Toward optimal matching for 3D reconstruction of brachytherapy seeds

X-ray C-arm fluoroscopy is a natural choice for intra-operative seed localization in prostate brachytherapy. Resolving the correspondence of seeds in the projection images can be modeled as an assignment problem that is NP-hard. Our approach rests on the practical observation that the optimal solution has almost zero cost if the pose of the C-arm is known accurately. This allowed us to to derive an equivalent problem of reduced dimensionality that, with linear programming, can be solved efficiently in polynomial time. Additionally, our method demonstrates significantly increased robustness to C-arm pose errors when compared to the prior art. Because under actual clinical circumstances it is exceedingly difficult to track the C-arm, easing on this constraint has additional practical utility.