Principal Spine Shape Deformation Modes Using Riemannian Geometry and Articulated Models

We present a method to extract principal deformation modes from a set of articulated models describing the human spine. The spine was expressed as a set of rigid transforms that superpose local coordinates systems of neighbouring vertebrae. To take into account the fact that rigid transforms belong to a Riemannian manifold, the Fréchet mean and a generalized covariance computed in the exponential chart of the Fréchet mean were used to construct a statistical shape model. The principal deformation modes were then extracted by performing a principal component analysis (PCA) on the generalized covariance matrix. Principal deformations modes were computed for a large database of untreated scoliotic patients and the obtained results indicate that combining rotation and translation into a unified framework leads to an effective and meaningful method of dimensionality reduction for articulated anatomical structures. The computed deformation modes also revealed clinically relevant information. For instance, the first mode of deformation appeared to be associated with patients’ growth, the second is a double thoraco-lumbar curve and the third is a thoracic curve.