  We introduce a novel approach for predicting the progression of adolescent
idiopathic scoliosis from 3D spine models reconstructed from biplanar X-ray
images. Recent progress in machine learning have allowed to improve
classification and prognosis rates, but lack a probabilistic framework to
measure uncertainty in the data. We propose a discriminative probabilistic
manifold embedding where locally linear mappings transform data points from
high-dimensional space to corresponding low-dimensional coordinates. A
discriminant adjacency matrix is constructed to maximize the separation between
progressive and non-progressive groups of patients diagnosed with scoliosis,
while minimizing the distance in latent variables belonging to the same class.
To predict the evolution of deformation, a baseline reconstruction is projected
onto the manifold, from which a spatiotemporal regression model is built from
parallel transport curves inferred from neighboring exemplars. Rate of
progression is modulated from the spine flexibility and curve magnitude of the
3D spine deformation. The method was tested on 745 reconstructions from 133
subjects using longitudinal 3D reconstructions of the spine, with results
demonstrating the discriminatory framework can identify between progressive and
non-progressive of scoliotic patients with a classification rate of 81% and
prediction differences of 2.1$^{o}$ in main curve angulation, outperforming
other manifold learning methods. Our method achieved a higher prediction
accuracy and improved the modeling of spatiotemporal morphological changes in
highly deformed spines compared to other learning methods.
