A Fully Differentiable Framework for 2D/3D Registration and the Projective Spatial Transformers

Image-based 2D/3D registration is a critical technique for fluoroscopic guided surgical interventions. Conventional intensity-based 2D/3D registration approa- ches suffer from a limited capture range due to the presence of local minima in hand-crafted image similarity functions. In this work, we aim to extend the 2D/3D registration capture range with a fully differentiable deep network framework that learns to approximate a convex-shape similarity function. The network uses a novel Projective Spatial Transformer (ProST) module that has unique differentiability with respect to 3D pose parameters, and is trained using an innovative double backward gradient-driven loss function. We compare the most popular learning-based pose regression methods in the literature and use the well-established CMAES intensity-based registration as a benchmark. We report registration pose error, target registration error (TRE) and success rate (SR) with a threshold of 10mm for mean TRE. For the pelvis anatomy, the median TRE of ProST followed by CMAES is 4.4mm with a SR of 65.6% in simulation, and 2.2mm with a SR of 73.2% in real data. The CMAES SRs without using ProST registration are 28.5% and 36.0% in simulation and real data, respectively. Our results suggest that the proposed ProST network learns a practical similarity function, which vastly extends the capture range of conventional intensity-based 2D/3D registration. We believe that the unique differentiable property of ProST has the potential to benefit related 3D medical imaging research applications. The source code is available at https://github.com/gaocong13/Projective-Spatial-Transformers.