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3D nonrigid registration via optimal mass transport on the GPU

Tauseef Rehman, Eldad Haber, Gallagher Pryor, John Melonakos, Allen Tannenbaum
Georgia Institute of Technology, School of ECE, 313 Ferst Drive, Atlanta, GA 30332, USA
Medical Image Analysis, Vol. 13, No. 6. (07 December 2009), pp. 931-940.

@article{rehman20093d,

   title={3D nonrigid registration via optimal mass transport on the GPU},

   author={Rehman, T. and Haber, E. and Pryor, G. and Melonakos, J. and Tannenbaum, A.},

   journal={Medical image analysis},

   volume={13},

   number={6},

   pages={931–940},

   issn={1361-8415},

   year={2009},

   publisher={Elsevier}

}

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In this paper, we present a new computationally efficient numerical scheme for the minimizing flow approach for optimal mass transport (OMT) with applications to non-rigid 3D image registration. The approach utilizes all of the gray-scale data in both images, and the optimal mapping from image A to image B is the inverse of the optimal mapping from B to A. Further, no landmarks need to be specified, and the minimizer of the distance functional involved is unique. Our implementation also employs multigrid, and parallel methodologies on a consumer graphics processing unit (GPU) for fast computation. Although computing the optimal map has been shown to be computationally expensive in the past, we show that our approach is orders of magnitude faster then previous work and is capable of finding transport maps with optimality measures (mean curl) previously unattainable by other works (which directly influences the accuracy of registration). We give results where the algorithm was used to compute non-rigid registrations of 3D synthetic data as well as intra-patient pre-operative and post-operative 3D brain MRI datasets.
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