Three-dimensional seed reconstruction for prostate brachytherapy using Hough trajectories

In order to perform intra-operative or post-implant dosimetry in prostate brachytherapy, the 3D coordinates of the implanted radioactive seeds must be determined. Film or fluoroscopy based seed reconstruction techniques use back projection of x-ray data obtained at two or three x-ray positions. These methods, however, do not perform well when some of the seed images are undetected. To overcome this problem we have developed an alternate technique for 3D seed localization using the principle of Hough transform. The Hough method utilizes the fact that, for each seed coordinate in three dimensions, there exists a unique trajectory in Hough feature space. In this paper we present the Hough transform parametric equations to describe the path of the seed projections from one view to the next and a method to reconstruct the 3D seed coordinates. The results of simulation and phantom studies indicate that the Hough trajectory method can accurately determine the 3D seed positions even from an incomplete dataset.