Fractured bone position and shape estimation based on recursive 2-D/3-D registration of deformable models

We present a deformable model based registration method to estimate bone fragment position and shape from intra-operative X-ray images for two-part bone fracture. Conventional deformable models are generated from CT volume images of normal persons. Thus it is difficult to describe diseased or broken bone shapes. For applying deformable model based registration to bone fractures, we propose a novel mathematical manner in the optimization process of registration. In the pre-processing, contour points on each X-ray image are interactively labelled as each of the fragment parts. In the registration stage, optimizations for bone position estimation and bone shape deformation are recursively performed by following the mathematical manner of projection onto convex sets (POCS). Our method provides not only fragment positions and a reduced bone shape but also relative transformation matrix between one fragment and the other. Because the relative matrix can lead the reducing motion path, our method effectively performs in the registration process for bone fracture surgeries. In the experiments, the error was 0.9 mm for translation and 11.8 degree for rotation. The shape estimation error was 10.9 % of the error volume ratio comparing with the whole volume of the deformable models.