  Three-dimensional medical imaging enables detailed understanding of
osteoarthritis structural status. However, there remains a vast need for
automatic, thus, reader-independent measures that provide reliable assessment
of subject-specific clinical outcomes. To this end, we derive a consistent
generalization of the recently proposed B-score to Riemannian shape spaces. We
further present an algorithmic treatment yielding simple, yet efficient
computations allowing for analysis of large shape populations with several
thousand samples. Our intrinsic formulation exhibits improved discrimination
ability over its Euclidean counterpart, which we demonstrate for predictive
validity on assessing risks of total knee replacement. This result highlights
the potential of the geodesic B-score to enable improved personalized
assessment and stratification for interventions.
