An efficient Riemannian statistical shape model using differential coordinates: With application to the classification of data from the Osteoarthritis Initiative

HighlightsNovel Riemannian framework for statistical shape analysis that is able to account for the nonlinearity in shape variation.Lie group structure with closed‐form expressions guaranteeing numerical efficiency.Results on the open‐access OAI and FAUST datasets demonstrate superior performance over state‐of‐the‐art. Graphical abstract Figure. No Caption available. Abstract We propose a novel Riemannian framework for statistical analysis of shapes that is able to account for the nonlinearity in shape variation. By adopting a physical perspective, we introduce a differential representation that puts the local geometric variability into focus. We model these differential coordinates as elements of a Lie group thereby endowing our shape space with a non‐Euclidean structure. A key advantage of our framework is that statistics in a manifold shape space becomes numerically tractable improving performance by several orders of magnitude over state‐of‐the‐art. We show that our Riemannian model is well suited for the identification of intra‐population variability as well as inter‐population differences. In particular, we demonstrate the superiority of the proposed model in experiments on specificity and generalization ability. We further derive a statistical shape descriptor that outperforms the standard Euclidean approach in terms of shape‐based classification of morphological disorders.