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

This paper presents a new and accurate three-dimensional (3-D) reconstruction technique for the scoliotic spine from a pair of planar and conventional (postero-anterior with normal incidence and lateral) calibrated radiographic images. 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 3-D statistical 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. An accurate 3-D reconstruction is then performed for each vertebra by a second template on which nonlinear admissible global, as well as local deformations, are defined. Global deformations are modeled using a statistical modal analysis of the pathological deformations observed on a representative scoliotic vertebra population. Local deformations are represented by a first-order Markov process. This unsupervised coarse-to-fine 3-D reconstruction procedure leads to two separate minimization procedures efficiently solved in our application with evolutionary stochastic optimization algorithms. In this context, we compare the results obtained with a classical genetic algorithm (GA) and a recent Exploration Selection (ES) technique. This latter optimization method with the proposed 3-D reconstruction model, is tested on several pairs of biplanar radiographic images with scoliotic deformities. The experiments reported in this paper demonstrate that the discussed method is comparable in terms of accuracy with the classical computed-tomography-scan technique while being unsupervised and while requiring only two radiographic images and a lower amount of radiation for the patient.