3D biplanar reconstruction of lower limbs using nonlinear statistical models

Three-dimensional (3D) reconstruction of lower limbs is of great interest in surgical planning, computer assisted surgery, and for biomechanical applications. The use of 3D imaging modalities such as computed tomography (CT) scan and magnetic resonance imaging (MRI) has limitations such as high radiation and expense. Therefore, three-dimensional reconstruction methods from biplanar X-ray images represent an attractive alternative. In this paper, we present a new unsupervised 3D reconstruction method for the patella, talus, and pelvis using calibrated biplanar (45- and 135-degree oblique) radiographic images and a prior information on the geometric/anatomical structure of these complex bones. A multidimensional scaling (MDS)-based nonlinear dimensionality reduction algorithm is applied to exploit this prior geometric/anatomical information. It represents relevant deformations existing in the training set. Our method is based on a hybrid-likelihood using regions and contours. The edge-based notion represents the relation between the external contours of the bone projections and an edge potential field estimated on the radiographic images. Region-based notion is the non-overlapping ratio between segmented and projected bone regions of interest (RoIs). Our automatic 3D reconstruction model entails stochastically minimizing an energy function allowing an estimation of deformation parameters of the bone shape. This 3D reconstruction method has been successfully tested on 13 biplanar radiographic image pairs, yielding very promising results.