  Statistical shape models (SSMs) are a popular tool to conduct morphological
analysis of anatomical structures which is a crucial step in clinical
practices. However, shape representations through SSMs are based on shape
coefficients and lack an explicit one-to-one relationship with anatomical
measures of clinical relevance. While a shape coefficient embeds a combination
of anatomical measures, a formalized approach to find the relationship between
them remains elusive in the literature. This limits the use of SSMs to
subjective evaluations in clinical practices. We propose a novel SSM controlled
by anatomical parameters derived from morphometric analysis. The proposed
anatomically parameterized SSM (ANAT-SSM) is based on learning a linear mapping
between shape coefficients and selected anatomical parameters. This mapping is
learned from a synthetic population generated by the standard SSM. Determining
the pseudo-inverse of the mapping allows us to build the ANAT-SSM. We further
impose orthogonality constraints to the anatomical parameterization to obtain
independent shape variation patterns. The proposed contribution was evaluated
on two skeletal databases of femoral and scapular bone shapes using clinically
relevant anatomical parameters. Anatomical measures of the synthetically
generated shapes exhibited realistic statistics. The learned matrices
corroborated well with the obtained statistical relationship, while the two
SSMs achieved moderate to excellent performance in predicting anatomical
parameters on unseen shapes. This study demonstrates the use of anatomical
representation for creating anatomically parameterized SSM and as a result,
removes the limited clinical interpretability of standard SSMs. The proposed
models could help analyze differences in relevant bone morphometry between
populations, and be integrated in patient-specific pre-surgery planning or
in-surgery assessment.
