Fast, open-source 2D/3D radiographic image registration using Grangeat's relation

Abstract

With computed tomography (CT) and X-ray imaging commonly used together in a wide range of applications, 2D/3D radiographic image registration remains a key part of many workflows. Fundamentally an optimisation problem, the greatest challenge lies in finding the desired alignment both quickly and accurately, as most approaches use an objective function that relies on expensive projection of the 3D volume data into 2D. Frysch, R., Pfeiffer, T., and Rose, G. propose a different objective function, based on Grangeat’s relation, that is significantly cheaper to compute. This approach leverages intermediate images, derived from 2D and 3D sinograms of the input images, that are pre-computed before the optimisation is begun. We present an open-source implementation of this method in the PyTorch framework, fully vectorised and GPU accelerated in line with other recent 2D/3D image registration developments. Applied to CT data from cochlear implantation procedures, we obtain an average speed-up in moving image evaluation of more than 20, compared to the standard projection-based method. We also address a known potential shortcoming of the original implementation of Frysch et al.’s approach, related to its uneven sampling of the intermediate 3D sinogram image. To obtain an approximately homogeneous sampling distribution, we use the HEALPix mapping between the plane and the sphere, modified for the 3D sinogram. With this innovation, we reduce the size of the pre-computed image by around 30%, resulting in a similar reduction in the time taken to perform the pre-calculation. In a series of experiments on 64 pairs of CT volumes and digitally reconstructed radiographs, we observe no significant difference in alignment accuracy between the projection-based, Grangeat and improved Grangeat approaches.