Registration Quality and the Limits of Statistical Shape Modeling Evaluation in Transtibial Residual Limb Modeling: A Cross-Sectional Shape Representation Framework

Background/Objectives: Statistical shape modeling (SSM) is used to describe transtibial residual-limb morphology for prosthetic socket design, simulation, and future structural testing. However, conventional intrinsic metrics such as compactness, generality, and specificity may not directly reflect geometric fidelity to the original shape. This study examined the relationship between geometric fidelity and SSM evaluation and assessed a cross-sectional shape representation framework for transtibial residual limbs. Methods: Residual-limb surfaces were acquired from 62 adults with unilateral transtibial amputation using a structured-light 3D scanner while preserving habitual limb posture. Two surface-based registration methods, non-rigid iterative closest point and Bayesian coherent point drift, were compared with a cross-sectional representation in which proximal and distal regions were sectioned separately and reconstructed by strip triangulation. Geometric fidelity to the original mesh was quantified using average symmetric surface distance (ASSD). SSM performance was evaluated using compactness, generality, and specificity. Results: The optimal cross-sectional configuration was 60 sections × 72 points. The proposed method showed the best geometric fidelity (ASSD, 1.30 ± 0.14 mm), followed by Bayesian coherent point drift (1.33 ± 0.14 mm) and non-rigid iterative closest point (1.48 ± 0.48 mm). Compactness was highest for the proposed method, reaching 95% cumulative variance in four modes, compared with five and seven modes, respectively, for the two surface-based methods. In geometry-space evaluation, the proposed method showed the lowest specificity error, while differences in generality were statistically significant but small in magnitude. Conclusions: Intrinsic SSM metrics alone were insufficient to judge registration quality in transtibial residual-limb modeling. The cross-sectional representation preserved the original surface geometry more faithfully than the evaluated surface-based methods while maintaining competitive SSM performance.