Multimodal inference of articulated spine models from higher order energy functions of discrete MRFS

In this paper, we introduce a novel approach based on higher order energy functions which have the ability to encode global structural dependencies to infer articulated 3D spine models to CT volume data. A personalized geometrical model is reconstructed from biplanar X-rays before spinal surgery in order to create a spinal column representation which is modeled by a series of intervertebral transformations based on rotation and translation parameters. The shape transformation between the standing and lying poses is then achieved through a Markov Random Field optimization graph, where the unknown variables are the deformations applied to the intervertebral transformations. Singleton and pairwise potentials measure the support from the data and geometrical dependencies between neighboring vertebrae respectively, while higher order cliques are introduced to integrate consistency in regional curves. Optimization of model parameters in a multi-modal context is achieved using efficient linear programming and duality. A qualitative evaluation of the vertebra model alignment obtained from the proposed method gave promising results while the quantitative comparison to expert identification yields an accuracy of 1.8 ± 0.7 mm based on the localization of surgical landmarks.