A hierarchical statistical modeling approach for the unsupervised 3D reconstruction of the scoliotic spine

In this paper, we propose a new and accurate 3D reconstruction technique for the scoliotic spine from a pair planar and conventional radiographic images (postero-anterior and lateral). The proposed model uses a priori hierarchical global knowledge, both on the geometric structure of the whole spine and of each vertebra. More precisely, it relies on the specification of two 3D templates. The first, a rough geometric template on which rigid admissible deformations are defined, is used to ensure a crude registration of the whole spine. 3D reconstruction is then refined for each vertebra, by a template on which non-linear admissible global deformations are modeled, with statistical modal analysis of the pathological deformations observed on a representative scoliotic vertebra population. This unsupervised coarse-to-fine 3D reconstruction procedure is stated as a double energy function minimization problems efficiently solved with a stochastic optimization algorithm. The proposed method, tested on several pairs of biplanar radiographic images with scoliotic deformities, is comparable in terms of accuracy with the classical CT-scan technique while being unsupervised and requiring a lower amount of radiation for the patient.