anatomy are essential for spinal research and clinical decision-making, particularly biomechanical analyses and the development of patient-specific interventions. However, in many practical settings, only partial information is available, making it difficult to obtain complete vertebral geometries. Statistical Shape Models (SSMs) provide a powerful way to characterize population-level anatomical variability, while Gaussian Process Regression (GPR) enables the reconstruction of full three-dimensional shapes from limited surface information. Objective: To reconstruct complete vertebral geometries from partial anatomical information using SSM and GPR and determine the minimum partial information needed for clinically acceptable reconstruction. Methods: Thirteen high-resolution CT datasets of healthy adult lumbar spines were segmented. A two-step registration framework was implemented: rigid registration followed by 3D-3D embedded deformation non-rigid registration. Principal Component Analysis (PCA) was used to generate SSMs of the lumbar spine. GPR was then employed for shape reconstruction from partial input data. Reconstruction performance was assessed with a leave-one-out cross-validation method. Results: In the full lumbar spine SSM, the first eight principal modes captured 92.7% of total shape variance. GPR enabled accurate reconstruction of full lumbar spines from sparse partial inputs. Shape reconstruction errors remained within the clinically acceptable range, with Average Distance (AD) within 1.23–3.64 mm, depending on input sparsity. Minimum information analysis revealed that as little as 30.67% surface data per vertebra was sufficient for clinically acceptable reconstructions. Conclusion: Combining SSMs with GPR enables accurate, anatomically realistic reconstruction of the lumbar spine from partial data. To the best of our knowledge, this study represents the first integration of SSMs and GPR for vertebral reconstruction. The proposed approach is suitable for future integration with sparse, ultrasound-derived anatomical information and establishes a foundation for radiation-free 3D guidance systems for lumbar facet joint injections and other spine interventions.