Reduced-dimensionality matching for 3-D reconstruction of prostate brachytherapy implants from incomplete data

X-ray fluoroscopy is widely used for intra-operative dosimetry in prostate brachytherapy. Three-dimensional locations of the implanted radioactive seeds can be calculated from multiple X-ray images upon resolving the correspondence of seeds. This is usually modeled as an assignment problem that is NP-hard. We propose an algorithm that allows us to derive an equivalent problem of reduced dimensionality based on practical observation that the optimal solution has almost zero cost if the C-arm pose is known. The reduced problem is efficiently solved by linear programming in polynomial time. Additionally, our method solves the hidden seeds problem. Simulation results demonstrate that the implanted seeds can be localized with a matching rate of ≥ 98.8 % and reconstruction error of ≤ 0.37 mm using three images with hidden seeds in a few seconds when the pose of the C-arm is known.