Nonlinear Embedding towards Articulated Spine Shape Inference Using Higher-Order MRFs

In this paper we introduce a novel approach for inferring articulated spine models from images. A low-dimensional manifold embedding is created from a training set of prior mesh models to establish the patterns of global shape variations. Local appearance is captured from neighborhoods in the manifold once the overall representation converges. Inference with respect to the manifold and shape parameters is performed using a Markov Random Field (MRF). Singleton and pairwise potentials measure the support from the data and shape coherence from neighboring models respectively, while higher-order cliques encode geometrical modes of variation for local vertebra shape warping. Optimization of model parameters is achieved using efficient linear programming and duality. The resulting model is geometrically intuitive, captures the statistical distribution of the underlying manifold and respects image support in the spatial domain. Experimental results on spinal column geometry estimation from CT demonstrate the approach's potential.