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.
In this paper we present a novel, computationally efficient algorithm for nonrigid 2D image registration based on the work of Haker et al. [1,2]. We formulate the registration task as an Optimal Mass Transport (OMT) problem based on the Monge-Kantorovich theory. This approach gives a number of advantages over other conventional registration methods: (1) It is parameter free and no landmarks need to be specified, (2) it is symmetrical and the energy functional has a unique minimiser, and (3) it can register images where brightness constancy is an invalid assumption. Our algorithm solves the Optimal Mass Transport program via multi-resolution, multi-grid, and parallel methodologies on a consumer graphics processing unit (GPU). Although solving the OMT problem has been shown to be computationally expensive in the past, we show that our approach is almost two orders magnitude faster than previous work and is capable of finding transport maps with optimality measures (mean curl) previously unattainable by other works (which directly influences the quality of registration). We give results where the algorithm was used to register 2D short axis cardiac MRI images and to morph two image sets from a SOHO solar flare image sequence.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.