@article {Jain2005e,
	title = {Matching and reconstruction of brachytherapy seeds using the Hungarian algorithm (MARSHAL)},
	journal = {Journal of Medical Physics},
	volume = {32},
	number = {11},
	year = {2005},
	month = {Nov},
	pages = {3475{\textendash}3492},
	abstract = {<p>Intraoperative dosimetric quality assurance in prostate brachytherapy critically depends on discerning the three-dimensional (3D) locations of implanted seeds The ability to reconstruct the implanted seeds intraoperatively will allow us to make immediate provisions for dosimetric deviations from the optimal implant plan A method for seed reconstruction from segmented C-arm fluoroscopy images is proposed The 3D coordinates of the implanted seeds can be calculated upon resolving the correspondence of seeds in multiple x-ray images We formalize seed-matching as a combinatorial optimization problem, which has salient features: (a) extensively studied solutions by the computer science community; (b) proof for the nonexistence of any polynomial time exact algorithm;, (c) a practical pseudo-polynomial algorithm that mostly runs in O(N3) time using any number of images We prove that two images are insufficient to correctly match the seeds, while a third image renders the matching problem to be of nonpolynomial complexity We utilize the special structure of the problem, propose a pseudopolynomial time algorithm Using three presegmented images, matching, reconstruction of brachytherapy seeds using the Hungarian algorithm achieved complete matching in simulation experiments;, 98 5\% in phantom experiments 3D reconstruction error for correctly matched seeds has a mean of 0 63 mm, and 0 9 mm for incorrectly matched seeds The maximum seed reconstruction error in each implant was typically around 1 32 mm Both on synthetic data, in phantom experiments, matching rate, reconstruction error achieved using presegmented images was found to be sufficient for prostate brachytherapy The algorithm is extendable to deal with arbitrary number of images without any loss in speed or accuracy The algorithm is sufficiently generic to provide a practical solution to any correspondence problem, across different imaging modalities, features</p>
},
	keywords = {Algorithms, Automated, Brachytherapy, Calibration, Computer Simulation, Computer-Assisted, Humans, Image Interpretation, Imaging, Male, methods, Models, Numerical Analysis, Pattern Recognition, Phantoms, Prostatic Neoplasms, Radiographic Image Enhancement, Radiographic Image Interpretation, Radiometry, Radiotherapy, Radiotherapy Dosage, Radiotherapy Planning, Reproducibility of Results, Statistical, Theoretical, Three-Dimensional, Time Factors, Ultrasonography},
	author = {Ameet K. Jain and Yu Zhou and Tabish Mustufa and E. Clif Burdette and Gregory Chirikjian and Gabor Fichtinger}
}
@article {Lee2002,
	title = {Numerical algorithms for spatial registration of line fiducials from cross-sectional images},
	journal = {Journal of Medical Physics},
	volume = {29},
	number = {8},
	year = {2002},
	month = {Aug},
	pages = {1881{\textendash}1891},
	abstract = {<p>We present several numerical algorithms for six-degree-of-freedom rigid-body registration of line fiducial objects to their marks in cross-sectional planar images, such as those obtained in CT, MRI, given the correspondence between the marks, line fiducials The area of immediate application is frame-based stereotactic procedures, such as radiosurgery, functional neurosurgery The algorithms are also suitable to problems where the fiducial pattern moves inside the imager, as is the case in robot-assisted image-guided surgical applications We demonstrate the numerical methods on clinical CT images, computer-generated data, compare their performance in terms of robustness to missing data, robustness to noise, and speed The methods show two unique strengths: (1) They provide reliable registration of incomplete fiducial patterns when up to two-thirds of the total fiducials are missing from the image;, (2) they are applicable to an arbitrary combination of line fiducials without algorithmic modification The average speed of the fastest algorithm is 0 3236 s for six fiducial lines in real CT data in a Matlab implementation</p>
},
	keywords = {Algorithms, Anatomy, anatomy /\&/ histology/radiography, Cross-Sectional, Head, Humans, Image Enhancement, Imaging, Magnetic Resonance Imaging, methods, Quality Control, Reproducibility of Results, Sensitivity, Specificity, Stereotaxic Techniques, Stochastic Processes, Subtraction Technique, Three-Dimensional, Tomography, X-Ray Computed},
	author = {Sangyoon Lee and Gabor Fichtinger and Gregory Chirikjian}
}
